A firm is considering the purchase of ONE machine (i.e., A and B are mutually ex

Question

A firm is considering the purchase of ONE machine (i.e., A and B are mutually exclusive). Machine A will cost $40,000, generate sales of $20,000 per year for 5 years and have annual costs of $7,500. Machine B will cost $45,000, generate sales of $25,000 per year for 6 years and have annual costs of $9,000. At the end of their useful lives, each machine will have a salvage value of zero. There is no expected change in net working capital, and the firm uses straight-line depreciation.. The firm's tax rate is 30%. The firm currently has a market value capital structure of 50% debt and 50% equity. The cost of equity is 15%, and the before-tax cost of debt is 10%. The return on the market portfolio is 10%, and the firm's level of systematic risk is 1. The risk free rate of return is 5%. Compute the WACC for the firm using the equation, WACC = Equity/Firm Value times Cost of Equity + Debt/Firm Value times Cost of Debt times (1 - T) Compute the required rate of return for the firm using the CAPM. If the level of systematic risk for the project is estimated to be 2.0: Find the required rate of return for the project. Find the NPV for each machine, A and B Which machine should the firm choose?

Explanation / Answer

a. WACC = 15% * 50% + 10% * (1-.30)*50%

WACC = 7.50% + 3.50% = 11%

b. CAPM Required Rate of Return = Risk Free Return + Beta * (Market rate - Risk Free Return)

= 5% + 1 (10%-5%) = 10%

c. If systematic risk i.e.beta = 2

i. Required rate of return = Risk Free Return + Beta * (Market rate - Risk Free Return)

= 5% + 2 * (10% -5%)

= 15%

ii. Using 15% as discount rate, NPV of the project is:

Machine A:

Machine B:

iii Since the NPV with machine B is positive this should be accepted

Year Cash Outflow Revenue Costs Depreciation Cash Flows Tax Cash Flows After Tax Net Operating Cash Flows (Cash Flows After Tax + Depreciation) PV Factor @15% PV 0 -40000 0 0 0 -40000 1 -40000 1 20000 7500 8000 4500 1350 3150 11150 0.8696 9695.65 2 20000 7500 8000 4500 1350 3150 11150 0.7561 8431.00 3 20000 7500 8000 4500 1350 3150 11150 0.6575 7331.31 4 20000 7500 8000 4500 1350 3150 11150 0.5718 6375.05 5 20000 7500 8000 4500 1350 3150 11150 0.4972 5543.52 Net Present Value -2623.47

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