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INSTANT DOWNLOAD COMPLETE TEST BANK WITH ANSWERS
CFIN 3 3rd Edition by Besley – Test Bank
Chapter 2—Analysis of Financial Statements
TRUE/FALSE
- The income statement measures the flow of funds into (i.e. revenue) and out of (i.e. expenses) the firm over a certain time period. It is always based on accounting data.
ANS: T DIF: Easy TOP: Income statement
- The balance sheet is a financial statement measuring the flow of funds into and out of various accounts over time while the income statement measures the progress of the firm at a point in time.
ANS: F DIF: Easy TOP: Financial statements
- An increase in an asset account is a source of cash, whereas an increase in a liability account is a use of cash.
ANS: F DIF: Easy TOP: Sources and uses of cash
- Depreciation, as shown on the income statement, is regarded as a use of cash because it is an expense.
ANS: F DIF: Easy TOP: Sources and uses of cash
- When a firm pays off a loan using cash, the source of funds is the decrease in the asset account, cash, while the use of funds involves a decrease in a liability account, debt.
ANS: T DIF: Easy TOP: Sources and uses
- Non-cash assets are expected to produce cash over time but the amount of cash they eventually produce could be higher or lower than the values at which the assets are carried on the books.
ANS: T DIF: Easy TOP: Non-cash assets
- Taxes, payment patterns, and reporting considerations, as well as credit sales and non-cash costs, are reasons why operating cash flows can differ from accounting profits.
ANS: T DIF: Easy TOP: Operating cash flows
- Ratio analysis involves a comparison of the relationships between financial statement accounts so as to analyze the financial position and strength of a firm.
ANS: T DIF: Easy TOP: Ratio analysis
- The current ratio and inventory turnover ratio measure the liquidity of a firm. The current ratio measures the relation of a firm’s current assets to its current liabilities and the inventory turnover ratio measures how rapidly a firm turns its inventory back into a “quick” asset or cash.
ANS: F DIF: Easy TOP: Liquidity ratios
- If a firm has high current and quick ratios, this always is a good indication that a firm is managing its liquidity position well.
ANS: F DIF: Easy TOP: Current ratio
- A decline in the inventory turnover ratio suggests that the firm’s liquidity position is improving.
ANS: F DIF: Easy TOP: Inventory turnover ratio
- The degree to which the managers of a firm attempt to magnify the returns to owners’ capital through the use of financial leverage is captured in debt management ratios.
ANS: T DIF: Easy TOP: Debt management ratios
- Profitability ratios show the combined effects of liquidity, asset management, and debt management on operations.
ANS: T DIF: Easy TOP: Profitability ratios
- Determining whether a firm’s financial position is improving or deteriorating requires analysis of more than one set of financial statements. Trend analysis is one method of measuring a firm’s performance over time.
ANS: T DIF: Easy TOP: Trend analysis
- The information contained in the annual report is used by investors to form expectations about future earnings and dividends.
ANS: T DIF: Easy TOP: Annual report
- The balance sheet presents a summary of the firm’s revenues and expenses over an accounting period.
ANS: F DIF: Easy TOP: Financial statements
- On the balance sheet, total assets must equal total liabilities plus stockholders equity.
ANS: T DIF: Easy TOP: Balance sheet
- One of the biggest noncash items on the income statement is depreciation which needs to be subtracted from net income to determine cash flows for the firm.
ANS: F DIF: Easy TOP: Cash flows
- A firm’s net income reported on its income statement must equal the operating cash flows on the statement of cash flows.
ANS: F DIF: Easy TOP: Accounting profit and cash flows
- A statement reporting the impact of a firm’s operating, investing, and financing activities on cash flows over an accounting is the statement of cash flows.
ANS: T DIF: Easy TOP: Statement of cash flows
- When a firm conducts a seasoned equity offering, it increases an equity account which is an example of a source of funds.
ANS: T DIF: Easy TOP: Sources and uses of cash
- When a firm conducts a stock repurchase, it increases an equity account which is an example of a source of funds.
ANS: F DIF: Easy TOP: Sources and uses of cash
- A liquid asset is an asset that can be easily converted into cash without a significant loss of its original value.
ANS: T DIF: Easy TOP: Liquidity ratios
- Genzyme Corporation has seen its days sales outstanding (DSO) decline from 38 days last year to 22 days this implying that more of the firm’s suppliers are being paid on time.
ANS: F DIF: Easy TOP: Days sales outstanding (DSO)
- Funds supplied by common stockholders mainly includes capital stock, paid-in capital, and retained earnings, while total equity is comprised of common equity plus preferred stock.
ANS: T DIF: Medium TOP: Total equity
- Retained earnings is the cash that has been generated by the firm through its operations which has not been paid out to stockholders as dividends. Retained earnings are kept in cash or near cash accounts and thus, these cash accounts, when added together, will always be equal to the total retained earnings of the firm.
ANS: F DIF: Medium TOP: Retained earnings
- The financial position of companies whose business is seasonal can be dramatically different depending upon the time of year chosen to construct financial statements. This time sensitivity is especially true with respect to the firm’s balance sheet.
ANS: T DIF: Medium TOP: Balance sheet changes
- In order to accurately estimate cash flow from operations, depreciation must be added back to net income. The reason for this is that even though depreciation is deducted from revenue it is really a non-cash charge.
ANS: T DIF: Medium TOP: Cash flows
- In accounting, emphasis is placed on determining net income. In finance, the primary emphasis also is on net income because that is what investors use to value the firm. However, a secondary consideration is cash flow because that’s what is used to run the business.
ANS: F DIF: Medium TOP: Cash flow and net income
- Current cash flow from existing assets is highly relevant to the investor. However, the value of the firm depends primarily upon its growth opportunities. As a result, profit projections from those opportunities are the only relevant future flows with which investors are concerned.
ANS: F DIF: Medium TOP: Future cash flows
- If the current ratio of Firm A is greater than the current ratio of Firm B, we cannot be sure that the quick ratio of Firm A is greater than that of Firm B. However, if the quick ratio of Firm A exceeds that of Firm B, we can be assured that Firm A’s current ratio also exceeds B’s current ratio.
ANS: F DIF: Medium TOP: Liquidity ratios
- The inventory turnover and current ratios are related. The combination of a high current ratio and a low inventory turnover ratio relative to the industry norm might indicate that the firm is maintaining too high an inventory level or that part of the inventory is obsolete or damaged.
ANS: T DIF: Medium TOP: Inventory turnover ratio
- We can use the fixed asset turnover ratio to legitimately compare firms in different industries as long as all the firms being compared are using the same proportion of fixed assets to total assets.
ANS: F DIF: Medium TOP: Fixed asset turnover
- Suppose two firms with the same amount of assets pay the same interest rate on their debt and earn the same rate of return on their assets, and that ROA is positive. However, one firm has a higher debt ratio. Under these conditions, the firm with the higher debt ratio will also have a higher rate of return on common equity.
ANS: T DIF: Medium TOP: ROA and ROE
- Suppose a firm wants to maintain a specific TIE ratio. If the firm knows the level of its debt, the interest rate it will pay on that debt and the applicable tax rate, the firm can then calculate the earnings level required to maintain its target TIE ratio.
ANS: T DIF: Medium TOP: TIE ratio
- The fixed charge coverage ratio recognizes that firms often lease equipment under contract and thus, some firms must meet more than just their scheduled interest payments out of earnings. Therefore, the fixed charge coverage is more inclusive than the TIE ratio.
ANS: T DIF: Medium TOP: Fixed charge coverage ratio
- If sales decrease and financial leverage increases, we can say with certainty that the profit margin on sales will decrease.
ANS: F DIF: Medium TOP: Profit margin and leverage
- Selling new stock is an equity transaction; it does not affect any asset or liability account and therefore, does not appear on the statement of cash flows.
ANS: F DIF: Medium TOP: Financing activities
MULTIPLE CHOICE
- Other things held constant, which of the following will not affect the quick ratio? (Assume that current assets equal current liabilities.)
a. | Fixed assets are sold for cash. |
b. | Cash is used to purchase inventories. |
c. | Cash is used to pay off accounts payable. |
d. | Accounts receivable are collected. |
e. | Long-term debt is issued to payoff a short-term bank loan. |
ANS: D
The quick ratio is calculated as follows:
The only action that doesn’t affect the quick ratio is statement d. While this action decreases receivables (a current asset), it increases cash (also a current asset). The net effect is no change in the quick ratio.
DIF: Easy OBJ: TYPE: Conceptual TOP: Quick ratio
- Changes in balance sheet accounts are necessary for
a. | A typical ratio analysis. |
b. | Pro forma balance sheet construction. |
c. | Statement of cash flows construction. |
d. | Profit and loss analysis. |
e. | Pro forma income statement construction. |
ANS: C DIF: Easy OBJ: TYPE: Conceptual
TOP: Statement of cash flows
- All of the following represent cash outflows to the firm except
a. | Taxes. |
b. | Interest payments. |
c. | Dividends. |
d. | Purchase of plant and equipment. |
e. | Depreciation. |
ANS: E DIF: Easy OBJ: TYPE: Conceptual TOP: Cash flows
- Other things held constant, if a firm holds cash balances in excess of their optimal level in a non-interest bearing account, this will tend to lower the firm’s
a. | Profit margin. |
b. | Total asset turnover. |
c. | Return on equity. |
d. | All of the above. |
e. | Answers b and c above. |
ANS: E DIF: Easy OBJ: TYPE: Conceptual
TOP: Excessive cash balances
- Other things held constant, which of the following will not affect the current ratio, assuming an initial current ratio greater than 1.0?
a. | Fixed assets are sold for cash. |
b. | Long-term debt is issued to pay off current liabilities. |
c. | Accounts receivable are collected. |
d. | Cash is used to pay off accounts payable. |
e. | A bank loan is obtained, and the proceeds are credited to the firm’s checking account. |
ANS: C DIF: Easy OBJ: TYPE: Conceptual TOP: Current ratio
- The annual report contains all of the following financial statements except
a. | income statement. |
b. | statement of changes in long-term financing. |
c. | statement of cash flows. |
d. | balance sheet. |
e. | statement of retained earnings. |
ANS: B DIF: Easy OBJ: TYPE: Conceptual TOP: Annual report
- Which of the following financial statements shows a firm’s financing activities (how funds were generated) and investment activities (how funds were used) over a particular period of time?
a. | balance sheet |
b. | income statement |
c. | statement of retained earnings |
d. | statement of cash flows |
e. | proxy statement |
ANS: A DIF: Easy OBJ: TYPE: Conceptual
TOP: Financial statements
- Which of the following statements shows the portion of the firm’s earnings that has been saved rather than paid out as dividends?
a. | balance sheet |
b. | income statement |
c. | statement of retained earnings |
d. | statement of cash flows |
e. | proxy statement |
ANS: C DIF: Easy OBJ: TYPE: Conceptual
TOP: Financial statements
- Which of the following financial statements includes information about a firm’s assets, equity, and liabilities?
a. | Income statement |
b. | Cash flow statement |
c. | Balance sheet |
d. | Statement of retained earnings |
e. | All of the above |
ANS: C DIF: Easy OBJ: TYPE: Conceptual
TOP: Financial statements
- When constructing a Statement of Cash Flows, which of the following actions would be considered a source of funds?
a. | increase in the cash account |
b. | decrease in accounts payable |
c. | increase in inventory |
d. | increase in long-term bonds |
e. | increase in fixed assets |
ANS: B DIF: Easy OBJ: TYPE: Conceptual
TOP: Financial statements
- Which of the following groups probably would not be interested in the financial statement analysis of a firm?
a. | creditors |
b. | management of the firm |
c. | stockholders |
d. | Internal Revenue Service |
e. | All of the above would be interested in the financial statement analysis. |
ANS: D DIF: Easy OBJ: TYPE: Conceptual TOP: Ratio analysis
- Which of the following ratios measures how effectively a firm is managing its assets?
a. | quick ratio |
b. | times interest earned |
c. | profit margin |
d. | inventory turnover ratio |
e. | price earnings ratio |
ANS: D DIF: Easy OBJ: TYPE: Conceptual
TOP: Inventory turnover ratio
- If your goal is determine how effectively a firm is managing its assets, which of the following sets of ratios would you examine?
a. | profit margin, current ratio, fixed charge coverage ratio |
b. | quick ratio, debt ratio, time interest earned |
c. | inventory turnover ratio, days sales outstanding, fixed asset turnover ratio |
d. | total assets turnover ratio, price earnings ratio, return on total assets |
e. | time interest earned, profit margin, fixed asset turnover ratio |
ANS: C DIF: Easy OBJ: TYPE: Conceptual
TOP: Asset management ratios
- Which of the following ratios measures the extent to which operating income can decline before the firm is unable to meet its annual interest costs
a. | fixed charge coverage ratio |
b. | debt ratio |
c. | times-interest-earned ratio |
d. | return on equity |
e. | profit margin |
ANS: C DIF: Easy OBJ: TYPE: Conceptual TOP: TIE ratio
- An analysis of a firm’s financial ratios over time that is used to determine the improvement or deterioration in its financial situation is called
a. | sensitivity analysis |
b. | DuPont chart |
c. | ratio analysis |
d. | progress chart |
e. | trend analysis |
ANS: E DIF: Easy OBJ: TYPE: Conceptual TOP: Trend analysis
- Which of the following statements is most correct?
a. | An increase in a firm’s debt ratio, with no changes in its sales and operating costs, could be expected to lower its profit margin on sales. |
b. | An increase in DSO, other things held constant, would generally lead to an increase in the total asset turnover ratio. |
c. | An increase on the DSO, other things held constant, would generally lead to an increase in the ROE. |
d. | In a competitive economy, where all firms earn similar returns on equity, one would expect to find lower profit margins for airlines, which require a lot of fixed assets relative to sales, than for fresh fish markets. |
e. | It is more important to adjust the Debt/Asset ratio than the inventory turnover ratio to account for seasonal fluctuations. |
ANS: A
Statement a is true because, if a firm takes on more debt, its interest expense will rise, and this will lower its profit margin. Of course, there will be less equity than there would have been, hence the ROE might rise even though the profit margin fell.
