Question

The acrosstown company has an equity beta of 0.5 and 50% debt in its capital structure. The company has risk-free debt that cost 6% before taxes, and the expected rate of return on the market is 18%. Acrosstown is considering the acquisition of a new project in the peanut-raising agribusiness that is expected to yield 25% on and after-tax operating cashflows. The Carternut Company, which is in the same product line (and risk class) as the project being considered, has an equity beta of 2 and has 10% debt in its capital structure. If Acrosstown finances the new project with 50% debt, should it be accepted or rejected? Assume the tax rate for both companies is 50%

Answer 1

Acrosstown's current WACC = weight of debt*cost of debt*(1-tax rate) + weight of equity*(risk-free rate + beta*(market return - risk-free rate)) =

0.5*6%*(1-50%) + 0.5*(6% + 0.5*(18%-6%)) = 7.5%

This is lower than the expected yield of a new project but if we look at Carternut's beta, the project could be a lot riskier. In order to better evaluate the value, we need to take into consideration the riskiness.

Unlevered beta of Carternut B_u = equity beta/(1+tax rate*(Debt/Equity)) = 2/(1+0.5*(10%/90%)) = 1.8947

Using this unlevered beta, we relever the beta of Acrosstown, at its capital structure of 50% debt and 50% equity, to better reflect the risk of the project:

B_L = B_u*(1+ tax-rate*(Debt/Equity)) = 1.8947*(1+0.5*(50%/50%)) = 2.8421

WACC of Acrosstown = weighted cost of debt + weighted cost of equity

= 0.5*6%*(1-50%) + 0.5*(6% + 2.8421*(18%-6%)) = 21.55%

This cost of capital is less than the expected return of 25% on the new project so the new project can be accepted.