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# Time Value of Money: Present Value and Interest

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You've been saving up for a new car that you think costs \$25,000. You already have \$10,000 and you think that, with interest and additional savings, the \$10,000 will grow to \$20,000 in three years. Suddenly, the phone rings and a voice at the other end of the line tells you that you've won \$5,000. You have the choice of collecting the \$5,000 immediately, or collecting it in three years which will give you enough money to buy the car. What would you do? Assume that the price of the car stays constant over the three years and that available interest for bank savings is 3%.

a) You get the same prize but the choice changes to \$5,000 now or \$5,250 in three years. What do you do?
b) You get the same prize but the choice changes to \$5,000 now or \$5,500 in three years. What do you do?
c) Explain the time value of money using this scenario as an example.

#### Solution Preview

Alternative 1
Collect the \$5,000 immediately.
In this PV of this alternative =\$5000

Alternative 2
Collect it in three years

Rate of interest =r=3%
Number of periods=n=3 years
FV of winning=FV=\$5000
PV of winning=FV/(1+r)^n=5000/(1+3%)^3=\$4575.71

PV of alternative 1 is higher. I should collect the money immediately.

a) You get the same prize but the choice changes to \$5,000 now or \$5,250 in three years. What do you do?

Alternative 1
Collect the \$5,000 immediately.
In this PV of this alternative =\$5000

Alternative ...

\$2.19

## 35 MQ questions: legal form, TVM concepts, NPV, financial analysis

1. The primary advantage of the proprietor form of business over the corporate form is:
a. ease of raising capital (money)
b. avoidance of double taxation
c. unlimited life
d. limited liability

2. All of the following are characteristics of proprietorships except:
a. ease of formation
b. income treated as part of the sole proprietor's income for tax purposes
c. ease of raising additional money for expansion
d. limited life

3. The principal financial advantage of the corporate form of organization is :
a. ease of transferability of ownership
b. accumulation of earnings for retention in the business
c. limited liability
d. ease of raising money through selling stock

4. Assume that pre-tax profit of \$50,000 has been earned by a business, and the owner/proprietor wants to
withdraw all of the after-tax profit for personal use. Assume the tax rate for a C corporation is 34%, while the
rate for a person is 28%. The after-tax earnings available under the corporate and proprietorship forms are:
a. For a corporation, \$33,000; for a proprietorship, \$36,000
b. For a corporation, \$23,760; for a proprietorship, \$36,000
c. For either a corporation or a proprietorship, \$36,000
d. For either a corporation or a proprietorship, \$23,760

5. In finance the primary goal of management is to:
a. utilize its economic resources in the most advantageous way
b. minimize all possible expenses
c. maximize shareholder wealth which is generally achieved by maximizing stock price
d. make the best use of its assets

6. Selected accounts are listed below. How much is the firm's operating income?
Accrued payroll \$ 2,000
Sales 45,000
Cost of goods sold 26,000
Interest expense 1,000
Expenses (other than interest) 8,000
a. \$8,000
b. \$10,000
c. \$9,000
d. \$11,000

7. Wessel Corp. plans to sell 1,000 units in 2002 at an average sale price of \$45 each. Cost of goods sold
will be 40% of the sale price. Depreciation expense will be \$3,000, interest expense \$2,500, and other
expenses will be \$4,000. Wessel's tax rate is 20%. What will Wessel Corp's net income be for 2002?
a. \$ 3,500
b. \$ 6,800
c. \$14,000
d. \$16,400
e. \$28,400

8. Holding all other variables constant, an increase in Cost of Goods Sold will lead to:
a. a decreased cost ratio
b. a higher gross margin
c. lower net income
d. paying more in taxes

9. Which of the following will increase equity?
a. An increase in dividends paid
b. Issuance of new stock
c. An increase in retained earnings from net income
d. Both b & c
e. All of the above

10. Which of the following would cause a decrease in cash:
a. An increase in the Average Collection Period from 15 days to 30 days
b. Selling off fixed assets for more than book value
c. An increase in accrued salaries expense
d. Paying suppliers in 60 days versus 45 days

11. A high average collection period may indicate:
a. Management's willingness to quickly write-off questionable receivables
b. Customers are paying for purchases quickly
c. A strict collection policy
d. None of the above

12. The Ragin Cajun had an operating income (EBIT) of \$260,000 last year. The firm had \$18,000 in depreciation expenses, \$15,000 in interest expenses, and \$60,000 in selling, general, and administrative expenses. If the Cajun has a marginal tax rate of 40 percent, what was its cash flow from operating activities last year?
a. \$165,000
b. \$230,000
c. \$132,000
d. \$162,000

13. Find the debt ratio of a firm with total debt equal to \$800,000 and net worth equal to \$2,400,000.
a. .33
b. .50
c. .75
d. .25
e. .67

14. If the firm's total equity is \$600,000, its long-term debt is \$300,000, and its current liabilities are
\$100,000, then its debt to equity ratio is:
a. 3:1
b. 2:1
c. 1:1
d. none of the above

15. Given the following information, calculate the inventory for J&C videos: Quick ratio = 1.2; Current
assets = \$12,000; Current ratio = 2.5
a. \$4,800
b. \$6,240
c. \$7,200
d. \$5,660

16. The higher the rate of interest:
a. the larger the present value of a future sum of money
b. the smaller the future value of an amount invested today
c. the smaller the present value of a future sum of money
d. all of the above

17. The principle behind time value of money is based on the fact that:
a. a sum of money in hand today is worth more than the same sum in the future
b. a sum of money in hand today is worth less than the same sum in the future
c. a sum of money in the future is worth less than the same sum in hand today
d. a and c