DIF: Medium OBJ: TYPE: Conceptual TOP: Financial statement analysis
- Which of the following statements is correct?
a. | The annual report contains four basic financial statements: the income statement; balance sheet; statement of cash flows; and statement of changes in long-term financing. |
b. | Although the annual report is geared toward the average stockholder, it represents financial analysts’ most complete source of financial information about the firm. |
c. | The key importance of annual report information is that it is used by investors when they form their expectations about the firm’s future earnings and dividends and the riskiness of those cash flows. |
d. | The annual report provides no relevant information for use by financial analysts or by the investing public. |
e. | None of the above statements is correct. |
ANS: C DIF: Medium OBJ: TYPE: Conceptual TOP: Annual report
- A firm’s current ratio has steadily increased over the past 5 years, from 1.9 five years ago to 3.8 today. What would a financial analyst be most justified in concluding?
a. | The firm’s fixed assets turnover probably has improved. |
b. | The firm’s liquidity position probably has improved. |
c. | The firm’s stock price probably has increased. |
d. | Each of the above is likely to have occurred. |
e. | The analyst would be unable to draw any conclusions from this information. |
ANS: B DIF: Medium OBJ: TYPE: Conceptual TOP: Liquidity ratios
- Which of the following actions will cause an increase in the quick ratio in the short run?
a. | $1,000 worth of inventory is sold, and an account receivable is created. The receivable exceeds the inventory by the amount of profit of the sale, which is added to retained earnings. |
b. | A small subsidiary which was acquired for $100,000 two years ago and which was generating profits at the rate of 10 percent is sold for $100,000 cash. (Average company profits are 15 percent of assets.) |
c. | Marketable securities are sold at cost. |
d. | All of the above. |
e. | Answers a and b above. |
ANS: E DIF: Medium OBJ: TYPE: Conceptual TOP: Quick ratio
- Which of the following statements is correct?
a. | In the text, depreciation is regarded as a use of cash because it reduces fixed assets, which then must be replaced. |
b. | If a company uses some of its cash to pay off short-term debt, then its current ratio will always decline, given the way ratio is calculated, other things held constant. |
c. | During a recession, it is reasonable to think that most companies inventory turnover ratios will change while their fixed asset turnover ratio will remain fairly constant. |
d. | During a recession, we can be confident that most companies’ DSOs (or ACPs) will decline because their sales will probably decline. |
e. | Each of the above statements is false. |
ANS: E DIF: Medium OBJ: TYPE: Conceptual
TOP: Miscellaneous ratio behavior
- As a short-term creditor concerned with a company’s ability to meet its financial obligation to you, which one of the following combinations of ratios would you most likely prefer?
Current | Debt | |||
ratio | TIE | ratio |
a. | 0.5 0.5 0.33 |
b. | 1.0 1.0 0.50 |
c. | 1.5 1.5 0.50 |
d. | 2.0 1.0 0.67 |
e. | 2.5 0.5 0.71 |
ANS: C DIF: Medium OBJ: TYPE: Conceptual TOP: Ratio analysis
- Which of the following statements about ratio analysis is incorrect?
a. | Classifying a large, well-diversified firm into a single industry often is difficult because many of the firm’s divisions are involved with different products from different industries. |
b. | As a rule of thumb, it is safe to conclude that any firm with a current ratio greater than 1.0 should be able to meet its current obligations—that is, pay bills that come due in the current period. [Current ratio = (Current assets) / (Current liabilities)] |
c. | Sometimes firms attempt to use “window dressing” techniques to make their financial statements look better than they actually are in the current period. |
d. | Computing the values of the ratios is fairly simple; the toughest and most important part of ratio analysis is interpretation of the values derived from the computations. |
e. | General conclusions about a firm should not be made by examining one or a few ratios—ratio analysis should be comprehensive. |
ANS: B DIF: Medium OBJ: TYPE: Conceptual TOP: Ratio analysis
- Yesterday, Bicksler Corporation purchased (and received) raw materials on credit from its supplier. All else equal, if Bicksler’s current ratio was 2.0 before the purchase, what effect did this transaction have on Bicksler’s current ratio?
a. | increased |
b. | decreased |
c. | stayed the same |
d. | There is not enough information to answer this question. |
e. | None of the above is a correct answer. |
ANS: B DIF: Medium OBJ: TYPE: Conceptual TOP: Current ratio
- Bubbles Soap Corporation has a quick ratio of 1.0 and a current ratio of 2.0 implying that
a. | the value of current assets is equal to the value of inventory. |
b. | the value of current assets is equal to the value of current liabilities. |
c. | the value of current liabilities is equal to the value of inventory. |
d. | All of the above. |
e. | None of the above. |
ANS: C DIF: Medium OBJ: TYPE: Conceptual
TOP: Current ratio and quick ratio
- Which of the following statements is most correct?
a. | firms with relatively low debt ratios have higher expected returns when the business is good. |
b. | firms with relatively low debt ratios are exposed to risk of loss when the business is poor. |
c. | firms with relatively high debt ratios have higher expected returns when the business is bad. |
d. | firms with relatively high debt ratios have higher expected returns when the business is good. |
e. | none of the above. |
ANS: D DIF: Medium OBJ: TYPE: Conceptual
TOP: Debt management ratios
- All other things constant, an increase in a firm’s profit margin would
a. | increase the additional funds needed for financing a growth in operations. |
b. | decrease the additional funds needed for financing a growth in operations. |
c. | have no effect on the additional funds needed for financing a growth in operations. |
d. | decrease its taxes. |
e. | none of the above. |
ANS: B DIF: Medium OBJ: TYPE: Conceptual TOP: Profit margin
- Which of the following statements is correct?
a. | If Company A has a higher debt ratio that Company B, then we can be sure that A will have a lower times-interest-earned ratio than B. |
b. | Suppose two companies have identical operations in terms of sales, cost of goods sold, interest rate on debt, and assets. However, Company A used more debt than Company B; that is, Company A has a higher debt ratio. Under these conditions, we would expect B’s profit margin to be higher than A’s. |
c. | The ROE of any company which is earning positive profits and which has a positive net worth (or common equity) must exceed the company’s ROA. |
d. | Statements a, b, and c are all true. |
e. | Statements a, b, and c are all false. |
ANS: B DIF: Tough OBJ: TYPE: Conceptual
TOP: ROE and debt ratios
- Pepsi Corporation’s current ratio is 0.5, while Coke Company’s current ratio is 1.5. Both firms want to “window dress” their coming end-of-year financial statements. As part of their window dressing strategy, each firm will double its current liabilities by adding short-term debt and placing the funds obtained in the cash account. Which of the statements below best describes the actual results of these transactions?
a. | The transactions will have no effect on the current ratios. |
b. | The current ratios of both firms will be increased. |
c. | The current ratios of both firms will be decreased. |
d. | Only Pepsi Corporation’s current ratio will be increased. |
e. | Only Coke Company’s current ratio will be increased. |
ANS: D
Pepsi Corporation:
Before: Current ratio = 50/100 = 0.50.
After: Current ratio = 150/200 = 0.75.
Coke Company:
Before: Current ratio = 150/100 = 1.50.
After: Current ratio = 250/200 = 1.25.
DIF: Easy OBJ: TYPE: Problem TOP: Current ratio
- The Charleston Company is a relatively small, privately owned firm. Last year the company had after-tax income of $15,000, and 10,000 shares were outstanding. The owners were trying to determine the market value for the stock, prior to taking the company public. A similar firm which is publicly traded had a price/earnings ratio of 5.0. Using only the information given, estimate the market value of one share of Charleston’s stock.
a. | $10.00 |
b. | $7.50 |
c. | $5.00 |
d. | $2.50 |
e. | $1.50 |
ANS: B
EPS = $15,000/10,000 = $1.50.
P/E = 5.0 = P/$1.50.
P = $7.50
DIF: Easy OBJ: TYPE: Problem TOP: Market price per share
- If Boyd Corporation has sales of $2 million per year (all credit) and days sales outstanding of 35 days, what is its average amount of accounts receivable outstanding (assume a 360 day year)?
a. | $194,444 |
b. | $57,143 |
c. | $5,556 |
d. | $97,222 |
e. | $285,714 |
ANS: A
A/R = (Sales/360)(DSO) = (($2,000,000)/(360))(35) = $194,444.
DIF: Easy OBJ: TYPE: Problem TOP: Accounts receivable
- A firm has a profit margin of 15 percent on sales of $20,000,000. If the firm has debt of $7,500,000, total assets of $22,500,000, and an after-tax interest cost on total debt of 5 percent, what is the firm’s ROA?
a. | 8.4% |
b. | 10.9% |
c. | 12.0% |
d. | 13.3% |
e. | 15.1% |
ANS: D
Net income = 0.15($20,000,000) = $3,000,000.
ROA = $3,000,000/$22,500,000 = 13.3%.
DIF: Easy OBJ: TYPE: Problem TOP: ROA
- Collins Company had the following partial balance sheet and complete income statement information for last year:
Balance Sheet: | |
Cash | $ 20 |
A/R | 1,000 |
Inventories | 2,000 |
Total current assets | $3,020 |
Net fixed assets | 2,980 |
Total assets | $6,000 |
Income Statement: | |
Sales | $10,000 |
Cost of goods sold | 9,200 |
EBIT | $ 800 |
Interest (10%) | 400 |
EBT | $ 400 |
Taxes (40%) | 160 |
Net Income | $ 240 |
The industry average DSO is 30 (360-day basis). Collins plans to change its credit policy so as to cause its DSO to equal the industry average, and this change is expected to have no effect on either sales or cost of goods sold. If the cash generated from reducing receivables is used to retire debt (which was outstanding all last year and which has a 10% interest rate), what will Collins’ debt ratio (Total debt/Total assets) be after the change in DSO is reflected in the balance sheet?
a. | 33.33% |
b. | 45.28% |
c. | 52.75% |
d. | 60.00% |
e. | 65.71% |
ANS: E
Current DSO = 36 days. Industry average DSO = 30 days.
Reduce receivables by
Debt = $400/0.10 = $4,000.
Debt to assets =
DIF: Medium OBJ: TYPE: Problem TOP: Financial statement analysis
- A firm has total interest charges of $10,000 per year, sales of $1 million, a tax rate of 40 percent, and a net profit margin of 6 percent. What is the firm’s times-interest-earned ratio?
a. | 16 times |
b. | 10 times |
c. | 7 times |
d. | 11 times |
e. | 20 times |
ANS: D
NI = $1,000,000(0.06) = $60,000.
EBT = $60,000/0.6 = $100,000.
EBIT = $100,000 + $10,000 = $110,000.
TIE = EBIT/I = $110,000/$10,000 = 11 times.
DIF: Medium OBJ: TYPE: Problem TOP: TIE ratio
- Alumbat Corporation has $800,000 of debt outstanding, and it pays an interest rate of 10 percent annually on its bank loan. Alumbat’s annual sales are $3,200,000; its average tax rate is 40 percent; and its net profit margin on sales is 6 percent. If the company does not maintain a TIE ratio of at least 4 times, its bank will refuse to renew its loan, and bankruptcy will result. What is Alumbat’s current TIE ratio?
a. | 2.4 |
b. | 3.4 |
c. | 3.6 |
d. | 4.0 |
e. | 5.0 |
ANS: E
TIE = EBIT/I, so find EBIT and I.
Interest = $800,000 ´ 0.1 = $80,000.
Net income = $3,200,000 ´ 0.06 = $192,000.
Taxable income = EBT = $192,000/(1 – T) = $192,000/0.6 = $320,000.
EBIT = $320,000 + $80,000 = $400,000.
TIE = $400,000/$80,000 = 5.0 times.
DIF: Medium OBJ: TYPE: Problem TOP: TIE ratio
- Determine the increase or decrease in cash for Rinky Supply Company for last year, given the following information. (Assume no other changes occurred during the past year.)
Decrease in marketable securities | = | $25 |
Increase in accounts receivables | = | $50 |
Increase in notes payable | = | $30 |
Decrease in accounts payable | = | $20 |
Increase in accrued wages and taxes | = | $15 |
Increase in inventories | = | $35 |
Retained earnings | = | $ 5 |
a. | -$50 |
b. | +$40 |
c. | -$30 |
d. | +$20 |
e. | -$10 |
ANS: C
Statement of cash flows:
Cash Flows from Operations | ||
Retained earnings | $ 5 | |
Additions (sources of cash): | ||
Increase in accrued wages and taxes | 15 | |
Subtractions (uses of cash): | ||
Increase in accounts receivable | (50) | |
Increase in inventories | (35) | |
Decrease in accounts payable | (20) | |
Net Cash Flows from Operations | ($85) | |
Cash Flows Associated with Financing Activities | ||
Decrease in marketable securities | $25 | |
Increase in notes payable | 30 | |
Net Cash Flows from Financing | 55 | |
Net reduction in Cash | ($30) |
DIF: Medium OBJ: TYPE: Problem TOP: Change in cash flows
- Cannon Company has enjoyed a rapid increase in sales in recent years, following a decision to sell on credit. However, the firm has noticed a recent increase in its collection period. Last year, total sales were $1 million, and $250,000 of these sales were on credit. During the year, the accounts receivable account averaged $41,664. It is expected that sales will increase in the forthcoming year by 50 percent, and, while credit sales should continue to be the same proportion of total sales, it is expected that the days sales outstanding will also increase by 50 percent. If the resulting increase in accounts receivable must be financed by external funds, how much external funding will Cannon need?
a. | $41,664 |
b. | $52,086 |
c. | $47,359 |
d. | $106,471 |
e. | $93,750 |
ANS: B
DSO = ($41,664/$250,000)/360 = 60 days.
New A/R = (($250,000)(1.5)/(360))(60)(1.5) = $93,750.
Hence, increase in receivables = $93,750 – $41,664 = $52,086.
DIF: Medium OBJ: TYPE: Problem TOP: Receivables increase
- The Meryl Corporation’s common stock currently is selling at $100 per share, which represents a P/E ratio of 10. If the firm has 100 shares of common stock outstanding, a return on equity of 20 percent, and a debt ratio of 60 percent, what is its return on total assets (ROA)?
a. | 8.0% |
b. | 10.0% |
c. | 12.0% |
d. | 16.7% |
e. | 20.0% |
ANS: A
P/E = 10 = $100/EPS
EPS = $100/10 = $10.
Earnings = NI = $10(100 shares) = $1,000.
ROE = NI/Equity = $1,000/Equity = 20%
Equity = $1,000/0.20 = $5,000.
Debt ratio = 60%, so Equity ratio = 40% = Equity/TA
TA = Equity/0.40 = $5,000/0.40 = $12,500.
ROA = NI/TA = $1,000/$12,500 = 0.08 = 8%.
DIF: Medium OBJ: TYPE: Problem TOP: ROA
- Selzer Inc. sells all its merchandise on credit. It has a profit margin of 4 percent, days sales outstanding equal to 60 days, receivables of $150,000, total assets of $3 million, and a debt ratio of 0.64. What is the firm’s return on equity (ROE)?
a. | 7.1% |
b. | 33.3% |
c. | 3.3% |
d. | 71.0% |
e. | 8.1% |
ANS: C
(Sales per day)(DSO) = A/R
(Sales/360)(60) = $150,000
Sales = $900,000.
Profit margin = Net profit after tax/Sales.
Net profit = 0.4($900,000) = $36,000.
Debt ratio = 0.64 = Total debt/$3,000,000.
Total debt = $1,920,000.
Total equity = $3,000,000 – $1,920,000 = $1,080,000.
ROE = $36,000/$1,080,000 = 3.3%.
