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

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

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follow.

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that end-of-period deposits are made and no interest is withdrawn, if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

semiannually.

(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

(DFL).

**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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