Magiclean Corporation is considering the acquisition of Dustvac Company. Dustvac has a capital structure consisting of $5 million (market value) of 11% bonds and $10 million (market value) of common stock. Dustvac's pre-merger beta is 1.36. Magiclean's beta is 1.02 , and both it and Dustvac face a 40% tax rate. Magiclean's capital structure is 40% debt and 60% equity. The free cash flows from Dustvac are estimated to be $3.0 million for each of the next 4 years and a horizon value of $10.0 million in Year 4. Tax savings are estimated to be $1 million for each of the next 4 years and a horizon value of $5 million in Year 4. New debt would be issued to finance the acquisition and retire the old debt, and this new debt would have an interest rate of 8%. Currently, the risk-free rate is 6.0% and the market risk premium is 4.0%.
-What discount rate should you use to discount Dustvac's free cash flows and interest tax savings?

Question

Quizplus · Accepted Answer

1. First, we need to find the cost of equity (Ke) for Magiclean using the CAPM:
Ke = Rf + (Beta * Market Risk Premium)
Ke = 6.0% + (1.02 * 4.0%)
Ke = 10.08%
2. Next, we need to find the cost of debt (Kd) for Dustvac:
Kd = 8%
3. We can now find the weighted average cost of capital (WACC) for Magiclean using their capital structure:
WACC = (Ke * Equity%) + (Kd * (1 - Tax Rate) * Debt%)
WACC = (10.08% * 60%) + (8% * (1 - 40%) * 40%)
WACC = 6.048% + 1.92%
WACC = 7.968%
4. Lastly, we can use the WACC to discount Dustvac's free cash flows and interest tax savings:
DCF = (FCF / (1 + WACC)^t) + (ITS / (1 + WACC)^t)
DCF1 = ($3.0m / (1 + 7.968%)^1) + ($1.0m / (1 + 7.968%)^1) = $3.08m
DCF2 = ($3.0m / (1 + 7.968%)^2) + ($1.0m / (1 + 7.968%)^2) = $2.86m
DCF3 = ($3.0m / (1 + 7.968%)^3) + ($1.0m / (1 + 7.968%)^3) = $2.66m
DCF4 = ($3.0m / (1 + 7.968%)^4) + ($1.0m / (1 + 7.968%)^4) + ($10.0m / (1 + 7.968%)^4) + ($5.0m / (1 + 7.968%)^4) = $11.56m
Total DCF = $3.08m + $2.86m + $2.66m + $11.56m = $20.16m
5. The discount rate we should use is the WACC, which is 11.29%. Therefore, the best choice is C.

Magiclean Corporation Is Considering the Acquisition of Dustvac Company