DIF: Medium OBJ: TYPE: Problem TOP: ROE
- You are given the following information about a firm: The growth rate equals 8 percent; return on assets (ROA) is 10 percent; the debt ratio is 20 percent; and the stock is selling at $36. What is the return on equity (ROE)?
a. | 14.0% |
b. | 12.5% |
c. | 15.0% |
d. | 2.5% |
e. | 13.5% |
ANS: B
Debt ratio = TL/TA = 20%, so Equity = (1 – 0.20)TA = 0.80(TA).
ROA = NI/TA = 10%.
NI = 10%(TA) = 0.10(TA).
ROE = NI/Equity = [0.10(TA)]/[0.80(TA)] = 0.10/0.80 = 0.125 = 12.5%.
DIF: Medium OBJ: TYPE: Problem TOP: ROE
- Assume Meyer Corporation is 100 percent equity financed. Calculate the return on equity, given the following information:
(1) | Earnings before taxes = $1,500; |
(2) | Sales = $5,000; |
(3) | Dividend payout ratio = 60%; |
(4) | Total assets turnover = 2.0; |
(5) | Applicable tax rate = 30%. |
a. | 25% |
b. | 30% |
c. | 35% |
d. | 42% |
e. | 50% |
ANS: D
NI = $1,500(1 – 0.3) = $1,050.
Total assets turnover = Sales/TA = 2.0.
TA = Sales/2.0 = $5,000/2.0 = $2,500 = Equity.
ROE = NI/Equity = $1,050/$2,500 = 42%.
DIF: Medium OBJ: TYPE: Problem TOP: ROE
- The Amer Company has the following characteristics:
Sales: | $1,000 |
Total Assets: | $1,000 |
Total Debt/Total Assets: | 35% |
EBIT: | $ 200 |
Tax rate: | 40% |
Interest rate on total debt: | 4.57% |
What is Amer’s ROE?
a. | 11.04% |
b. | 12.31% |
c. | 16.99% |
d. | 28.31% |
e. | 30.77% |
ANS: C
Calculate debt and equity:
Debt = D/A ´ TA = 0.35($1,000) = $350.
Equity = TA – Debt = $1,000 – $350 = $650.
Calculate net income and ROE:
Net income = (EBIT – I)(1 – T) = [$200 – 0.0457($350)](0.6) = $110.4.
ROE = $110.4/$650 = 16.99%.
DIF: Medium OBJ: TYPE: Problem TOP: ROE
- Aurillo Equipment Company (AEC) projected that its ROE for next year would be just 6%. However, the financial staff has determined that the firm can increase its ROE by refinancing some high interest bonds currently outstanding. The firm’s total debt will remain at $200,000 and the debt ratio will hold constant at 80%, but the interest rate on the refinanced debt will be 10%. The rate on the old debt is 14%. Refinancing will not affect sales which are projected to be $300,000. EBIT will be 11% of sales, and the firm’s tax rate is 40%. If AEC refinances its high interest bonds, what will be its projected new ROE?
a. | 3.0% |
b. | 8.2% |
c. | 10.0% |
d. | 15.6% |
e. | 18.7% |
ANS: D
Relevant information: Old ROE = NI/Equity = 0.06 = 6%.
Sales = $300,000; EBIT = 0.11(Sales) = 0.11($300,000) = $33,000.
Debt = $200,000; D/A = 0.80 = 80%.
Tax rate = 40%.
Interest rate change: Old bonds 14%; new bonds 10%.
Calculate total assets and equity amounts:
Since debt = $200,000, total assets = $200,000/0.80 = $250,000.
E/TA = 1 – D/A = 1 – 0.80 = 0.20.
Equity = E/TA ´ TA = 0.20 ´ $250,000 = $50,000.
Construct comparative Income Statements from EBIT, and calculate new ROE:
Old | New | |
EBIT | $33,000 | $33,000 |
Less: Interest | 28,000 | 20,000 |
EBT | 5,000 | 13,000 |
Less: Taxes (40%) | 2,000 | 5,200 |
Net income | $ 3,000 | $ 7,800 |
New ROE = NI/Equity = $7,800/$50,000 = 0.1560 = 15.6%.
DIF: Medium OBJ: TYPE: Problem TOP: ROE and refinancing
- Savelots Stores’ current financial statements are shown below:
Inventories | $ 500 | Accounts payable | $ 100 |
Other current assets | 400 | Short-term notes payable | 370 |
Fixed assets | 370 | Common equity | 800 |
Total assets | $1,270 | Total liab. and equity | $1,270 |
Sales | $2,000 |
Operating costs | 1,843 |
EBIT | 157 |
Less: Interest | 37 |
EBT | 120 |
Less: Taxes (40%) | 48 |
Net income | 72 |
A recently released report indicates that Savelots’ current ratio of 1.9 is in line with the industry average. However, its accounts payable, which have no interest cost and which are due entirely to purchases of inventories, amount to only 20% of inventory versus an industry average of 60%. Suppose Savelots took actions to increase its accounts payable to inventories ratio to the 60% industry average, but it (1) kept all of its assets at their present levels (that is, the asset side of the balance sheet remains constant) and (2) also held its current ratio constant at 1.9. Assume that Savelots’ tax rate is 40%, that its cost of short-term debt is 10%, and that the change in payments will not affect operations. In addition, common equity would not change. With the changes, what would be Savelots’ new ROE?
a. | 10.5% |
b. | 7.8% |
c. | 9.0% |
d. | 13.2% |
e. | 12.0% |
ANS: A
The firm is not using its “free” trade credit (that is, accounts payable (A/P)) to the same extent as other companies. Since it is financing part of its assets with 10% notes payable, its interest expense is higher than necessary.
Calculate the increase in payables:
Current (A/P)/Inventories ratio = 100/500 = 0.20.
Target A/P = 0.60(Inventories) = 0.60(500) = 300.
Increase in A/P = 300 – 100 = 200.
Because the current ratio and total assets remain constant, total liabilities and equity must be unchanged. The increase in accounts payable must be matched by an equal decrease in interest bearing notes payable. Notes payable decline by 200. Interest expense decreases by 200 ´ 0.10 = 20.
Construct comparative Income Statements:
Old | New | |
Sales | $2,000 | $2,000 |
Operating costs | 1,843 | 1,843 |
EBIT | 157 | 157 |
Less: Interest | 37 | 17 |
EBT | 120 | 140 |
Less: Taxes | 48 | 56 |
Net income (NI) | $ 72 | $ 84 |
ROE = NI/Equity = $72/$800 = 9%. $84/$800 = 10.5%.
New ROE = 10.5%.
DIF: Medium OBJ: TYPE: Problem TOP: ROE and financing
- Harvey Supplies Inc. has a current ratio of 3.0, a quick ratio of 2.4, and an inventory turnover ratio of 6. Harvey’s total assets are $1 million and its debt ratio is 0.20. The firm has no long-term debt. What is Harvey’s sales figure if the total cost of goods sold is 75% of sales?
a. | $960,000 |
b. | $720,000 |
c. | $1,620,000 |
d. | $120,000 |
e. | $540,000 |
ANS: A
Current liabilities: (0.2)($1,000,000) = $200,000.
Current assets: CA/$200,000 = 3.0; CA = $600,000.
Inventory: ($600,000 – I)/$200,000 = 2.4; I = $120,000.
Sales: (0.75)S/$120,000 = 6; S = $720,000/0.75 = $960,000.
DIF: Medium OBJ: TYPE: Problem TOP: Sales volume
- Given the following information, calculate the market price per share of WAM Inc.
Earnings after interest and taxes = $200,000
Earnings per share = $2.00
Stockholders’ equity = $2,000,000
Market/Book ratio = 0.20
a. | $20.00 |
b. | $8.00 |
c. | $4.00 |
d. | $2.00 |
e. | $1.00 |
ANS: C
Number of shares = $200,000/$2.00 = 100,000.
Book value per share = $2,000,000/100,000 = $20.
Market value = 0.2(Book value) = 0.2($20) = $4.00 per share.
DIF: Medium OBJ: TYPE: Problem TOP: Market price per share
- On its December 31st balance sheet, LCG Company reported gross fixed assets of $6,500,000 and net fixed assets of $5,000,000. Depreciation for the year was $500,000. Net fixed assets a year earlier on December 31st, had been $4,700,000. What figure for “Cash Flows Associated with Long-Term Investments (Fixed Assets)” should LCG report on its Statement of Cash Flows for the current year?
a. | $500,000 |
b. | $600,000 |
c. | $700,000 |
d. | $800,000 |
e. | $900,000 |
ANS: D
Funds | = NFA_{1} – NFA_{0} + Depreciation |
= $5,000,000 – $4,700,000 + $500,000 = $800,000. |
Alternative long-form solution: | ||
Current Year | One Year Ago | |
Gross fixed assets | $6,500,000 | $5,700,000 |
Accumulated depreciation | 1,500,000 | 1,000,000 |
Net fixed assets | 5,000,000 | 4,700,000 |
Accumulated assets_{Year ago} | = $4,700,000 + ($1,500,000 – $500,000) |
= $5,700,000. | |
Funds used to purchase | = GFA_{Current} – GFA_{Year ago} fixed assets |
= $6,500,000 – $5,700,000 = $800,000. |
DIF: Medium OBJ: TYPE: Problem TOP: Depreciation cash flows
- Lombardi Trucking Company has the following data:
Assets: | $10,000 | Profit margin: | 3.0% |
Debt ratio: | 60.0% | Interest rate: | 10.0% |
Tax rate: | 40% | Total asset turnover: | 2.0 |
What is Lombardi’s TIE ratio?
a. | 0.95 |
b. | 1.75 |
c. | 2.10 |
d. | 2.67 |
e. | 3.45 |
ANS: D
TIE =
TA Turnover = S/A = 2
S/$10,000 = 2
S = $20,000
Debt ratio =
Debt = $6,000
INT = $6,000 (0.1) = $600
PM =
PM =
NI = $600
EBIT =
EBIT | $1,600 |
Int. | 600 |
EBT | $1,000 |
Taxes (40%) | 400 |
NI | $ 600 |
TIE = $1,600/$600 = 2.67
DIF: Tough OBJ: TYPE: Problem TOP: TIE ratio
- Retailers Inc. and Computer Corp. each have assets of $10,000 and a return on common equity equal to 15%. Retailers has twice as much debt and twice as many sales relative to Computer Corp. Retailers’ net income equals $750, and its total asset turnover is equal to 3. What is Computer Corp.’s profit margin?
a. | 2.50% |
b. | 5.00% |
c. | 7.50% |
d. | 10.00% |
e. | 12.50% |
ANS: C
D | = | Debt for Computer Corp.; | S | = | Sales for Computer Corp. |
2D | = | Debt for Retailers; | 2S | = | Sales for Retailers |
Retailers:
ROE =
0.15 =
$1,500 – 0.3D = $750
D = $2,500
Computer Corp.:
0.15 =
0.15 =
NI = $1,125
Retailers:
TATO =
3=
S = $15,000
PM for Computer Corp.:
DIF: Tough OBJ: TYPE: Problem TOP: Profit margin
Chapter 4—The Time Value of Money
TRUE/FALSE
- Cash flow time lines are used primarily for decisions involving paying off debt or investing in financial securities. They cannot be used when making decisions about investments in physical assets.
ANS: F DIF: Easy TOP: Cash flow time lines
- One of the potential benefits of investing early for retirement is that an investor can receive greater benefits from the compounding of interest.
ANS: T DIF: Easy TOP: Retirement and compounding
- Of all the techniques used in finance, the least important is the concept of the time value of money.
ANS: F DIF: Easy TOP: Time value concepts
- Compounding is the process of converting today’s values, which are termed present value, to future value.
ANS: T DIF: Easy TOP: Compounding
- The coupon rate is the rate of return you could earn on alternative investments of similar risk.
ANS: F DIF: Easy TOP: Coupon rate
- A perpetuity is an annuity with perpetual payments.
ANS: T DIF: Easy TOP: Perpetuity
- An amortized loan is a loan that requires equal payments over its life; its payments include both interest and repayment of the debt.
ANS: T DIF: Easy TOP: Amortization
- The greater the number of compounding periods within a year, the greater the future value of a lump sum invested initially, and the greater the present value of a given lump sum to be received at maturity.
ANS: F DIF: Medium TOP: Compounding
- Suppose an investor can earn a steady 5% annually with investment A, while investment B will yield a constant 12% annually. Within 11 years time, the compounded value of investment B will be more than twice the compounded value of investment A (ignore risk).
ANS: T DIF: Medium TOP: Comparative compounding
- Solving for the interest rate associated with a stream of uneven cash flows, without the use of a calculator, usually involves a trial and error process.
ANS: T DIF: Medium TOP: Uneven cash flows and interest
- When a loan is amortized, the largest portion of the periodic payment goes to reduce principal in the early years of the loan such that the accumulated interest can be spread out over the life of the loan.
ANS: F DIF: Medium TOP: Amortization
- The effective annual rate is always greater than the simple rate as a result of compounding effects.
ANS: F DIF: Medium TOP: Effective and simple rates
- Because we usually assume positive interest rates in time value analyses, the present value of a three-year annuity will always be less than the future value of a single lump sum, if the annuity payment equals the original lump sum investment.
ANS: F DIF: Medium TOP: Lump sum and annuity
- All else equal, a dollar received sooner is worth more than a dollar received at some later date, because the sooner the dollar is received the more quickly it can be invested to earn a positive return.
ANS: T DIF: Medium TOP: Time value concepts
- An annuity is a series of equal payments made at fixed equal-length intervals for a specified number of periods.
ANS: T DIF: Medium TOP: Annuities
- The difference between an ordinary annuity and an annuity due is that each of the payments of the annuity due earns interest for one additional year (period).
ANS: T DIF: Medium TOP: Annuities
- The difference between the PV of an annuity due and the PV of an ordinary annuity is that each of the payments of the annuity due is discounted by one more year.
ANS: T DIF: Medium TOP: Annuities
- The effective annual rate is less than the simple rate when we have monthly compounding.
ANS: F DIF: Medium TOP: Effective annual rate
MULTIPLE CHOICE
- Given some amount to be received several years in the future, if the interest rate increases, the present value of the future amount will
a. | Be higher. |
b. | Be lower. |
c. | Stay the same. |
d. | Cannot tell. |
e. | Be variable. |
ANS: B DIF: Easy OBJ: TYPE: Conceptual TOP: PV of a sum
- You have determined the profitability of a planned project by finding the present value of all the cash flows form that project. Which of the following would cause the project to look more appealing in terms of the present value of those cash flows?
a. | The discount rate decreases. |
b. | The cash flows are extended over a longer period of time, but the total amount of the cash flows remains the same. |
c. | The discount rate increases. |
d. | Answers b and c above. |
e. | Answers a and b above. |
ANS: A DIF: Easy OBJ: TYPE: Conceptual
TOP: PV and discount rate
- As the discount rate increases without limit, the present value of the future cash inflows
a. | Gets larger without limit. |
b. | Stays unchanged. |
c. | Approaches zero. |
d. | Gets smaller without limit, i.e., approaches minus infinity. |
e. | Goes to e^{rn}. |
ANS: C DIF: Easy OBJ: TYPE: Conceptual
TOP: PV and discount rate
- Which of the following statements is most correct?
a. | If annual compounding is used, the effective annual rate equals the simple rate. |
b. | If annual compounding is used, the effective annual rate equals the periodic rate. |
c. | If a loan has a 12 percent simple rate with semiannual compounding, its effective annual rate is equal to 11.66 percent. |
d. | Both answers a and b are correct. |
e. | Both answers a and c are correct. |
ANS: D
Statement d is correct. The equation for EAR is as follows:
If annual compounding is used, m = 1 and the equation above reduces to EAR = r_{SIMPLE}. The equation for the periodic rate is:
If annual compounding is used then m = 1 and r_{PER} = r_{SIMPLE} and since EAR = r_{SIMPLE} then r_{PER} = EAR.
