Question

First and Ten Corporation’s stock returns have a covariance with the market portfolio of .0421. The standard deviation of the returns on the market portfolio is 18 percent and the expected market risk premium is 6.4 percent. The company has bonds outstanding with a total market value of $55.1 million and a yield to maturity of 5.3 percent. The company also has 4.3 million shares of common stock outstanding, each selling for $50. The company’s CEO considers the firm’s current debt-equity ratio optimal. The corporate tax rate is 21 percent and Treasury bills currently yield 2.7 percent. The company is considering the purchase of additional equipment that would cost $49.5 million. The expected unlevered cash flows from the equipment are $16.55 million per year for 5 years. Purchasing the equipment will not change the risk level of the firm.

  

Calculate the NPV of the project. (Do not round intermediate calculations and enter your answer in dollars, not millions of dollars, rounded to 2 decimal places, e.g., 1,234,567.89)

Answer 1

To calculate the NPV of the project, we need to discount the future cash flows by a discount factor. The discount factor in this case shall be Weighted Average Cost of Capital(WACC).

WACC = Cost of Debt X Debt /(Debt + Equity) X (1-Tax Rate) + Equity/ (Debt + Equity) X Cost of Equity

Cost of Debt = 5.3%

Debt = $ 55.1 m

Equity = 4.3 x 50 = $ 215m

Debt /(Debt + Equity) = 55.1/(55.1+215)= 0.20

Equity/ (Debt + Equity) = 215/(215+55.1) = 0.80

Cost of Equity = Treasury bills yield + Beta unlevered(market risk premium)

Beta levered = Covariance of market returns and stock's return/ (standard deviation of market portfolio)² = .0421/(0.18)²= 1.30

Beta Unlevered = 1.30 /[1 + (1- 0.21) X 55.1/215] = 1.08

Cost of Equity = 0.027 + 1.08 X 0.064 = 0.096 = 9.6%

WACC = 0.20 X (1- 0.21) X 0.053 + 0.80 X 0.096 = 0.085 = 8.5%

Year	0	1	2	3	4	5
Cash flows	-49,500,000.00	16,550,000.00	16,550,000.00	16,550,000.00	16,550,000.00	16,550,000.00
Discount factor	1.00	1.09	1.18	1.28	1.39	1.50
Discounted cash flows	-49,500,000.00	15,253,456.22	14,058,485.00	12,957,129.03	11,942,054.40	11,006,501.76
NPV	15,717,626.41

Note: NPV = -49.50 /(1+0.085)⁰ + 16.55/(1+0.085)¹ +.........+16.55/(1+0.085)⁵