The CFO of Firm XYZ hired you as a consultant to help estimate its cost of equity based on the three most commonly used methods and then indicate the difference between the highest and lowest of these estimates. What is that difference?
Q2Chapter 10WACC and equity from retained earnings
Firm XYZ recently hired you as a consultant to estimate the company's WACC. The firm uses the CAPM to estimate the cost of equity, and it does not expect to issue any new common stock. What is its WACC?
Bond coupon rate
8.00% annually
Bond maturity
20 years
Par value
$1,000
Bond price
$1,050.00
Tax rate
40%
Risk-free rate
4.50%
Market risk premium
5.50%
Beta
1.20
Target weight of debt
35%
Target weight of common equity
65%
Correct answer: e. 8.79%
Cost of debt before tax: solve for the bond's YTM using price = $1,050. That gives rd ≈ 7.51%.
Firm XYZ is considering a project that has the following cash flow data. What is the project's payback?
Year 0
-$1,100
Year 1
$300
Year 2
$310
Year 3
$320
Year 4
$330
Year 5
$340
Correct answer: e. 3.52 years
Cumulative after Year 1: -1100 + 300 = -800.
After Year 2: -800 + 310 = -490.
After Year 3: -490 + 320 = -170.
Fraction of Year 4 needed: 170 / 330 = 0.5152.
Payback: 3 + 0.5152 = 3.52 years.
Q9Chapter 11Discounted payback
Firm XYZ is considering a project that has the following cash flow and WACC data. What is the project's discounted payback?
WACC
10.00%
Year 0
-$900
Year 1
$500
Year 2
$500
Year 3
$500
Correct answer: b. 2.09 years
Discounted CF, Year 1: 500/1.10 = 454.55.
Discounted CF, Year 2: 500/1.102 = 413.22.
After Year 1: still unrecovered = 900 − 454.55 = 445.45.
Fraction of Year 2 needed: 445.45 / 413.22 = 1.0780 of the discounted Year 2 flow, so discounted payback = 1 + 1.0780 ≈ 2.09 years.
Q10Chapter 11NPV vs. IRR
Firm XYZ is considering Projects S and L. If the decision is made by choosing the project with the higher IRR rather than the one with the higher NPV, how much value will be forgone?
WACC
7.50%
Project S cash flows
-1100, 550, 600, 100, 100
Project L cash flows
-2700, 650, 725, 800, 1400
Correct answer: a. $138.10
IRR(Project S) ≈ 12.24%; IRR(Project L) ≈ 10.71%. So IRR would choose Project S.
NPV at 7.50%: NPV(S) ≈ $86.20; NPV(L) ≈ $224.31. NPV would choose Project L.
Your company, Firm XYZ, is considering a new project. What is the project's Year 1 cash flow?
Sales revenues
$22,250
Depreciation
$8,000
Other operating costs
$12,000
Tax rate
35.0%
Correct answer: c. $9,463
EBIT: 22,250 − 12,000 − 8,000 = $2,250.
Taxes: 2,250(0.35) = $787.50.
Net income: 2,250 − 787.50 = $1,462.50.
Operating cash flow: net income + depreciation = 1,462.50 + 8,000 = $9,462.50 ≈ $9,463.
Q12Chapter 12Annual cash flow with MACRS
Firm XYZ is considering a new project. The equipment has a 3-year tax life with MACRS rates of 33%, 45%, 15%, and 7% for Years 1 through 4. What is the Year 1 cash flow?
Your company, Firm XYZ, is considering a new project. The required equipment is classified as 3-year MACRS property. Under MACRS, depreciation is taken over 4 tax years using 33%, 45%, 15%, and 7% for Years 1 through 4. What is the project's Year 4 cash flow?
Reminder: Even though this is 3-year MACRS property, depreciation appears over 4 tax years because of the MACRS half-year convention. Assume zero salvage value.
Equipment cost (depreciable basis)
$70,000
Sales revenues, each year
$42,500
Operating costs (excl. deprec.)
$25,000
Tax rate
35.0%
Correct answer: c. $13,090
Year 4 depreciation: 0.07($70,000) = $4,900.
EBIT: 42,500 − 25,000 − 4,900 = $12,600.
Taxes: 12,600(0.35) = $4,410.
OCF: 12,600(0.65) + 4,900 = $13,090.
Q14Chapter 12Project NPV
Firm XYZ is considering a new project. The equipment is depreciated straight-line over 3 years, has zero salvage, and no new working capital is required. What is the project's NPV?
Firm XYZ is considering the purchase of a new machine for $50,000, installed. The machine will be sold at the end of Year 4 for $12,500. If the tax rate is 40%, what will the after-tax salvage value be?
Hint: Find the book value at the end of Year 4 first. Then compare the sale price with the book value to determine whether there is a taxable gain or a tax-deductible loss.
Initial cost
$50,000
Depreciation rates, Years 1-4
20%, 32%, 19%, 12%
Expected sale price at end of Year 4
$12,500
Tax rate
40%
Correct answer: e. $10,900
Total depreciation through Year 4: (0.20 + 0.32 + 0.19 + 0.12)($50,000) = 0.83($50,000) = $41,500.
Book value at end of Year 4: 50,000 − 41,500 = $8,500.
Q16Chapter 12Project NPV with salvage value and working capital
Firm XYZ is considering some new equipment. The equipment will have a positive salvage value at the end of Year 3, and some working capital will be recovered at the end of the project's life. What is the project's NPV?
Hint: Set up the project cash flows by year. • Year 0: include the fixed-asset purchase and the required new working capital investment. • Years 1 and 2: include only the annual operating cash flow (OCF). There are no working-capital gains or losses in Years 1 and 2. • Year 3: include the annual OCF, after-tax salvage value, and full recovery of working capital.
Timeline: Year 0 cash flow = − Fixed assets − New working capital Year 1 cash flow = OCF Year 2 cash flow = OCF Year 3 cash flow = OCF + After-tax salvage value + Recovery of working capital
WACC
10.0%
Net investment in fixed assets (depreciable basis)