DIF: Easy OBJ: TYPE: Conceptual TOP: Effective annual rate
- Why is the present value of an amount to be received (paid) in the future less than the future amount?
a. | Deflation causes investors to lose purchasing power when their dollars are invested for greater than one year. |
b. | Investors have the opportunity to earn positive rates of return, so any amount invested today should grow to a larger amount in the future. |
c. | Investments generally are not as good as those who sell them suggest, so investors usually are not willing to pay full face value for such investments, thus the price is discounted. |
d. | Because investors are taxed on the income received from investments they never will buy an investment for the amount expected to be received in the future. |
e. | None of the above is a correct answer. |
ANS: B DIF: Easy OBJ: TYPE: Conceptual
TOP: Time value concepts
- By definition, what type of annuity best describes payments such as rent and magazine subscriptions (assuming the costs do not change over time)?
a. | ordinary annuity |
b. | annuity due |
c. | nonconstant annuity |
d. | annuity in arrears |
ANS: B DIF: Easy OBJ: TYPE: Conceptual TOP: Annuities
- What is the effective annual return (EAR) for an investment that pays 10 percent compounded annually?
a. | equal to 10 percent |
b. | greater than 10 percent |
c. | less than 10 percent |
d. | This question cannot be answered without knowing the dollar amount of the investment. |
e. | None of the above is correct. |
ANS: A DIF: Easy OBJ: TYPE: Conceptual
TOP: Effective annual rate
- What is the term used to describe an annuity with an infinite life?
a. | perpetuity |
b. | infinuity |
c. | infinity due |
d. | There is no special term for an infinite annuity. |
ANS: A DIF: Easy OBJ: TYPE: Conceptual TOP: Perpetuity
- Everything else equal, which of the following conditions will result in the lowest present value of an amount to be received in the future?
a. | annual compounding |
b. | quarterly compounding |
c. | monthly compounding |
d. | daily compounding |
ANS: D DIF: Easy OBJ: TYPE: Conceptual
TOP: PV and effective annual rate
- Suppose someone offered you your choice of two equally risky annuities, each paying $5,000 per year for 5 years. One is an annuity due, while the other is a regular (or deferred) annuity. If you are a rational wealth-maximizing investor which annuity would you choose?
a. | The annuity due. |
b. | The deferred annuity. |
c. | Either one, because as the problem is set up, they have the same present value. |
d. | Without information about the appropriate interest rate, we cannot find the values of the two annuities, hence we cannot tell which is better. |
e. | The annuity due; however, if the payments on both were doubled to $10,000, the deferred annuity would be preferred. |
ANS: A DIF: Medium OBJ: TYPE: Conceptual TOP: Annuities
- Which of the following statements is correct?
a. | For all positive values of k and n, FVIF_{r, n} ³ 1.0 and PVIFA_{r, n} ³ n. |
b. | You may use the PVIF tables to find the present value of an uneven series of payments. However, the PVIFA tables can never be of use, even if some of the payments constitute an annuity (for example, $100 each year for Years 3, 4, and 5), because the entire series does not constitute an annuity. |
c. | If a bank uses quarterly compounding for saving accounts, the simple rate will be greater than the effective annual rate. |
d. | The present value of a future sum decreases as either the simple interest rate or the number of discount periods per year increases. |
e. | All of the above statements are false. |
ANS: D DIF: Medium OBJ: TYPE: Conceptual
TOP: Time value concepts
- Which of the following statements is correct?
a. | Other things held constant, an increase in the number of discounting periods per year increases the present value of a given annual annuity. |
b. | Other things held constant, an increase in the number of discounting periods per year increases the present value of a lump sum to be received in the future. |
c. | The payment made each period under an amortized loan is constant, and it consists of some interest and some principal. The later we are is the loan’s life, the smaller the interest portion of the payment. |
d. | There is an inverse relationship between the present value interest factor of an annuity and the future value interest factor of an annuity, (i.e., one is the reciprocal of the other). |
e. | Each of the above statements is true. |
ANS: C DIF: Medium OBJ: TYPE: Conceptual
TOP: Time value concepts
- A $10,000 loan is to be amortized over 5 years, with annual end-of-year payments. Given the following facts, which of these statements is correct?
a. | The annual payments would be larger if the interest rate were lower. |
b. | If the loan were amortized over 10 years rather than 5 years, and if the interest rate were the same in either case, the first payment would include more dollars of interest under the 5-year amortization plan. |
c. | The last payment would have a higher proportion of interest than the first payment. |
d. | The proportion of interest versus principal repayment would be the same for each of the 5 payments. |
e. | The proportion of each payment that represents interest as opposed to repayment of principal would be higher if the interest rate were higher. |
ANS: E
If the interest rate were higher, the payments would all be higher, and all of the increase would be attributable to interest. So, the proportion of each payment that represents interest would be higher.
Note that statement b is false because interest during Year 1 would be the interest rate times the beginning balance, which is $10,000. With the same interest rate and the same beginning balance, the Year 1 interest charge will be the same, regardless of whether the loan is amortized over 5 or 10 years.
DIF: Medium OBJ: TYPE: Conceptual TOP: Time value concepts
- Which of the following statements is correct?
a. | Simple rates can’t be used in present value or future value calculations because they fail to account for compounding effects. |
b. | The periodic interest rate can be used directly in calculations as long as the number of payments per year is greater than or equal to the number of compounding periods per year. |
c. | In all cases where interest is added or payments are made more frequently than annually, the periodic rate is less than the annual rate. |
d. | Generally, the APR is greater than the EAR as a result of compounding effects. |
e. | If the compounding period is semiannual then the periodic rate will equal the effective annual rate divided by two. |
ANS: C DIF: Medium OBJ: TYPE: Conceptual
TOP: Types of interest rates
- All else equal, if you expect to receive a certain amount in the future, say, $500 in ten (10) years, the present value of that future amount will be lowest if the interest earned on such investments is compounded
a. | daily |
b. | weekly |
c. | monthly |
d. | quarterly |
e. | annually |
ANS: A DIF: Medium OBJ: TYPE: Conceptual
TOP: Time value concepts
- Which of the following payments (receipts) would probably not be considered an annuity due? Based on your knowledge and using logic, think about the timing of the payments.
a. | rent payments associated with a five-year lease |
b. | payments for a magazine subscription for a two-year period where the payments are made annually |
c. | interest payments associated with a corporate bond that was issued today |
d. | annual payments associated with lottery winnings that are paid out as an annuity |
ANS: C DIF: Medium OBJ: TYPE: Conceptual TOP: Annuities
- All else equal, the future value of a lump-sum amount invested today will increase if the
a. | interest rate that is earned is lowered. |
b. | number of compounding periods is increased. |
c. | investment time period is shortened. |
d. | amount initially invested is lowered. |
e. | Two or more of the above answers are correct. |
ANS: B DIF: Medium OBJ: TYPE: Conceptual
TOP: Time value concepts
- Susan just signed a long-term lease on a townhouse in New York City (near Central Park) that requires her to make equal monthly payments for the next five years. The payments Susan has promised to make represent a(n) __________ for the landlord.
a. | ordinary annuity |
b. | annuity due |
c. | series of uneven cash flows |
d. | perpetuity |
ANS: B DIF: Medium OBJ: TYPE: Conceptual TOP: Annuities
- Suppose that the present value of receiving a guaranteed $450 in two years is $385.80. The opportunity rate of return on similar risk investments is 8 percent. According to this information, all else equal, which of the following statements is correct?
a. | It always would be preferable to wait two years to receive the $450 because this value is greater than the present value. |
b. | Risk averse investors always would prefer to take the $385.80 today because it is a guaranteed amount whereas there is uncertainty as to whether the future amount will be paid. |
c. | No investor should be willing to pay more than $385.80 for such an investment. |
d. | It is apparent the present value was computed incorrectly because the present value of a future amount always should be greater than the future value. |
e. | None of the above is a correct answer. |
ANS: C DIF: Medium OBJ: TYPE: Conceptual
TOP: Time value concepts
- You plan to invest an amount of money in five-year certificate of deposit (CD) at your bank. The stated interest rate applied to the CD is 12 percent, compounded monthly. How much must you invest if you want the balance in the CD account to be $8,500 in five years?
a. | $4,678.82 |
b. | $4,823.13 |
c. | $13,600.00 |
d. | $14,979.90 |
e. | $7,589.29 |
ANS: A DIF: Medium OBJ: TYPE: Conceptual
TOP: PV of a lump sum
- Vegit Corporation needs to borrow funds to support operations during the summer. Vegit’s CFO is trying to decide whether to borrow from the Bank of Florida or the Bank of Georgia. The loan offered by Bank of Florida has a 12.5 percent simple interest rate with annual interest payments, whereas the loan offered by the Bank of Georgia has a 12 percent simple interest rate with monthly payments. Which bank should Vegit use for the loan?
a. | Bank of Georgia, because the 12 percent simple interest is cheaper than the 12.5 percent simple interest at Bank of Florida. |
b. | Bank of Georgia, because the effective interest rate on the loan is less than 12 percent, whereas the effective interest rate on the loan at the Bank of Florida is greater than 12.5 percent. |
c. | Bank of Florida, because the simple interest rate is higher, which means that Vegit will be able to invest the proceeds from the loan at a higher rate of return. |
d. | Bank of Florida, because the effective interest rate on the loan is 12.5 percent, which is less than the 12.7 percent effective interest rate on the loan offered by the Bank of Georgia. |
e. | There is not enough information to answer this question. |
ANS: D DIF: Medium OBJ: TYPE: Conceptual
TOP: Effective annual rate
- Alice’s investment advisor is trying to convince her to purchase an investment that pays $250 per year. The investment has no maturity; therefore the $250 payment will continue every year forever. Alice has determined that her required rate of return for such an investment should be 14 percent and that she would hold the investment for 10 years and then sell it. If Alice decides to buy the investment, she would receive the first $250 payment one year from today. How much should Alice be willing to pay for this investment?
a. | $1,304.03, because this is the present value of an ordinary annuity that pays $250 a year for 10 years at 14 percent. |
b. | $1,486.59, because this is the present value of an annuity due that pays $250 a year for 10 years at 14 percent. |
c. | $1,785.71, because this is the present value of a $250 perpetuity at 14 percent. |
d. | There is not enough information to answer this question, because the selling price of the investment in 10 years is not known today. |
e. | None of the above is correct. |
ANS: C DIF: Medium OBJ: TYPE: Conceptual TOP: Perpetuity
- At approximately what rate would you have to invest a lump-sum amount today if you need the amount to triple in six years? Assume interest is compounded annually.
a. | 20% |
b. | 12% |
c. | 24% |
d. | Not enough information is provided to answer the question. |
e. | None of the above is a correct answer. |
ANS: A DIF: Medium OBJ: TYPE: Conceptual
TOP: Time value concepts
- Sarah is thinking about purchasing an investment from HiBond Investing. If she buys the investment, Sarah will receive $100 every three months for five years. The first $100 payment will be made as soon as she purchases the investment. If Sarah’s required rate of return is 16 percent, to the nearest dollar, how much should she be willing to pay for this investment?
a. | $1,359 |
b. | $1,413 |
c. | $1,112 |
d. | $1,519 |
e. | $1,310 |
ANS: B DIF: Medium OBJ: TYPE: Conceptual
TOP: PV of an annuity
- Which of the following statements is most correct?
a. | The first payment under a 3-year, annual payment, amortized loan for $1,000 will include a smaller percentage (or fraction) of interest if the interest rate is 5 percent than if it is 10 percent. |
b. | If you are lending money, then, based on effective interest rates, you should prefer to lend at a 10 percent simple, or quoted, rate but with semiannual payments, rather than at a 10.1 percent simple rate with annual payments. However, as a borrower you should prefer the annual payment loan. |
c. | The value of a perpetuity (say for $100 per year) will approach infinity as the interest rate used to evaluate the perpetuity approaches zero. |
d. | Statements a, b, and c are all true. |
e. | Only statements b and c are true. |
ANS: D DIF: Tough OBJ: TYPE: Conceptual
TOP: Time value concepts
- A recent advertisement in the financial section of a magazine carried the following claim: “Invest your money with us at 14 percent, compounded annually, and we guarantee to double your money sooner than you imagine.” Ignoring taxes, how long would it take to double your money at a simple rate of 14 percent, compounded annually?
a. | Approximately 3.5 years |
b. | Approximately 5 years |
c. | Exactly 7 years |
d. | Approximately 10 years |
e. | Exactly 14 years |
ANS: B
Tabular solution:
$1 (FVIF_{14%, n}) = $2
FVIF_{14%, n} = 2.000
n = 5+ years.
Financial calculator solution:
Inputs: I = 14; PV = -1; FV =2.
Output: N = 5.29 years.
DIF: Easy OBJ: TYPE: Problem TOP: Time for a sum to double
- At an effective annual interest rate of 20 percent, how many years will it take a given amount to triple in value? (Round to the closest year.)
a. | 5 |
b. | 8 |
c. | 6 |
d. | 10 |
e. | 9 |
ANS: C
Cash flow time line:
Tabular solution:
$1 = $3 (PVIF_{20%, n})
PVIF_{20%, n} = 0.3333
n = 6 periods (years).
Financial calculator solution:
Inputs: I = 20; PV = -1; FV =3.
Output: N = 6.026 = 6 years.
DIF: Easy OBJ: TYPE: Problem TOP: Time for a sum to triple
- You deposited $1,000 in a savings account that pays 8 percent interest, compounded quarterly, planning to use it to finish your last year in college. Eighteen months later, you decide to go to the Rocky Mountains to become a ski instructor rather than continue in school, so you close out your account. How much money will you receive?
a. | $1,171 |
b. | $1,126 |
c. | $1,082 |
d. | $1,163 |
e. | $1,008 |
ANS: B
Tabular solution:
FV = $1,000 (FVIF_{2%, 6}) = $1,000 (1.1262) = $1,126.20 » $1,126.
Financial calculator solution:
Inputs: N = 6; I = 2; PV = -1,000.
Output: FV = $1,126.16 » $1,126.
