P4–31 Relationship between future value and present value—Mixed stream Using

only the information in the accompanying table, answer the questions that



Year (t) Cash flow – Future value interest factor at 5% (FVIF 5%, n)

1 -$ 800 – 1.050

2 -900 -1.102

3 -1,000 -1.158

4 -1,500 -1.216

5 -2,000 -1.276


a. Determine the present value of the mixed stream of cash flows using a 5%

discount rate.

b. How much would you be willing to pay for an opportunity to buy this

stream, assuming that you can at best earn 5% on your investments?

c. What effect, if any, would a 7% rather than a 5% opportunity cost have on

your analysis? (Explain verbally.)


P4–37 Annuities and compounding Janet Boyle intends to deposit $300 per year in a

credit union for the next 10 years, and the credit union pays an annual interest

rate of 8%.


a. Determine the future value that Janet will have at the end of 10 years, given

that end-of-period deposits are made and no interest is withdrawn, if

(1) $300 is deposited annually and the credit union pays interest annually.

(2) $150 is deposited semiannually and the credit union pays interest


(3) $75 is deposited quarterly and the credit union pays interest quarterly.

b. Use your finding in part a to discuss the effect of more frequent deposits and

compounding of interest on the future value of an annuity.


P4–43 Loan amortization schedule Joan Messineo borrowed $15,000 at a 14%

annual rate of interest to be repaid over 3 years. The loan is amortized into

three equal, annual, end-of-year payments.


a. Calculate the annual, end-of-year loan payment.

b. Prepare a loan amortization schedule showing the interest and principal

breakdown of each of the three loan payments.

c. Explain why the interest portion of each payment declines with the passage

of time.


P4–51 Interest rate for an annuity Anna Waldheim was seriously injured in an industrial

accident. She sued the responsible parties and was awarded a judgment of

$2,000,000. Today, she and her attorney are attending a settlement conference

with the defendants. The defendants have made an initial offer of $156,000 per

year for 25 years. Anna plans to counteroffer at $255,000 per year for 25 years.

Both the offer and the counteroffer have a present value of $2,000,000, the

amount of the judgment. Both assume payments at the end of each year.


a. What interest rate assumption have the defendants used in their offer

(rounded to the nearest whole percent)?

b. What interest rate assumption have Anna and her lawyer used in their

counteroffer (rounded to the nearest whole percent)?

c. Anna is willing to settle for an annuity that carries an interest rate assumption

of 9%. What annual payment would be acceptable to her?


P11–6 EBIT sensitivity Stewart Industries sells its finished product for $9 per unit. Its

fixed operating costs are $20,000, and the variable operating cost per unit is $5.


a. Calculate the firm’s earnings before interest and taxes (EBIT) for sales of

10,000 units.

b. Calculate the firm’s EBIT for sales of 8,000 and 12,000 units, respectively.

c. Calculate the percentage changes in sales (from the 10,000-unit base level)

and associated percentage changes in EBIT for the shifts in sales indicated

in part b.

d. On the basis of your findings in part c, comment on the sensitivity of changes

in EBIT in response to changes in sales.


P11–7 Degree of operating leverage Grey Products has fixed operating costs of

$380,000, variable operating costs of $16 per unit, and a selling price of $63.50

per unit.


a. Calculate the operating breakeven point in units.

b. Calculate the firm’s EBIT at 9,000, 10,000, and 11,000 units, respectively.

c. With 10,000 units as a base, what are the percentage changes in units sold

and EBIT as sales move from the base to the other sales levels used in part b?

d. Use the percentages computed in part c to determine the degree of operating

leverage (DOL).

e. Use the formula for degree of operating leverage to determine the DOL at

10,000 units.


P11–10 Degree of financial leverage Northwestern Savings and Loan has a current capital

structure consisting of $250,000 of 16% (annual interest) debt and 2,000

shares of common stock. The firm pays taxes at the rate of 40%.


a. Using EBIT values of $80,000 and $120,000, determine the associated earnings

per share (EPS).

b. Using $80,000 of EBIT as a base, calculate the degree of financial leverage


c. Rework parts a and b assuming that the firm has $100,000 of 16% (annual

interest) debt and 3,000 shares of common stock.


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