# Chapter 10 Solutions Essay

Submitted By Liu16gC
Words: 533
Pages: 3

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…