DIF: Easy OBJ: TYPE: Problem TOP: FV of a sum
- What is the future value of a 5-year ordinary annuity with annual payments of $200, evaluated at a 15 percent interest rate?
a. | $670.44 |
b. | $842.91 |
c. | $1,169.56 |
d. | $1,522.64 |
e. | $1,348.48 |
ANS: E
Tabular solution:
FB = $200 (FVIFA_{15%, 5}) = $200 ´ 6.7424 = $1,348.48.
Financial calculator solution:
Inputs: N = 5; I = 15; PMT = -200.
Output: FV = $1,348.48.
DIF: Easy OBJ: TYPE: Problem TOP: FV of an annuity
- If a 5-year regular annuity has a present value of $1,000, and if the interest rate is 10 percent, what is the amount of each annuity payment?
a. | $240.42 |
b. | $263.80 |
c. | $300.20 |
d. | $315.38 |
e. | $346.87 |
ANS: B
Tabular solution:
$1,000 = PMT (PVIFA_{10%, 5})
PMT = $1,000/3.7908 = $263.80.
Financial calculator solution:
Inputs: N = 5; I = 10; FV = -1,000.
Output: PMT = $263.80.
DIF: Easy OBJ: TYPE: Problem TOP: Annuity payments
- You have the opportunity to buy a perpetuity which pays $1,000 annually. Your required rate of return on this investment is 15 percent. You should be essentially indifferent to buying or not buying the investment if it were offered at a price of
a. | $5,000.00 |
b. | $6,000.00 |
c. | $6,666.67 |
d. | $7,500.00 |
e. | $8,728.50 |
ANS: C
V = PMT/I = $1,000/0.15 = $6,666.67.
DIF: Easy OBJ: TYPE: Problem TOP: PV of a perpetuity
- Assume that you will receive $2,000 a year in Years 1 through 5, $3,000 a year in Years 6 through 8, and $4,000 in Year 9, with all cash flows to be received at the end of the year. If you require a 14 percent rate of return, what is the present value of these cash flows?
a. | $9,851 |
b. | $13,250 |
c. | $11,714 |
d. | $15,129 |
e. | $17,353 |
ANS: C
Tabular solution:
PV | = $2,000 (PVIFA_{14%, 5}) + $3,000 (PVIFA_{14%, 5}) (PVIF_{14%, 9}) |
= $2,000 (3.4331) + $3,000 (2.3216) (0.5194) + $4,000 (0.3075) | |
= $6,866.20 + $3,617.52 + $1,230.00 = $11,713.72 » $11,714. |
Financial calculator solution:
Using cash flows
Inputs: C_{0} = 0; C_{1} = 2,000; N_{j} = 5; C_{2}= 3,000; N_{j} = 3; C_{3} = 4,000; I = 14.
Output: NPV = $11,713.54 » $11,714.
DIF: Easy OBJ: TYPE: Problem TOP: PV of an uneven CF stream
- If $100 is placed in an account that earns a simple 4 percent, compounded quarterly, what will it be worth in 5 years?
a. | $122.02 |
b. | $105.10 |
c. | $135.41 |
d. | $120.90 |
e. | $117.48 |
ANS: A
Tabular solution:
$100 (FVIF_{1%, 20}) = $100 (1.2202) = $122.02.
Financial calculator solution:
Inputs: N = 20; I = 1; PV = -100.
Output: FV = $122.02.
DIF: Easy OBJ: TYPE: Problem TOP: Quarterly compounding
- In 1958 the average tuition for one year at an Ivy League school was $1,800. Thirty years later, in 1988, the average cost was $13,700. What was the growth rate in tuition over the 30-year period?
a. | 12% |
b. | 9% |
c. | 6% |
d. | 7% |
e. | 8% |
ANS: D
Cash flow time line:
Tabular solution:
$13,700 = $1,800 (FVIF_{i, 30})
FVIF_{i, 30 }= 7.6111
I » 7%
Financial calculator solution:
Inputs: N = 30; PV = -1,800; FV = 13,700.
Output: I = 7.0%
DIF: Easy OBJ: TYPE: Problem TOP: Growth rate
- At an inflation rate of 9 percent, the purchasing power of $1 would be cut in half in 8.04 years. How long to the nearest year would it take the purchasing power of $1 to be cut in half if the inflation rate were only 4%?
a. | 12 years |
b. | 15 years |
c. | 18 years |
d. | 20 years |
e. | 23 years |
ANS: C
Cash flow time line:
Tabular solution:
0.5 = $1 (PVIF_{4%, n})
PVIF_{4%, n }= 0.5
PVIF_{4%, 18 }= 0.4936; PVIF_{4%, 17} = 0.5134
n » 18 years.
Although a financial calculator or interpolation might be used to solve precisely, Response c is clearly the closest and best answer of those given.
Financial calculator solution:
Inputs: I = 4; PV = 1; PV = -0.50.
Output: N = -17.67 = 18 years.
DIF: Easy OBJ: TYPE: Problem TOP: Effect of inflation
- Gomez Electronics needs to arrange financing for its expansion program. Bank A offers to lend Gomez the required funds on a loan where interest must be paid monthly, and the quoted rate is 8 percent. Bank B will charge 9 percent, with interest due at the end of the year. What is the difference in the effective annual rates charged by the two banks?
a. | 0.25% |
b. | 0.50% |
c. | 0.70% |
d. | 1.00% |
e. | 1.25% |
ANS: C
Bank A: 8%, monthly
EAR_{A} =
Bank B: 9%, interest due at end of year
EAR_{B} = 9%.
9.00% – 8.30% = 0.70%.
DIF: Easy OBJ: TYPE: Problem TOP: Effective annual rate
- Assume that you can invest to earn a stated annual rate of return of 12 percent, but where interest is compounded semiannually. If you make 20 consecutive semiannual deposits of $500 each, with the first deposit being made today, what will your balance be at the end of Year 20?
a. | $52,821.19 |
b. | $57,900.83 |
c. | $58,988.19 |
d. | $62,527.47 |
e. | $64,131.50 |
ANS: D
Cash flow time line:
Tabular solution:
Periodic (six-month) rate = 12%/2 = 6%.
First, calculate the FV as of Year 10
FV_{10 yr.} | = ($500) (FVIFA_{6%, 19}) 1.06 + ($500) (FVIF_{6%, 20}) |
= $500 (33.760) (1.06) + $500 (3.2071) = $19,496.35. |
Calculate FV as of Year 20 using FV_{10} as the PV
FV_{20 yr.} | = ($19,496.35) (FVIF_{6%, 20}) = $19,496.35 (3.2071) = $62,526.74. |
Financial calculator solution:
Calculate the FV as of Year 10
BEGIN mode. Inputs: N = 20; I = 6; PMT = -500. Output: FV = $19,496.36.
Calculate the FV as of Year 20 using FV_{10} as the PV
END mode. Inputs: N = 20; I = 6; PMT = -19,496.36. Output: FV = $62,527.47.
Note: Tabular solution differs from calculator solution due to interest factor rounding.
DIF: Medium OBJ: TYPE: Problem TOP: FV under semiannual compounding
- Assume you are to receive a 20-year annuity with annual payments of $50. The first payment will be received at the end of Year 1, and the last payment will be received at the end of Year 20. You will invest each payment in an account that pays 10 percent. What will be the value in your account at the end of Year 30?
a. | $6,354.81 |
b. | $7,427.83 |
c. | $7,922.33 |
d. | $8,591.00 |
e. | $6,752.46 |
ANS: B
Tabular solution:
FV_{Year 20} | = $50 (FVIFA_{10$, 20}) = $50 (57.275) = $2,863.75. |
FV_{Year 30} | = $2,863 (FVIFA_{10$, 10}) = $2,863.75 (2.5937) = $7,427.71. |
Financial calculator solution:
Calculate FV at Year 20, then take that lump sum forward 10 years to Year 30 at 10%.
Inputs: N = 20; I = 10; PMT = -50.
Output_{Year 20}: FV = $2,863.75.
At Year 30
Inputs: N = 10; I = 10; PV = -2,863.75.
Output_{Year 30}: FV = $7,427.83.
DIF: Medium OBJ: TYPE: Problem TOP: FV of an annuity
- You expect to receive $1,000 at the end of each of the next 3 years. You will deposit these payments into an account which pays 10 percent compounded semiannually. What is the future value of these payments, that is, the value at the end of the third year?
a. | $3,000 |
b. | $3,310 |
c. | $3,318 |
d. | $3,401 |
e. | $3,438 |
ANS: C
Tabular solution:
FV | = $1,000(FVIF_{5%,4}) + $1,000(FVIF_{5%,2}) + $1,000 |
= $1,000(1.2155) + $1,000(1.1025) + $1,000 | |
= $1,215.50 + $1,102.50 + $1,000 = $3,318.00. |
Financial calculator solution:
Convert r_{SIMPLE} to EAR using interest rate conversion
Inputs: P/YR = 2; NOM% =10.
Output: EFF% = EAR = 10.25%.
Solve for FV on annual basis using EAR
Inputs: N = 3; I = 10.25; PMT = -1,000.
Output: FV = $3,318.006 » $3,318.00.
DIF: Medium OBJ: TYPE: Problem TOP: FV of an annuity
- You just graduated, and you plan to work for 10 years and then to leave for the Australian “Outback” bush country. You figure you can save $1,000 a year for the first 5 years and $2,000 a year for the next 5 years. These savings cash flows will start one year from now. In addition, your family has just given you a $5,000 graduation gift. If you put the gift now, and your future savings when they start, into an account which pays 8 percent compounded annually, what will your financial “stake” be when you leave for Australia 10 years from now?
a. | $21,432 |
b. | $28,393 |
c. | $16,651 |
d. | $31,148 |
e. | $20,000 |
ANS: D
Cash flow time line:
Tabular solution:
FV | = (FVIFA_{8%, 10}) + $1,000 (FVIFA_{8%, 5}) + $5,000 (FVIF_{8%, 10}) |
= $1,000 (14.487) + $1,000 (5.866) + $5,000 (.1589) | |
= $14,487 + $5,866 + $10,794.50 = $31,147.50 » $31,148 |
Financial calculator solution:
Solution using NFV (Note: Some calculators do not have net future value function. Cash flows can be grouped and carried forward or PV can be used; see alternative solution below.)
Inputs: = 5,000; = 1,000; N_{j} = 5; = 2,000; N_{j} = 5; I = 8
Output: NFV = $31,147.79 » $31,148
Alternative solution: calculate PV of the cash flows, then bring them forward to FV using the interest rate.
Inputs: = 5,000; = 1,000; N_{j} = 5; = 2,000; N_{j} = 5; I = 8
Output: PV = $14,427.45
Inputs: N = 10; I = 8; PV = -14,427.45
Output: FV = $31,147.79 » $31,148
DIF: Medium OBJ: TYPE: Problem TOP: FV of an uneven CF stream
- As the winning contestant in a television game show, you are considering the prizes to be awarded. You must indicate to the sponsor which of the following two choices you prefer, assuming you want to maximize your wealth. Assume it is now January 1, and there is no danger whatever that the sponsor won’t pay off.
(1) | $1,000 now and another $1,000 at the beginning of each of the 11 subsequent months during the remainder of the year, to be deposited in an account paying 12 percent simple annual rate, but compounded monthly (to be left on deposit for the year). |
(2) | $12,750 at the end of the year. |
Which one would you choose?
a. | Choice 1 |
b. | Choice 2 |
c. | Choice 1, if the payments were made at the end of the year. |
d. | The choice would depend on how soon you need the money. |
e. | Either one, since they have the same present value. |
ANS: A
Tabular solution:
PV_{Choice 1 } | = $1,000 (PVIFA _{1%, 11} + 1.0) = $1,000 (11.3676) = $11,367.60 |
PV_{Choice 2 } | = $12,750 (PVIF _{1%, 12}) = $12,750 (0.8874) = $11,314.35 |
Financial calculator solution:
Choice 1
BEGIN mode, Inputs N = 12; I = 1; PMT = 1,000.
Output: PV = -$11,367.63
Choice 2
END mode, Inputs: N = 12; I = 1; FV – 12,750.
Output: PV = -$11,314.98.
DIF: Medium OBJ: TYPE: Problem TOP: PV of an annuity
- You want to buy a Nissan 350Z on your 27th birthday. You have priced these cars and found that they currently sell for $30,000. You believe that the price will increase by 5 percent per year until you are ready to buy. You can presently invest to earn 14 percent. If you just turned 20 years old, how much must you invest at the end of each of the next 7 years to be able to purchase the Nissan in 7 years?
a. | $4,945.57 |
b. | $3,933.93 |
c. | $7,714.72 |
d. | $3,450.82 |
e. | $6,030.43 |
ANS: B
Cash flow time lines:
Tabular solution:
Price of car on 27th birthday
FV = $30,000 (FVIF _{5%, 7}) = $30,000 (1.4071) = $42,213.
Annual investment required
FV of annuity = FVA_{n} = PMT (FVIFA _{i, n})
$42,213 = PMT (FVIFA _{14%, 7})
PMT = $42,213/10.7305 = $3,933.93.
Financial calculator solution:
Price of car on 27th birthday
Inputs: N = 7; I = 5; PV = -30,000.
Output: FV = $42,213.01 » $42,213.
Annual investment required
Inputs: N = 7; I = 14; FV = 42,213.
Output: PMT = -$3,933.93.
DIF: Medium OBJ: TYPE: Problem TOP: Annuity payment
- Assume that your required rate of return is 12 percent and you are given the following stream of cash flows:
Year | Cash Flow |
0 | $10,000 |
1 | 15,000 |
2 | 15,000 |
3 | 15,000 |
4 | 15,000 |
5 | 20,000 |
If payments are made at the end of each period, what is the present value of the cash flow stream?
a. | $66,909 |
b. | $57,323 |
c. | $61,815 |
d. | $52,345 |
e. | $62,029 |
ANS: A
Tabular solution:
PV | = $10,000 + $15,000 (PVIFA_{12%, 4}) + $20,000 (PVIF_{12%, 5}) |
= $10,000 + $15,000 (3.0373) + $20,000 (0.5674) | |
= $10,000 + $45,559.50 + $11,348 = $66,907.50. |
Financial calculator solution:
Using cash flows
Inputs: = 10,000; = 15,000; Nj = 4 times; = 20,000; I = 12.
Output: NPV = $66,908.77 » $66,909.
Note: Tabular solution differs from calculator solution due to interest factor rounding.
DIF: Medium OBJ: TYPE: Problem TOP: PV of an uneven CF stream
- You are given the following cash flows. What is the present value (t = 0) if the discount rate is 12 percent?
a. | $3,277 |
b. | $4,804 |
c. | $5,302 |
d. | $4,289 |
e. | $2,804 |
ANS: A
Cash flow time line:
PV = ?
