The overall leveraged beta for Dunphy is 1.2. The Land Resources division\'s cap
ID: 2785697 • Letter: T
Question
The overall leveraged beta for Dunphy is 1.2. The Land Resources division's capital structure is 65% debt and 35% equity. Dunphy is planning to finance new projects in that division with a capital structure of 80% debt and 20% equity. The risk free rate is 3%, and the market risk premium is 8%. The pretax cost of debt for the company is 9% and the marginal tax rate is 39%. What discount rate should Dunphy apply to the cash flows for new projects in the Land Resources division? (Hint, calculate the Land Resources levered beta, then unlever, relever, etc...)
Division Leveraged Beta Proportion of firm's assets Property Management 1.3 40% Land Resources ? 30% Financial Services 0.9 30%Explanation / Answer
Leveraged beta of land resource = [1.20 - (1.30 × 40%) + (0.90 × 30%)] / 30%
= (1.20 - 0.52 - 0.27) / 30%
= 0.41 / 30%
= 1.37.
Leverage beta of land resource is 1.37.
Now, unlevered beta of land resource = beta (levered) / 1 + (1 - tax rate) x (Debt/Equity)
= 1.37 / [1+ (1 – 39%) × (65% / 35%)]
= 1.37 / [1+ 1.1329]
= 0.64
Hence, unlevered beta of land resource is 0.964.
Now,
levered beat of Dunphy with 80% debt and 20% equity.
Levered beta = Unlevered beta × [1 + (1 - tax rate) x (Debt/Equity)]
= 0.65 × [1 + (1 - 39%) × (80 / 20)]
= 0.64 × (1+ 2.44)
= 2.21
Hence, Levered beta of Dunphy is 2.21.
now cost of equity for Dunphy = 3% + (8% × 2.21)
= 3% + 17.68%
= 20.68%
New cost of equity is 20.68%.
Before tax cost of debt = 9%
After tax cost of debt = 9% × (1 - 39%)
= 5.49%
After tax cost of debt is 5.49%.
Now, discount rate that is WACC is calculated below:
WACC = (80% × 5.49%) + (20% × 20.68%)
= 4.392% + 4.136%
= 8.53%
Discount rate that is WACC is 8.53%
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