Question

QUESTION 42

A company has a proposed 2-year project with the cash flows shown below and would like to calculate the NPV of this project so that they can decide whether to pursue the project or not. The company has a target capital structure of 60% equity and 40% debt. The beta for this firms stock is 0.8, the risk-free rate is 4.8, and the expected market risk premium is 6%. The bonds for this company pay interest semiannually and have a coupon interest rate of 9%, 11 years to maturity, a face value of $1,000, and a current price of 1,137.7. If the corporate tax rate is 38%, what is the NPV of the proposed project for this firm? (Answer to the nearest dollar, but do not use a dollar sign).

  

Years	Cash Flows
0	-4,000
1	3,000
2	4,000

Answer 1

Answer:

Debt:

Face Value = $1,000
Current Price = $1,137.7

Annual Coupon Rate = 9%
Semiannual Coupon Rate = 4.50%
Semiannual Coupon = 4.50%*$1,000 = $45

Time to Maturity = 11 years
Semiannual Period to Maturity = 22

Let semiannual YTM be i%

$1,137.7 = $45 * PVIFA(i%, 22) + $1,000 * PVIF(i%, 22)

Using financial calculator:
N = 22
PV = -1137.7
PMT = 45
FV = 1000

I = 3.585%

Semiannual YTM = 3.585%
Annual YTM = 2 * 3.585%
Annual YTM = 7.17%

Before-tax Cost of Debt = 7.17%
After-tax Cost of Debt = 7.17% * (1 - 0.38)
After-tax Cost of Debt = 4.445%

Equity:

Risk-free Rate = 4.8%
Market Risk Premium = 6%
Beta = 0.8

Cost of Equity = Risk Free Rate + Beta * Market Risk Premium
Cost of Equity = 0.048 + (0.8 * 0.06)
Cost of Equity = 0.048 + 0.048
Cost of Equity = 0.096 or 9.60%

WACC = Weight of Debt * After-tax Cost of Debt + Weight of Equity * Cost of Equity
WACC = 40% * 4.445% + 60% * 9.60%
WACC = 7.538%

NPV = -$4,000 + $3,000/1.07538 + $4,000/1.07538^2
NPV = $2,248.60

So, NPV of the proposed project is $2,248.60