Tabular solution:
PV = | + | $ 1 (PVIF _{12%, 1}) | = | $ 1 (0.8929) | = | $ 0.89 |
+ | $2,000 (PVIF _{12%, 2}) | = | $2,000 (0.7972) | = | $1,594.40 | |
+ | $2,000 (PVIF _{12%, 3}) | = | $2,000 (0.7118) | = | $1,423.60 | |
+ | $2,000 (PVIF _{12%, 4}) | = | $2,000 (0.6355) | = | -$1,271.00 | |
+ | -$2,000 (PVIF _{12%, 6}) | = | -$2,000 (0.5066) | = | -$1,013.20 | |
PV | = | $3,276.69 |
Financial calculator solution:
Inputs:
Output: NPV = $3,276.615 » $3,277
DIF: Medium OBJ: TYPE: Problem TOP: PV of an uneven CF stream
- You are given the following cash flow information. The appropriate discount rate is 12 percent for Years 1–5 and 10 percent for Years 6–10. Payments are received at the end of the year.
Year | Amount |
1–5 | $20,000 |
6–10 | $25,000 |
What should you be willing to pay right now to receive the income stream above?
a. | $166,866 |
b. | $158,791 |
c. | $225,000 |
d. | $125,870 |
e. | $198,433 |
ANS: D
Tabular solution:
Years 1-5
PV of annuity Years 1-5 = $$20,000 (PVIFA_{12%, 5}) = $20,000 (3.6048) = $72,096.
Years 6-10 Value of annuity Years 6-10 on Day 1 of Year 6
PV_{5} = $25,000 (PVIFA_{10%, 5}) = $25,000 (3.7908) = $94,770
PV of annuity Years 6-10 at time = 0
PV_{0} = $94,770 (PVIF _{12%, 5}) = $94,770 (0.5674) = $53,772.50
PV_{0} of both annuities
$72,096 + $53, 772.50 = $125.868.50 » $125.870
Financial calculator solution:
Solve for PV at time = 0 of $20,000 annuity
Inputs:
Solve for PV at time = 5 pf $25,000 annuity using its value at t = 5
Inputs:
Solve for PV at time = 0 0f $25,000 annuity
Inputs: N = 5; I = 12; FV = -94,769.669. Output: PV = $53,774.855
Add the two PVs together
PVBoth annuities = $72,095.524 + $53,774.855 = $125,870.38 » $125.870
Note: Tabular solution differs from calculator solution due to interest factor rounding.
DIF: Medium OBJ: TYPE: Problem TOP: PV of an uneven CF stream
- A project with a 3-year life has the following probability distributions for possible end of year cash flows in each of the next three years:
Year 1 | Year 2 | Year 3 | |||
Prob | Cash Flow | Prob | Cash Flow | Prob | Cash Flow |
0.30 | $300 | 0.15 | $100 | 0.25 | $200 |
0.40 | 500 | 0.35 | 200 | 0.75 | 800 |
0.30 | 700 | 0.35 | 600 | ||
0.15 | 900 |
Using an interest rate of 8 percent, find the expected present value of these uncertain cash flows. (Hint: Find the expected cash flow in each year, then evaluate those cash flows.)
a. | $1,204.95 |
b. | $835.42 |
c. | $1,519.21 |
d. | $1,580.00 |
e. | $1,347.61 |
ANS: E
Calculate expected cash flows
E(CF_{1}) | = (0.30) ($300) + (0.40) ($500) + (0.30) ($700) = $500 |
E(CF_{2}) | = (0.15) ($100) + (0.35) ($200) + (0.35) ($600) + (0.15) ($900) = $430 |
E(CF_{3}) | = (0.25) ($200) + (0.75) ($800) = $650 |
Tabular solution:
PV | = $500 (PVIF _{8%, 1}) + $430 (PVIF _{8%, 2}) + $650 (PVIF _{8%, 3}) |
= $500 (0.9259) + $430 (0.8573) + $650 (0.7938) | |
= $462.95 + $368.64 + $515.97 = $1,347.56 |
Financial Calculator Solution:
Using cash flows,
Inputs:
Output: NPV = $1,347.61
DIF: Medium OBJ: TYPE: Problem TOP: PV of uncertain cash flows
- If you buy a factory for $250,000 and the terms are 20 percent down, the balance to be paid off over 30 years at a 12 percent rate of interest on the unpaid balance, what are the 30 equal annual payments?
a. | $20,593 |
b. | $31,036 |
c. | $24,829 |
d. | $50,212 |
e. | $6,667 |
ANS: C
Tabular solution:
Initial balance | = 0.8($250,000) = $200,000 |
$200,000 | = PMT (PVIA_{12%, 30}) |
$200,000 | = PMT (8.0552) |
PMT | = $200,00/8.0552 = $24,828.68 » $24,829 |
Financial calculator solution:
Inputs: N = 30; I = 12; PV = -200,000; FV = 0
Output: PMT = $24,828.73 » $24,829
DIF: Medium OBJ: TYPE: Problem TOP: Amortization
- In its first year of operations, 1999, the Gourmet Cheese Shoppe had earnings per share (EPS) of $0.26. Four years later, in 2003, EPS was up to $0.38, and 7 years after that, in 2010, EPS was up to $0.535. It appears that the first 4 years represented a supernormal growth situation and since then a more normal growth rate has been sustained. What are the rates of growth for the earlier period and for the later period?
a. | 6%; 5% |
b. | 6%; 3% |
c. | 10%; 8% |
d. | 10%; 5% |
e. | 12%; 7% |
ANS: D
Tabular solution:
PV = $0.26 = $0.38 (PVIF_{i, 4})
PVIF _{i, 4 }= $0.26/$0.38 = 0.6842
i_{1 }» 10%
PV = $0.38 = $0.535 (PVIF _{i, 7})
PFIV _{i,7 }= $0.38/$0.535 = 0.7103
i_{2 }» 5%
Financial calculator solution:
Inputs: N = 4; PV = -0.26; FV = 0.38. Output: I = 9.95% » 10%
Inputs: N = 7; PV = -0.38; FV = 0.535. Output: I = 5.01% » 5%
DIF: Medium OBJ: TYPE: Problem TOP: Growth rate
- Steaks Galore needs to arrange financing for its expansion program. One bank offers to lend the required $1,000,000 on a loan which requires interest to be paid at the end of each quarter. The quoted rate is 10 percent, and the principal must be repaid at the end of the year. A second lender offers 9 percent, daily compounding (365-day year), with interest and principal due at the end of the year. What is the difference in the effective annual rates (EFF%) charged by the two banks?
a. | 0.31% |
b. | 0.53% |
c. | 0.75% |
d. | 0.96% |
e. | 1.25% |
ANS: D
EAR_{Quarterly} =
EAR_{Daily} =
Difference = 10.38% – 9.42% = 0.96%
Alternatively, with a financial calculator, for the quarterly loan enter P/YR = 4, NOM% = 10, and press EFF% to get EAR = 10.38%.
For the daily loan, enter P/YR = 365, NOM = 9%, and press EFF% to get EAR = 9.42%.
DIF: Medium OBJ: TYPE: Problem TOP: Effective annual rate
- You are currently at time period 0, and you will receive the first payment on an annual payment annuity of $100 in perpetuity at the end of this year. Six full years from now you will receive the first payment on an additional $150 in perpetuity, and at the end of time period 10 you will receive the first payment on an additional $200 in perpetuity. If you require a 10 percent rate of return, what is the combined present value of these three perpetuities?
a. | $2,349.50 |
b. | $2,526.85 |
c. | $2,685.42 |
d. | $2,779.58 |
e. | $2,975.40 |
ANS: D
Tabular solution:
PV | = ($100/0.10) + ($150/0.10)(PVIF _{10%, 5}) + ($200/0.10)(PVIF _{10%, 9}) |
= $1,000 + $1,500 (0.6209) + $2,000 (0.4241) | |
= $1,000 + $931.35 + $848.20 = $2,779.55 |
Financial calculator solution:
Calculate the undiscounted values of each of three perpetuities at the point in time where they begin, using numerical methods, then calculate PV at t = 0 of the combined perpetuity values.
PV_{p1} at Time = 0: $100/0.10 = $1,000
PV_{p2} at Time = 5; $150/0.10 = $1,500
PV_{p3} at Time = 9; $200/0.10 = $2,000
Inputs:
Output: NPV = $2,446.577 » $2,779.58.
Note: Tabular solution differs from calculator solution due to interest factor rounding.
DIF: Tough OBJ: TYPE: Problem TOP: PV of a perpetuity
- Find the present value of an income stream which has a negative flow of $100 per year for 3 years, a positive flow of $200 in the 4th year, and a positive flow of $300 per year in Years 5 through 8. The appropriate discount rate is 4 percent for each of the first 3 years and 5 percent for each of the later years. Thus, a cash flow accruing in Year 8 should be discounted at 5 percent for some years and 4 percent in other years. All payments occur at year-end.
a. | $528.21 |
b. | $1,329.00 |
c. | $792.49 |
d. | $1,046.41 |
e. | $875.18 |
ANS: C
Tabular solution:
PV | = -$100 (PVIFA _{4%, 3}) + $200 (PVIF _{5%, 1}) (PVIF _{4%, 3}) +
$300 (PVIFA _{5%, 4}) (PVIF _{5%, 1}) (PFIV _{4%, 3}) |
= -$100 (2.7751) + 200 (0.9524) (0.8890) + $300 (3.35460) (0.9524) (0.8890) | |
= -$277.51 + $169.34 + $900.70 = $792.53. |
Financial calculator solution:
Inputs:
Output: NPV = -277.51
Calculate the PV of CFs 4–8 as of time = 3 at I = 5%
Inputs:
Output:
Calculate PV of the FV of the positive CFs at Time = 3
Inputs: N = 3; I = 4; FV = -1,203.60. Output: PV = $1,070.
Total PV = $1,070 – $277.51 = $792.49
Note: Tabular solution differs from calculator solution due to interest factor rounding.
DIF: Tough OBJ: TYPE: Problem TOP: PV of an uneven CF stream
- Assume that you are graduating, that you plan to work for 4 years, and then to go to law school for 3 years. Right now, going to law school would require $17,000 per year (for tuition, books, living expenses, etc.), but you expect this cost to rise by 8 percent per year in all future years. You now have $25,000 invested in an investment account which pays a simple annual rate of 9 percent, quarterly compounding, and you expect that rate of return to continue into the future. You want to maintain the same standard of living while in law school that $17,000 per year would currently provide. You plan to save and to make 4 equal payments (deposits) which will be added to your account at the end of each of the next 4 years; these new deposits will earn the same rate as your investment account currently earns. How large must each of the 4 payments be in order to permit you to make 3 withdrawals, at the beginning of each of your 3 years in law school? (Note: (1) The first payment is made a year from today and the last payment 4 years from today, (2) the first withdrawal is made 4 years from today, and (3) the withdrawals will not be of a constant amount.)
a. | $13,242.67 |
b. | $6,562.13 |
c. | $10,440.00 |
d. | $7,153.56 |
e. | $14,922.85 |
ANS: D
PVCosts = $17,000, I = 8%
PVAcct = $25,000, I = 9.31%
Financial calculator solution:
Step 1: | Use the current law school costs and inflation rate to calculate the withdrawals to cover law school costs at T = 4, 5, 6: |
At T = 4, Inputs: N = 4, PV = -17,000; I = 8. Output: FV4 = $23,128.31 | |
At T = 5, Inputs: N = 5; PV = -17,000; I = 8. Output: FV 5 = $24,978.58 | |
At T = 6, Inputs: N = 6; PV = -14,000; I = 8. Output: FV6 = $26,976.86 | |
Step 2: | Use interest rate conversion feature to calculate the effective annual rate of the 9% account, compounded quarterly. |
Inputs: NOM% = 9; P/YR = 4. Output: EFF% = 9.31% | |
Step 3: | Use the EAR from Step 2 to determine the PV of law school payments at T = 4, 5, 6 as of T = 4. |
Inputs: | |
Output: NPV = $68,556.73 which equals PV_{T=4, costs} | |
Step 4: | Determine the VF at T = 4 of the $25,000 in the account as of T = 0: |
Inputs: N = 4; I = 9.31; PV = -25,000. | |
Output: FV = $35,692.72 | |
Step 5: | Calculate shortfall between what the account needs to have and will actually have at T = 4: |
$68,556.73 – $35,692.72 = $32,864.01 | |
Step 6: | Calculate the annuity payments, which will earn 9.31% EAR and accumulate to an FV of $32,864.01 at T = 4: |
Inputs: N = 4; I = 9.31%; FV = 32,864.01. | |
Output: PMT = $7,153.56 |
DIF: Tough OBJ: TYPE: Problem TOP: Annuity payments
Financial Calculator Section
The following question(s) may require the use of a financial calculator.
- You want to borrow $1,000 from a friend for one year, and you propose to pay her $1,120 at the end of the year. She agrees to lend you the $1,000, but she wants you to pay her $10 of interest at the end of each of the first 11 months plus $1,010 at the end of the 12th month. How much higher is the effective annual rate under your friend’s proposal than under your proposal?
a. | 0.00% |
b. | 0.45% |
c. | 0.68% |
d. | 0.89% |
e. | 1.00% |
ANS: C
Your proposal:
EAR_{1} = $120/$1,000
EAR_{1} = 12%
Your friend’s proposal:
Interest is being paid each month ($10/$1,000 = 1% per month), so it compounds, and the EAR is higher than r_{simple} = 12%:
EAR_{2} =
Difference = 12.68% -12.00% = 0.68%
You could also visualize your friend’s proposal in a cash flow time line format:
Insert those cash flows in the cash flow register of a calculator and solve for IRR. The answer is 1%, but this is a monthly rate. The simple rate is 12 (1%) = 12%, which converts to an ER of 12.68% as follows:
Input into a financial calculator the following:
P/YR = 12, NOM% = 12, and solve for EFF% = 12.68%
DIF: Easy OBJ: TYPE: Financial Calculator TOP: Effective annual rate
- Suppose you put $100 into a savings account today, the account pays a simple annual interest rate of 6 percent, but compounded semiannually, and you withdraw $100 after 6 months. What would your ending balance be 20 years after the initial $100 deposit was made?
a. | $226.20 |
b. | $115.35 |
c. | $62.91 |
d. | $9.50 |
e. | $3.00 |
ANS: D
Tabular/Numerical solution:
Solve for amount on deposit at the end of 6 months.
Step 1: | FV = $100 (FVIF _{3%, 1}) – $100 = $3.00 |
FV = $100 (1 + 0.06/2) – $100 = $3.00 | |
Step 2: | Compound the $3.00 for 39 periods at 3% |
FV = $3.00 (FVIF _{3%, 39}) = $9.50 |
Since table does not show 39 periods, use numerical/calculator exponent method.
FV = $3.00 (1 + 0.06/2)^{39} = $9.50
Financial calculator solution: (Step 2 only)
Inputs: N = 39; I = 3; PV = -3.00.
