please show work Proportion of firm\'s assets 40% 30% 30% Leveraged Beta Divisio
ID: 2785742 • Letter: P
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Proportion of firm's assets 40% 30% 30% Leveraged Beta Division Property Management Land Resources Financial Services 1.3 0.9 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 m 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,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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