DEF Inc., a conglomerate with multiple business divisions, is evaluating a project in its transportation division. The transportation industry has an average debt-to-total-assets ratio of 30% and an average levered beta of 1.28. DEF will finance this project with a debt-to-total-assets ratio of 40%. Both DEF and the transportation industry have a tax rate of 40%. The risk-free rate is 5% and the expected market rate of return is 10%. What is the required rate of return for this project?
debt-to-total-assets ratio for a transport industry = 30%
So, Debt equity ratio of the industry = 30%/(1-30%) = 42.86%
tax rate T = 40%
Levered beta of industry = 1.28
So unlevered beta using formula
Bu = BL/(1 + (D/E)*(1-T)) = 1.28/(1 + 0.4286*(1-0.4)) = 1.018
DEF Inc.'s Debt-to-total-assets ratio = 40%
So, Debt equity ratio = 40%/(1-40%) = 66.67%
Using unlevered beta of industry, levered beta of the firm is
BL = Bu*(1 + (D/E)*(1-T)) = 1.018*(1 + 0.6667*(1-0.4)) = 1.425
Risk free rate Rf = 5%
Expected return on market Rm = 10%
using CAPM model, expected rate of return on DEF Inc's project is
E(r) = Rf + Beta*(Rm-Rf) = 5 + 1.425*(10-5) = 12.1%
Option A is correct.
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