Question

KST Ltd manufactures running gear for athletes. The returns of KST Ltd shares have a covariance with the market portfolio of 0.02. The standard deviation of the market portfolio’s return is 12.5 percent, the market risk premium is 8.2 percent, and the riskfree rate of return is 8 percent. KST Ltd has $23 million of 13 percent bonds on issue which currently have a market yield to maturity of 12 percent. The market value of the bonds is $24 million. KST Ltd has 16 million shares outstanding which are currently trading at $3.00 per share. The company’s marginal tax rate is 30 percent and management considers KST Ltd’s level of financial leverage to be optimal for its current operations. ]

a) Calculate KST Ltd’s after-tax weighted average cost of capital. Show all calculations.

b) For this part assume the after-tax weighted average cost of capital is 16 percent. KST Ltd has to decide whether to purchase new capital equipment. The equipment will cost $18 million, and a further $2 million to install. To date, the company has spent $400,000 on research and development related to this investment decision. The equipment is expected to generate additional net after-tax cash flows of $6.2 million a year for the next five years. Based on the information given, calculate the net present value of this project. Show all calculations.

c) What difference would it make to your answer in part 2.2 if the new equipment is to be used to manufacture ventilators? Provide a brief explanation (no calculations needed).

Answer 1

Solution) The beta of the stock = Cov(Rs, Rm)/Variance of Market return

= (0.02)/(12.5%)^2 = 1.28

Market risk premium (Rm - Rf) = 8.2%

Risk-free rate of return (Rf) = 8%

According to the Capital Asset Pricing Model (CAPM), the cost of equity (Ke) is calculated as:

= Rf + Beta*(Rm - Rf)

= 8% + 1.28*8.2%

= 8% + 10.496%

Ke = 18.496%

Market price of share = $3

Number of shares outstanding =  16 million

Market value of equity (E) = 3*16 = $48 million

Market value of debt (D) = $24 million

Total capital = D + E = 48 + 24 = $72 million

Weight of debt (Wd) = D/(D+E) = 24/72 = 1/3

Weight of equity (We) = E/(D+E) = 48/72 = 2/3

Tax rate = 30%

Cost of debt (Kd) = Yield-to-matuirty of the bond = 12%

Solution a) After-tax weighted average cost of capital (WACC) = Wd*Kd*(1 - Tax%) + We*Ke

= (1/3)*12%*(1 -30%) + (2/3)*18.496%

= 0.028 + 0.1233067

= 0.15130667

= 15.13%

Solution b) Equipment Cost = $18 million

Installation Cost = $2 million

Total cost = 18 + 2 = $20 million

Life of the machine = 5 years

Depreciation per year = 20/5 = $4 million

Net after-tax cash flows = $6.2 million

Net cash flows per year = 6.2 + 4 = $10.2 million

The cash flows are shown as follows:

Solution 3) Please provide the question in part 2.2

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