GBA 522 MIDTERM A firm is considering the purchase of ONE machine (i.e., A and B
ID: 2766396 • Letter: G
Question
GBA 522 MIDTERM
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,
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
Capital Structure of the firm
Debt = 50% and Equity = 50%
Cost of Equity = 15%
Pre-tax cost of debt =10%
Tax rate = 30%
WACC = E/V * Return on Equity + D/V * Pre-tax cost of debt * (1-tax rate)
= 0.5 * 15% + 0.5 * 10% * (1-0.30)
= 7.5% + 0.5 * 10% * 0.7
= 7.5% + 1.75%
= 9.25%
Return on market portfolio = 10%
Level of systematic risk = 1
Risk-free rate of return = 5%
Required rate of return of the firm using CAPM = 5% + 1 * (10%-5%) = 5%+5% = 10%
If the level of systematic risk = 2.0
Required rate of return on equity of the firm = 5% + 2 * (10%-5%) = 5%+10% = 15%
Required rate of return of the project = 0.5 * 15% + 0.5 * 10%*(1-0.30) = 9.25%
Calculation of NPV of Machine A
Cost of Machine = 40000
Life of machine = 5 years
Annual sales = 20000
Annual costs = 7500
Annual Depreciation = 40000/5 = 8000
Annual pre-tax profit = 20000 – 7500 – 8000 = 4500
Annual Net Profit = 4500 * (1-0.3) = 4500 * 0.7 =3150
Annual cash flow = Annual Net Profit + Depreciation = 3150 + 8000 =11150
Net present Value of the machine = -40000 + 11150 * [(1-(1.0925^-5)/0.0925]
= -40000 + 11150 * [(1-0.6425290)/0.0925]
= -40000 + 11150 * 0.357470944 / 0.0925
= -40000 + 11150 * 3.86455
= -40000 + 43089.7408
= 3089.7408 or $3089.74 (rounded off)
Calculation of NPV of Machine B
Cost of Machine = 45000
Life of machine = 6 years
Annual sales = 25000
Annual costs = 9000
Annual Depreciation = 45000/6 = 7500
Annual pre-tax profit = 25000 – 9000 – 7500 = 8500
Annual Net Profit = 8500 * (1-0.3) = 8500 * 0.7 =5950
Annual cash flow = Annual Net Profit + Depreciation = 5950 + 7500 =13450
Net present Value of the machine = -45000 + 13450 * [(1-(1.0925^-6)/0.0925]
= -45000 + 134550 * [(1-0.58812728)/0.0925]
= -45000 + 13450 * 0.411873 / 0.0925
= -45000 + 13450 * 4.452578
= -45000 + 59888.5195
= 14888.5195 or $14888.52 (rounded off)
Since Machine B has a higher net present value, the same can be chosen.
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