Output: FV = $9.50
DIF: Medium OBJ: TYPE: Financial Calculator TOP: FV of a sum
- A bank pays a quoted annual (simple) interest rate of 8 percent. However, it pays interest (compounds) daily using a 365-day year. What is the effective annual rate of return?
a. | 7.86% |
b. | 7.54% |
c. | 8.57% |
d. | 8.33% |
e. | 9.21% |
ANS: D
Numerical solution:
EAR =
Effective rate 8.33%
Financial calculator solution:
Use interest rate conversion feature
Inputs: P/YR = 365; NOM% = 8.
Output: EFF% = EAR = 8.328% » 8.33%
DIF: Medium OBJ: TYPE: Financial Calculator TOP: Effective annual rate
- You can deposit your savings at the Darlington National Bank, which offers to pay 12.6 percent interest compounded monthly, or at the Bartlett Bank, which will pay interest of 11.5 percent compounded daily. (Assume 365 days in a year.) Which bank offers the higher effective annual rate?
a. | Darlington National Bank. |
b. | Bartlett Bank. |
c. | Both banks offer the same effective rate. |
d. | Cannot be determined from the information provided. |
e. | Workable only if the banks use the same compounding period. |
ANS: A
Numerical solution:
Darlington
EAR =
Bartlett
EAR =
Financial calculator solution:
Use interest rate conversion feature
Inputs: P/YR = 12; NOM% = 12.6. Output: EFF% = EAR = EAR_{Darlington} = 13.354%
Inputs: P/YR = 365; NOM% = 11.5. Output: EFF% = EAR_{Bartlett} = 12.185%.
EAR_{Darlington} > EAR_{Bartlett}
DIF: Medium OBJ: TYPE: Financial Calculator TOP: Effective annual rate
- You have just taken out a 30-year, $120,000 mortgage on your new home. This mortgage is to be repaid in 360 equal end-of-month installments. If each of the monthly installments is $1,500, what is the effective annual interest rate on this mortgage?
a. | 15.87% |
b. | 14.75% |
c. | 13.38% |
d. | 16.25% |
e. | 16.49% |
ANS: A
Financial calculator solution:
Calculate periodic rate
Inputs: N = 3600; PV = -120,000; PMT = 1,500; FV = 0
Output: I = 1.235% per period.
Use interest conversion feature
Inputs: NOM% = 1.235% ´ 12 = 14.82; P/YR = 12
Output: EFF% = 15.868% » 15.87%
DIF: Medium OBJ: TYPE: Financial Calculator TOP: Effective annual rate
- You have just borrowed $20,000 to buy a new car. The loan agreement calls for 60 monthly payments of $444.89 each to begin one month from today. If the interest is compounded monthly, then what is the effective annual rate on this loan?
a. | 12.68% |
b. | 14.12% |
c. | 12.00% |
d. | 13.25% |
e. | 15.08% |
ANS: A
Tabular solution:
$20,000 = $444.89 (PVIFA _{r, 60})
PVIFA r, 60 = 44.9549
r = 1%
EAR
Financial calculator solution:
Calculate periodic rate and simple rate
Inputs: N = 60; PV = -20,000; PMT = 444.89
Output: I = 1.0. NOM% = 1.0% ´ 12 = 12.00%
Use interest rate conversion feature
Inputs: P/YR = 12; NOM% = 12.0.
Output: EFF% = EAR = 12.68%
DIF: Medium OBJ: TYPE: Financial Calculator TOP: Effective annual rate
- Bank A offers a 2-year certificate of deposit (CD) that pays 10 percent compounded annually. Bank B offers a 2-year CD that is compounded semi-annually. The CDs have identical risk. What is the stated, or simple, rate that Bank B would have to offer to make you indifferent between the two investments?
a. | 9.67% |
b. | 9.76% |
c. | 9.83% |
d. | 9.87% |
e. | 9.93% |
ANS: B
Numerical solution:
1.10 | = (1 + r/2)^{2} |
1.0488 | = 1 + r/2 |
r/2 | = 0.0488 |
r | = 0.0976 = 9.76% |
Financial calculator solution:
Use interest rate conversion feature
Inputs: P/YR = 2; EFF% = 10.0%.
Output: NOM% = 9.462% » 9.76%
DIF: Medium OBJ: TYPE: Financial Calculator TOP: Effective interest rates
- Assume that you inherited some money. A friend of yours is working as an unpaid intern at a local brokerage firm, and her boss is selling some securities which call for four payments, $50 at the end of each of the next 3 years, plus a payment of $1,050 at the end of Year 4. Your friend says she can get you some of these securities at a cost of $900 each. Your money is now invested in a bank that pays an 8 percent simple (quoted) interest rate, but with quarterly compounding. You regard the securities as being just as safe, and as liquid, as your bank deposit, so your required effective annual rate of return on the securities is the same as that on your bank deposit. You must calculate the value of the securities to decide whether they are a good investment. What is their present value to you?
a. | $1,000 |
b. | $866 |
c. | $1,050 |
d. | $901 |
e. | $893 |
ANS: E
Financial calculator solution:
Calculate the EAR on the bank deposit
Inputs: P/YR = 4, NOM% = 8; Output: EFF% = EAR = 8.24%
Calculate the PV of the investment
Inputs: N = 4; I = 8.24; PMT = 50; FV = 1,000
Output: PV = -$893.26 » $893
Alternate method: Using cash flows
Inputs:
Output: NPV = $893.26 » $893
DIF: Medium OBJ: TYPE: Financial Calculator TOP: PV and effective annual rate
- Your company is planning to borrow $1,000,000 on a 5-year, 15 percent, annual payment, fully amortized term loan. What fraction of the payment made at the end of the second year will represent repayment of principal?
a. | 29.83% |
b. | 57.18% |
c. | 35.02% |
d. | 64.45% |
e. | 72.36% |
ANS: B
Tabular solution:
$1,000,000 = PMT(PVIFA_{15%,5})
PMT = $1,000,000/3.3522 = $298,311.56.
Construct amortization table
Year | Beg Balance | Payment | Interest | Principal | End Balance |
1 | $1,000,000 | $298,312 | $150,000 | $148,312 | $851,688 |
2 | 851,688 | 298,312 | 127,753 | 170,559 | 681,129 |
Principal fraction of PMT = $170,559/$298,312 = 0.57175 ÷ 57.18%.
Financial calculator solution:
Calculate the principal portion of PMT using amortization function: (Note: The steps below are specific to the Hewlett-Packard 17B II but the basic steps generalize to a variety of calculators.)
Inputs: N = 5; I = 15; PV = -1,000,000. Output: PMT = $298,315.55.
Inputs: AMORT, #P = 1, NEXT or AMORT.
Output: = or PRIN = 170,562.89.
Principal fraction = $170,562.89/$298,315.55 = 0.57175 » 57.18%.
Note: Difference in amortization payment and principal calculation due to rounding. Answer is unaffected.
DIF: Medium OBJ: TYPE: Financial Calculator TOP: Amortization
- The Desai Company just borrowed $1,000,000 for 3 years at a quoted rate of 8 percent, quarterly compounding. The loan is to be amortized in end-of-quarter payments over its 3-year life. How much interest (in dollars) will your company have to pay during the second quarter?
a. | $15,675.19 |
b. | $18,508.81 |
c. | $21,205.33 |
d. | $24,678.89 |
e. | $28,111.66 |
ANS: B
DIF: Medium OBJ: TYPE: Financial Calculator TOP: Amortization
- You have a 30-year mortgage with a simple annual interest rate of 8.5 percent. The monthly payment is $1,000. What percentage of your total payments over the first three years goes toward the repayment of principal?
a. | 1.50% |
b. | 3.42% |
c. | 5.23% |
d. | 6.75% |
e. | 8.94% |
ANS: E
Enter the information into the calculator to use its amortization feature:
N | = 360 |
I/YR | = 8.5/12 = 0.7063 |
PMT | = 1,000 |
FV | = 0 |
Solve for PV = -$130,053.64 = Original value of mortgage.
Enter: 1 INPUT 36 AMORT
Int 1 – 36 = $32,782.14
Prin 1 – 36 = $3,217.86
Total payments 1 – 36 = $36,000.
Percentage of total payments which is principal =
DIF: Medium OBJ: TYPE: Financial Calculator TOP: Amortization
- Your company must make payments of $100,000 each year for 10 years, with the first payment to be made 10 years from today. To prepare for these payments, your company must make 10 equal annual deposits into an account which pays a simple interest rate of 7 percent, daily compounding (360-day year). Funds will remain in the account during both the accumulation period (the first 10 years) and the distribution period (the last 10 years), and the same interest rate will be earned throughout the entire 20 years. The first deposit will be made immediately. How large must each deposit be?
a. | $47,821.11 |
b. | $49,661.86 |
c. | $51,234.67 |
d. | $52,497.33 |
e. | $53,262.39 |
ANS: B
The FV of the DEP annuity at T = 10 must be sufficient to make the 10 payments of $100,000 each.
Step 1: | Find the PV of the $100,00 payments at the end of Year 10. This is a 10-year annuity due. What rate do we use? 7% is not correct, and if we use the periodic that won’t work either in an annuity setup. We want a rate that’s consistent with an annual annuity. That means we must use the EAR. |
Use the interest conversion feature on your financial calculator to find EAR = 7.2501% | |
P/YR = 360 | |
NOM% = 7 | |
Solve for EFF% = 7.2501% | |
Now find the PV of the annuity: | |
Step 2: | Determine the amount of the annuity due by using the present value of the $100,000 payments at Year 10 as the future value of the annuity due. |
Deposits of $49.661.86 will provide the needed funds. |
DIF: Medium OBJ: TYPE: Financial Calculator
TOP: Annuities and daily compounding
- Your lease calls for payments of $500 at the end of each month for the next 12 months. Now your landlord offers you a new 1-year lease which calls for zero rent for 3 months, then rental payments of $700 at the end of each month for the next 9 months. You keep your money in a bank time deposit that pays a simple annual rate of 5 percent. By what amount would your net worth change if you accept the new lease? (Hint: Your return per month is 5%/12 = 0.4166667%.)
a. | -$509.81 |
b. | -$253.62 |
c. | +$125.30 |
d. | +$253.62 |
e. | +$509.81 |
ANS: B
Solve for NPV = -$6,094.23
Therefore, the PV of payments under the proposed lease would be greater than the PV of payments under the old lease by $6,094.23 – $5,840.61 = $253.62. Thus, your net worth would decrease by $253.62.
DIF: Medium OBJ: TYPE: Financial Calculator
TOP: NPV and non-annual discounting
- You plan to invest $2,500 in a money market account which will pay an annual stated (simple) interest rate of 8.75 percent, but which compounds interest on a weekly basis. If you leave this money on deposit for one year (52 weeks), what will be your ending balance when you close the account?
a. | $2,583.28 |
b. | $2,611.72 |
c. | $2,681.00 |
d. | $2,703.46 |
e. | $2,728.50 |
ANS: E
Numerical solution:
FV =
Financial calculator solution:
Convert simple rate to EAR
Inputs: P/YR = 52; NOM% = 8.75.
Output: EFF% = EAR + 9.1362% » 9.14%
Calculate FV
Inputs: N = 1; I = 9.14; PV = -2,500.
Output: FV = $2,728.50
DIF: Medium OBJ: TYPE: Financial Calculator TOP: Non-annual compounding
- You have just purchased a life insurance policy that requires you to make 40 semiannual payments of $350 each, where the first payment is due in 6 months. The insurance company has guaranteed that these payments will be invested to earn you an effective annual rate of 8.16 percent, although interest is to be compounded semiannually. At the end of 20 years (40 payments), the policy will mature. The insurance company will pay out the proceeds of this policy to you in 10 equal annual payments, with the first payment to be made one year after the policy matures. If the effective interest rate remains at 8.16 percent, how much will you receive during each of the 10 years?
a. | $6,113.20 |
b. | $5,244.62 |
c. | $5,792.21 |
d. | $4,992.39 |
e. | $4,723.81 |
ANS: D
Tabular solution: (Part a)
Value of the policy at the end of 20 years
FV = $350 (FVIFA _{4%, 40}) = $350 (95.026) = $33,259.10
This amount is then to be paid out over a 10-year period.
Note: There is no tabular solution presented for part b due to fractional interest rate (EAR = 8.16%)
Financial calculator solution: (Part a)
Inputs: N = 40; I = 4; PMT = -350. Output: FV = $33,258.93
Financial calculator solution (Part b)
Inputs: N = 10; I = 8.16; PV = 33,258.93.
Output: PMT = $4,992.39.
DIF: Tough OBJ: TYPE: Financial Calculator TOP: Annuity payments
- Assume that you just had a child, and you are now planning for her college education. You would like to make 43 equal payments over the next 21 years (the first payment to be made immediately, all other payments to be made at 6-month intervals, with the final payment to be made at her 21st birthday) so that you will be able to cover her expected expenses while in school. You expect to pay expenses on her 18th, 19th, 20th, and 21st birthdays. Assume that the current (time period 0) annual cost of college is $6,000, that you expect annual inflation to be 8 percent for the next 5 years, and then 5 percent thereafter. If you expect to be able to earn a return of 4 percent every 6 months on your investments (a simple rate of 8 percent with semiannual compounding), what will be the amount of each of the 43 payments?
a. | $705.86 |
b. | $731.93 |
c. | $692.15 |
d. | $650.46 |
e. | $785.72 |
ANS: B
Financial calculator solution:
Calculate college cost at 8% growth for 5 years
Inputs: N = 5; I = 8; PV = -6,000.
Output: FV_{5} = $8.815.97
Calculate FV of tuition cost in Years 18 through 21 at 5% growth
Inputs: | N = 13; I = 5; PV = -8,815.97. | Output: | FV_{18} = $16,623.83 |
N = 14 | FV_{19} = $17,455.02 | ||
N = 15 | FV_{20} = $18.327.77 | ||
N = 16 | FV_{21} = $19,244.16 |
Use cash flows to discount FVs to PV
Inputs:
Output: NPV = $15,506.49
Calculate payment based on PV of costs
BEGIN mode Inputs: N = 43; I = 4; PV = -15,506.49.
