Question

First and Ten Corporation’s stock returns have a covariance with the market portfolio of .0511. The standard deviation of the returns on the market portfolio is 22 percent and the expected market risk premium is 6.4 percent. The company has bonds outstanding with a total market value of $56.9 million and a yield to maturity of 6.7 percent. The company also has 6.1 million shares of common stock outstanding, each selling for $32. The company’s CEO considers the firm’s current debt-equity ratio optimal. The corporate tax rate is 24 percent and Treasury bills currently yield 4.5 percent. The company is considering the purchase of additional equipment that would cost $58.5 million. The expected unlevered cash flows from the equipment are $19.25 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

Covariance of Stock returns with market portfolio = 0.0511, Standard deviation of returns of market portfolio = 22%

Variance of returns of market portfolio = (Standard deviation of returns of market portfolio)² = (22%)² = 0.22 x 0.22 = 0.0484

Beta of stock of First & Ten= Covariance of Stock returns with market portfolio / Variance of returns of market portfolio = 0.0511 / 0.0484 = 1.0557

Expected market risk premium = 6.4%, Risk free rate = Treasury bill yield = 4.5%

According to Capital Asset Pricing Model

Cost of equity = Risk free rate + Beta x Expected market risk premium = 4.5% + 1.0557 x 6.4% = 4.5% + 6.7564% = 11.2564%

Pre tax cost of debt = Yield to maturity of bonds of First and Ten corporation = 6.7%

Value of Equity = E = Price per share x No of shares outstanding = $32 x 6.1 million = 195.20 million

Value of Debt = D = $56.9 million

Value of company = V = E + D = 195.20 + 56.9 = $252.10 million

WACC of the firm = (E/V)(Cost of equity) + (D/V)(Pre tax cost of debt)(1-tax rate)

WACC of the firm = (195.20/252.10)(11.2564%) + (56.9/252.10)(6.7%)(1-24%)

WACC of the firm = (195.20/252.10)(11.2564%) + (56.9/252.10)(6.7%)(76%)

WACC of the firm = 8.7157% + 1.1492% = 9.8649%

Price of additional equipment = $58.5 million = 58.5 x 1000000 = $58500000

Unlevered cash flow for year 1 to 5 = $19.25 million = 19.25 x 1000000 = 19250000

We will choose WACC of the company will be used as discount rate for the project because project does not change the risk level of firm

NPV of the project = - Price of additional Equipment + Sum of present values of Unlevered cash flows discounted at WACC

NPV of the project = -58500000 + 19250000 / (1 + 9.8649%) + 19250000 / (1 + 9.8649%)² + 19250000 / (1 + 9.8649%)³ + 19250000 / (1 + 9.8649%)⁴ + 19250000 / (1 + 9.8649%)⁵

NPV of the project = -58500000 + 17521519.6118 + 15948241.5328 + 14516229.9632 + 13212800.4150 + 12026407.3558 = 14725198.8786 = $14725198.88 ( Rounded to two decimal places)

Hence NPV of the project = $14725198.88