18. Holding all other variables constant, an increase in the interest rate will cause ________ to decrease.
a. Future values
b. Present values
c. Annuity payments
d. Growth rates

19. You have just calculated the present value of the expected cash flows of a potential investment. Management
thinks your figures are too low. Which of the following actions would increase the present value of your cash
flows?
a. assume a longer stream of cash flows of the same amount
b. increase the discount rate
c. decrease the discount rate
d. a and c

20. Your bank balance is exactly \$10,000. Three years ago you deposited \$7,938 and have not touched the account since. What annually compounded rate of interest has the bank been paying?
a. 8.65%
b. 26.00%
c. 8.00%
d. 6.87%

21. Find the present value of \$100 to be received at the end of two years if the discount rate is 12%
compounded monthly.
a. \$66.50
b. \$78.76
c. \$68.80
d. \$91.80
e. \$79.72

22. The Florida lottery agrees to pay the winner \$250,000 at the end of each year for the next 20 years.
What is the future value of this prize if each payment is put in an account earning 9 percent?
a. \$2.28 million
b. \$12.79 million
c. \$14.32 million
d. \$ 5.00 million

23. Which of the following interest rates will come closest to doubling invested money in five years?
a. 13%
b. 14%
c. 15%
d. 16%

24. Suppose you put \$100 into a savings account today, the account pays 8% compounded semiannually, and you withdraw \$50 one year after your initial deposit. What would your ending balance be 20 years after the initial \$100 deposit was made, assuming that you make no additional deposits?
a. \$250.31
b. \$257.45
c. \$258.16
d. \$430.10
e. \$480.10

25. Calculate the NPV of a project requiring a \$3,000 investment followed by an outflow of \$500 in Year
1, and inflows of \$1,000 in Year 2 and \$4000 in Year 3. The cost of capital is 12%. (Round to nearest \$)
a. \$52
b. \$198
c. \$257
d. \$486

26. What are the two primary drawbacks to the payback period method?
a. difficult to calculate; ignores time value of money
b. difficult to calculate; only works for long projects (e.g. 5 years or more)
c. ignores time value of money ; ignores cash flows after payback is reached
d. only works for long projects ; ignores cash flows after payback is reached
e. difficult to calculate ; ignores cash flows after payback is reached

27. If a project's NPV is negative
a. the project earns less than the cost of capital
b. the investment will not add value or contribute to shareholder wealth
c. the present value of expected cash outflows is greater than the present value of expected cash
inflows
d. all of the above

28. An investor's goal can be described best as
a. maximizing returns while minimizing risk
b. maximizing returns
c. capturing the high average returns of equity investing while limiting the associated risk as much as possible
d. avoiding risk regardless of the risk premium offered

29. If you invest 30% of your funds in AT&T stock with an expected rate of return of 10% and the
remainder in GM stock with an expected rate of return of 15%, the expected return on your portfolio is
a. 12.5%.
b. 13.0%.
c. 13.5%.
d. 14.5%.
e. none of the above

30. A project has the following cash flows:
0 1 2 3
(\$500) \$100 \$200 \$250
What is the project's NPV if the interest rate is \$6% ?
a. (\$17.76)
b. \$482.24
c. (\$537.78)
d. \$22.44

31. Use the following information to calculate your company's expected return.
State Probability Return
Boom 20% 40%
Normal 60% 15%
Recession 20% (20%)
a. 11%
b. 13%
c. 15%
d. 17%

32. Sentry Oil Inc. is considering two mutually exclusive projects as follows:
Year 0 1 2 3 4
Cash flow A (\$185,000) \$60,000 \$75,000 \$70,000 \$70,000
Cash flow B (\$125,000) (\$60,000) \$95,000 \$90,000 \$95,000
Sentry's a cost of capital is 14%. It can spend no more than \$350,000 on capital projects this year, which of the following statements is applicable when evaluating the projects by the NPV method?
a. both projects add shareholder wealth and should be undertaken
b. project B appears to add more shareholder wealth than project A and should be done
c. project A appears to add more shareholder wealth than project B and should be done
d. project B should be undertaken because it requires a smaller investment

33. A firm has current assets of \$10,000 and current liabilities of \$6,000. Cash and marketable securities total \$4,000, the balance in accounts receivable is \$2,000, and the book value of inventory is \$4,000. The firm's net working capital is:
a. \$2,000
b. \$4,000
c. \$6,000
d. \$9,000
e. none of the above

34. You are considering buying a new car. The sticker price is \$15,000 and you have \$2,000 to put toward a down
payment. If you can negotiate a nominal annual interest rate of 10% and you wish to pay for the car over a 5-
year period, what are your monthly car payments?
a. \$216.67
b. \$252.34
c. \$276.21
d. \$285.78
e. \$318.71

35. Muggles Manufacturing has asked you to calculate the company's current ratio. All you have is the partial balance sheet below, the year's sales revenue, and two ratios also shown below. Using that information, calculate Muggles' current ratio.
Sales = \$3,000
Cost Ratio (Cost of Goods sold/ Sales) = 45%
Inventory Turnover (Cost of goods sold/Inv) = 5.0

Assets Liabilities & Equity
Cash ? Accounts Payable \$ 50
AR \$ 40 Accruals ?
Inventory ? Long-term Debt \$380
Net Fixed Assets \$500 Equity \$250
Total Assets \$830 Total Liabilities & Equity ?

a. .35
b. .85
c. 1.65
d. 2.25

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