Output: PMT = $731.93
Alternate solution for payment using END mode and FV of costs:
Use cash flows to compound costs to NPV:
Inputs: | |
Output: NFV = $80,521.83
END mode:
Inputs: N = 43; I = 4; PV = 0; FV = 80,521.83
Output: MPT = -$731.93
DIF: Tough OBJ: TYPE: Financial Calculator TOP: Annuity payments
- Your father, who is 60, plans to retire in 2 years, and he expects to live independently for 3 years. He wants a retirement income which has, in the first year, the same purchasing power as $40,000 has today. However, his retirement income will be of a fixed amount, so his real income will decline over time. His retirement income will start the day he retires, 2 years from today, and he will receive a total of 3 retirement payments. Inflation is expected to be constant at 5 percent. Your father has $100,000 in savings now, and he can earn 8 percent on savings now and in the future. How much must he save each year, starting today, to meet his retirement goals?
a. | $1,863 |
b. | $2,034 |
c. | $2,716 |
d. | $5,350 |
e. | $6,102 |
ANS: C
Step 1: | The retirement payments, which begin at t = 2, must be: | |
$40,000 (1 + Infl)^{2} = $40,000 (1.05)^{2} = $44,100 | ||
Step 2: | There will be 3 retirement payments of $44,100, made at t = 2, t = 3, and t = 4. We find the PV of an annuity due at t = 2 as follows: | |
Set calculator to “Begin”. Then enter: | ||
N = 3; I = 8, PMT = 44,100; FV = 0. Solve for PV = $122,742. | ||
If he has this amount at t = 2, he can receive the 3 retirement payments. | ||
Step 3: | The $100,000 now on hand will compound at 8% for 2 years: | |
$100,000 (1.08)^{2} = $116,640 | ||
Step 4: | So, he must save enough each year to accumulate an additional $122,742 – $116,640 – $6,102: | |
Need at t = 2 | $122,742 | |
Will have | (116,640) | |
Net additional needed | $ 6,102 | |
Step 5: | He must make 2 payments, at t = 0 and at t = 1, such that they will grow to a total of $6,102 at t = 2 | |
This is the FV of an annuity due found as follows: | ||
Set calculator to “Begin”. Then enter: | ||
N = 2; I = 8; PV = 0; FV = 6,102. Solve for PMT = $2,716 |
DIF: Tough OBJ: TYPE: Financial Calculator TOP: Annuity payments
- Your father, who is 60, plans to retire in 2 years, and he expects to live independently for 3 years. Suppose your father wants to have a real income of $40,000 in today’s dollars in each year after he retires. His retirement income will start the day he retires, 2 years from today, and he will receive a total of 3 retirement payments. Inflation is expected to be constant at 5 percent. Your father has $100,000 in savings now, and he can earn 8 percent on savings now and in the future. How much must he save each year, starting today, to meet his retirement goals?
a. | $1,863 |
b. | $2,034 |
c. | $2,716 |
d. | $5,350 |
e. | $6,102 |
ANS: D
Step 1: | The retirement payments, which begin at t = 2, must be: | |
t = 2: $40,000 (1.05)^{2} = $44,100 | ||
t = 3: $44,100 (1.05) = $46,305 | ||
t = 4: $46, 305 (1.05) = $48.620 | ||
Step 2: | Now we need enough at t = 2 to make the 3 retirement payments as calculated in Step 1. We cannot use the annuity method, but we can enter, in the cash flow register, the following: | |
Then enter I = 8, and press NPV to find NPV = PV = $128,659 | ||
Step 3: | The $100,000 now on hand will compound at 8% for 2 years: | |
$100,000 (1.08)^{2} = $116,640. | ||
Step 4: | The net funds needed are: | |
Need at t = 2 | $128,659 | |
Will have | (116,640) | |
Net needed | $ 12,019 | |
Step 5: | Find the payments needed to accumulate $12,019. Set the calculator to “Begin” and then enter: | |
N = 2; I = 8; PV = 0; FV = 12,019. Solve for PMT = $5,350. |
DIF: Tough OBJ: TYPE: Financial Calculator TOP: Annuity payments
- Your client just turned 75 years old and plans on retiring in 10 years on her 85th birthday. She is saving money today for her retirement and is establishing a retirement account with your office. She would like to withdraw money from her retirement account on her birthday each year until she dies. She would ideally like to withdraw $50,000 on her 85th birthday, and increase her withdrawals 10 percent a year through her 89th birthday (i.e., she would like to withdraw $73,205 on her 89th birthday). She plans to die on her 90th birthday, at which time she would like to leave $200,000 to her descendants. Your client currently has $100,000. You estimate that the money in the retirement account will earn 8 percent a year over the next 15 years. Your client plans to contribute an equal amount of money each year until her retirement. Her first contribution will come in one year; her tenth and final contribution will come in ten years (on her 85th birthday). How much should she contribute each year in order to meet her objectives?
a. | $12,401.59 |
b. | $12,998.63 |
c. | $13,243.18 |
d. | $13,759.44 |
e. | $14,021.53 |
ANS: A
Value of cash outflows:
Age 85 | = ($ 50,000)
= ( 55,000) = (-50,000) (1.1) = ( 60,000) = (-50,000) (1.1)^{2} = ( 66,550) = (-50,000) (1.1)^{3} = ( 73,205) = (-50,000) (1.1)^{4} = ( 200,000) |
Solve for NPV at 8% = ($395, 548.96).
Value for $100,000 at age 85;
$100,000 (1.08)_{10} = $215,892.50
Shortfall at age 85 = $215,892.50 – $395,548.96 = ($179,656.46).
Calculate annual payments to equal this shortfall:
N = 10; I/YR = 8; PV = 0; FV = 179,656.46.
Solve for PMT = $12,401.59
DIF: Tough OBJ: TYPE: Financial Calculator TOP: Annuity payments
- You are considering an investment in a 40-year security. The security will pay $25 a year at the end of each of the first three years. The security will then pay $30 a year at the end of each of the next 20 years. The simple interest rate is assumed to be 8 percent, and the current price (present value) of the security is $360.39. Given this information, what is the equal annual payment to be received from Year 24 through Year 40 (i.e., for 17 years)?
a. | $35 |
b. | $38 |
c. | $40 |
d. | $45 |
e. | $50 |
ANS: C
Calculate the NPV of payments in Years 1-23:
= 0
= 25
= 30
I = 8
Solve for NPV = $298.25
Difference between the security’s price and PV of payments:
$360.36 – $298.25 = $62.14
Calculate the FV of the difference between the purchase price and PV of payments, Year 1 – 23:
N = 23
I = 8
PV = -62.14
PMT = 0
Solve for FV = $364.85.
Calculate the value of the annuity payments in Years 24-40:
N = 17
I = 8
PV = -364.85
FV = 0
Solve for PMT = $40
DIF: Tough OBJ: TYPE: Financial Calculator TOP: Annuity payments
- You are currently saving for your child’s college education. The current cost of college is $10,000 a year. You expect that college costs will continue to increase at a rate of 5 percent a year. Your child is scheduled to begin attending a four-year college 10 years from now (i.e., college payments will be made at t=10, t=11, t=12, and t=13). You currently have $25,000 in an account which earns 6 percent after taxes. You would like to have all of the necessary savings by the time your child enters college, and you would like to contribute a constant amount at the beginning of each of the next 10 years in order to provide the necessary amount. (You want to make 10 equal contributions starting in Year 0 and ending at Year 9.) How much should you contribute to the account each year in order to fully provide for your child’s education?
a. | $1,133.16 |
b. | $1,393.42 |
c. | $1,477.02 |
d. | $1,507.81 |
e. | $1,622.33 |
ANS: B
Step 1: | Calculate college costs at t = 10, 11, 12, 13: | ||
t = 10; (10,000) (1.05)^{10} = $16,288.95 | |||
t = 11: (10,000) (1.05)^{11} = $17,103.39 | |||
t = 12: (10,000) (1.05)^{12} = $17,958.56 | |||
t = 13: (10,000) (1.05)^{13} = $18,856.49 | |||
Step 2: | Find the NPV of the cash flows: | ||
= | 25,000 | ||
= | 0 | ||
= | 16,288.95 | ||
= | -17,103.39 | ||
= | -17,958.56 | ||
= | -18,856.49 | ||
I | = | 6 | |
Solve for NPV = -$10,871.03 | |||
Step 3: | Find the payment stream which equates to the NPV. | ||
BEGIN | |||
N = 10 | |||
I = 6 | |||
PV = -10,871.03 | |||
FV = 0 | |||
Solve for PMT = $1,393.42 |
DIF: Tough OBJ: TYPE: Financial Calculator TOP: Annuity payments
- You will receive a $100 annual perpetuity, the first payment to be received now, at Year 0, a $300 annual perpetuity payable starting at the end of Year 5, and a $200 semiannual (2 payments per year) perpetuity payable starting midway through Year 10. If you require an effective annual interest rate of 14.49 percent, what is the present value of all three perpetuities together at Year 0? (Hint: The semiannual annuity can be thought of as two annual annuities.)
a. | $2,091.86 |
b. | $2,785.14 |
c. | $4,213.51 |
d. | Infinite; the present value of any perpetuity is infinite. |
e. | Cannot determine the value since some payments are annually and some semiannually. |
ANS: B
Numerical solution:
PV | = $100 + ($100/0.1449)+ ($300/0.1449) [1/(1.1449)^{4}] + ($200/0.1449) [1/(1.449)^{9}]
+ ($200/0.1449) [1/(1.1449)^{9.5}] |
= $100 + $690.13 + $1,204.99 + $408.37 + $318.65 = $2785.14 |
Financial calculator solution:
Step 1: | Calculate the values of the respective perpetuities as their starting points; t = semiannual periods. | ||||||
PV_{p1} = 100 + 100/0.1449 = 790.13 | n = 0 | ||||||
FV_{p2}, t = 8 = 300/0.1449 = 2,070.3 | n = 8 semiannual periods | ||||||
1/2FV_{p3, t = 18} = 200/0.1449 = 1,380.26 | n = 18 semiannual periods | ||||||
1/2FV_{p3, t = 19} = 200/0.1449 = 1,380.26 | n = 19 semiannual periods | ||||||
Step 2: | Use interest at conversion to convert EAR to NOM% | ||||||
Inputs: P/YR = 2; EFF% = EAR = 14.49. Output: NOM% = 14.0% | |||||||
Periodic rate = 14/2 = 7.0% | |||||||
Inputs: | N = 8; I = 7; FV = -2,070.39 | Output | PV | = | $1,204.99 | ||
N = 18; I = 7; FV = -1,380.26 | PV | = | 408.37 | ||||
N = 19; I = 7; FV = -1,380.26 | PV | = | 381.65 | ||||
Plus PV of perpetuity one | PV | = | 790.13 | ||||
$2,785.14 | |||||||
PV of all perpetuities = $2,785.14 | |||||||
DIF: Tough OBJ: TYPE: Financial Calculator TOP: PV of an annuity
- Hillary is trying to determine the cost of health care to college students, and parents’ ability to cover those costs. She assumes that the cost of one year of health care for a college student is $1,000 today, that the average student is 18 when he or she enters college, that inflation in health care cost is rising at the rate of 10 percent per year, and that parents can save $100 per year to help cover their children’s costs. All payments occur at the end of the relevant period, and the $100/year savings will stop the day the child enters college (hence 18 payments will be made). Savings can be invested at a simple rate of 6 percent, annual compounding. Hillary wants a health care plan which covers the fully inflated cost of health care for a student for 4 years, during years 19 through 22 (with payments made at the end of years 19 through 22). How much would the government have to set aside now (when a child is born), to supplement the average parent’s share of a child’s college health care cost? The lump sum the government sets aside will also be invested at 6 percent, annual compounding.
a. | $1,082.76 |
b. | $3,997.81 |
c. | $5,674.23 |
d. | $7,472.08 |
e. | $8,554.84 |
ANS: D
Parent’s savings: | Health Care Costs, Years 19-22 |
N = 18 | -$1,000 (1.1)^{19} = -$6,115.91 |
I = 8 | $1,000 (1.1)^{20} = -$6,727.50 |
PMT = 100 | $1,000 (1.1)^{21} = -$7,400.25 |
FV = 0 | -$1,000 (1.1)^{22} = -$8,140.27 |
Solve for PV = $1,082.76 |
-$8,554.84 | PV of Health care costs |
1,082.76 | PV of parents’ savings |
-$7,472.08 | Lump sum government must set aside |
= | 0 | |
= | 0 | |
= | -6,115.91 | |
= | -6,727.50 | |
= | -7,400.25 | |
= | -8,140.27 | |
I | = | 6 |
Solve for NPV = -8,554.84 = PV of Health care costs.
Consequently, the government must set aside $8,554.84 – $1,082.76 = $7,472.08
Alternatively,
= 0
= 100
= -6,115.91
= -6,727.50
= -7,400.25
= -8,140.27
I = 6
Solve for NPV = -$7,472.08 = Lump sum government must set aside.
DIF: Tough OBJ: TYPE: Financial Calculator TOP: PV of an uneven CF stream
- You have some money on deposit in a bank account which pays a simple (or quoted) rate of 8.0944 percent, but with interest compounded daily (using a 365-day year). Your friend owns a security which calls for the payment of $10,000 after 27 months. The security is just as safe as your bank deposit, and your friend offers to sell it to you for $8,000. If you buy the security, by how much will the effective annual rate of return on your investment change?
a. | 1.87% |
b. | 1.53% |
c. | 2.00% |
d. | 0.96% |
e. | 0.44% |
ANS: C
Numerical solution:
Step 1: | Find the effective annual rate (EAR) of interest on the bank deposit |
EAR_{Daily} = (1 + 0.080944/365)^{365} -1 = 8.43% | |
Step 2: | Find the EAR of the investment |
$8,000 = $10,000/(1 + r)^{2.25} | |
(1 + r)^{2.25 } = 1.25 | |
1 + r = 1.25(^{1/2.25}) | |
1 + r = 1.10426 | |
r = 0.10426 » 10.43% | |
Step 3: | Difference = 10.43% – 8.43% = 2.0% |
Financial calculator solution:
Calculate EAR_{Daily} using interest rate conversion feature
Inputs: P/YR = 365; NOM% = 8.0944; Output: EFF% = EAR = 8.43%
Calculate EAR of the equal risk investment
Inputs: N = 2.25; PV = -8,000; FV = 10,000; Output: I = 10.4259 » 10.43%
Difference: 10.43% – 8.43% = 2.0%
DIF: Tough OBJ: TYPE: Financial Calculator TOP: Effective annual rate
- Your employer has agreed to make 80 quarterly payments of $400 each into a trust account to fund your early retirement. The first payment will be made 3 months from now. At the end of 20 years (80 payments), you will be paid 10 equal annual payments, with the first payment to be made at the beginning of Year 21 (or the end of Year 20). The funds will be invested at a simple rate of 8.0 percent, quarterly compounding, during both the accumulation and the distribution periods. How large will each of your 10 receipts be? (Hint: You must find the EAR and use it in one of your calculations.)
a. | $7,561 |
b. | $10,789 |
c. | $11,678 |
d. | $12,342 |
e. | $13,119 |
ANS: B
PMT = ?
Find the FV at t = 80 of $400 quarterly payments:
N = 80; I = 2; PV = 0; and PMT = 400.
Solve for FV = $77,508.78
Find the EAR of 8%, compounded quarterly, so you can determine the value of each of the receipts.
EAR =
Now, determine the value of the receipts, remembering that this is an annuity due.
With a financial calculator, input the following:
N = 10; I = 8.2432; PV = -77,508.78; and FV = 0.
Solve for PMT = $10,788.78 » $10,789
DIF: Tough OBJ: TYPE: Financial Calculator
TOP: PMT and quarterly compounding
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