Solutions to Chapter 10

REVIEW CH. 9 CASH FLOW EQUATIONS ON P. 309 - 310 5. Revenue = Price  quantity = $2  6 million = $12 million

Expense = Variable cost + fixed cost = $1  6 million + $2 million = $8 million Depreciation = $5 million/5 years = $1 million per year

CF = (1  T)  (Revenue – expenses) + T  depreciation = .60  ($12 million – $8 million) + .4  $1 million = $2.8 million a. NPV = –$5 million + $2.8 million  annuity factor(5 years, 12%) = –$5 million + $2.8 million  3.605 = $5.1 million

b. If variable cost = $1.20, then expenses increase to $1.20  6 million + $2 million = $9.2 million.

CF = .60  ($12 million – $9.2 million) + .4  $1 million = $2.08 million

NPV = –$5 million + $2.08 million  3.605 = $2.5 million c. If fixed costs = $1.5 million, expenses fall to ($1  6 million) + $1.5 million = $7.5 million

CF = .60  ($12 million – $7.5 million) + .4  $1 million = $3.1 million NPV = –$5 million + $3.1 million  3.605 = $6.2 million d. Call P the price per jar. Then

Revenue = P  6 million Expense = $1  6 million + $2 million = $8 million

CF = (1 – .40)  (6P – 8) + .40  1 = 3.6P – 4.4 NPV = –5 + (3.6P – 4.4)  3.605 = –20.862 + 12.978P NPV = 0 when P = $1.61 per jar

9. a. Each dollar of sales generates $0.70 of pretax profit. Depreciation is $100,000 and fixed costs are $200,000. Accounting break-even revenues are therefore:

(200,000 + 100,000)/.70 = $428,571

The firm must sell 4,286 diamonds annually.

b. Call Q the number of diamonds sold. Cash flow equals

= (1 – .35)(Revenue – expenses) + .35  depreciation

= .65 (100Q – 30Q – 200,000) + .35 (100,000)

= 45.5Q – 95,000 The 12%, 10-year annuity factor is 5.650. Therefore, for NPV to equal zero,

(45.5Q – 95,000)  5.650 = $1,000,000

257.075Q – 536,750 = 1,000,000

Q = 5,978 diamonds per year

14. a. Variable cost = 75% of revenue. Additional profit per $1 of additional sales is therefore $0.25. Depreciation per year = $3000/5 = $600.

Break-even sales level = = = $6400/year

This sales level corresponds to a production level of $6400/$80 per unit = 80 units.

To find NPV break-even sales, first calculate cash flow. With no taxes, CF = .25  Sales – 1000.

The 10%, 5-year annuity factor is 3.7908. Therefore, if project