Question

Tag, Inc is considering a project in the paper business. It has 8m bond and 2m common shares, a marginal tax rate of 37.5%, and its debt currently has a rate of return of 14%.

R, a publicly traded firm that operates only in the paper business. its market value of equity is 3,800m and market value of debt is 0. It has an equity beta of 1.053 and a marginal tax rate of 37.5%.The risk-free rate is 4.25%, and the market risk premium is 6.7%.

Calculate R’s asset beta, the project’s equity beta, project cost of capital, and the appropriate WACC to use in evaluating the project.  

Please show the Excel formulas to solve.

Answer 1

The asset beta (A) and equity beta (B) of any entity are related by means of the following relationship:

B = A x [1 + (Debt / Equity) x (1-Tax Rate)]

As is observable the asset beta of Company R is equal to its equity beta of 1.053. In fact, any entity which is entirely equity financed (has zero debt) will have its asset beta equal to that of its equity beta.

As company R is entirely in the paper's business, the risk of Tag Inc's planned paper business will be adequately represented by Company R's business risk. Company R's business risk, in turn, is represented by the firm's asset beta (only as equity beta represents financial as well as business risk). Hence Tag Inc's asset beta of paper's business will be equal to Company R's asset beta of 1.053

Tag Inc's Capital Structure:

Equity = 2 million (common shares) and Debt = Bond = 8 million

Tax Rate = 37.5 %

Equity Beta of Project = 1.053 x [1+(8/2) x (1-0.375)] = 3.6855

Risk-Free Rate = 4.25 % and Market Risk Premium = 6.7 %

Cost of Equity = ke = Risk-Free Rate + Equity Beta x Market Risk Premium = 4.25 + 3.6855 x 6.7 = 28.94285 %

Cost of Debt = Rate of Return on Debt = kd = 14 %

Tag Inc's Weighted Average Cost of Capital = (1-Tax Rate) x kd x Debt Proportion + ke x Equity Proportion = (1-0.375) x 14 x [8/(8+2)] + 28.94285 x [2/(8+2)] = 12.78857 % approximately.

The appropriate WACC or cost of capital to be used for the project is Tag Inc's WACC because the project is assumed to have the same capital structure as the firm undertaking it and the risks of the paper business are appropriately captured by using an asset beta from a paper's industry firm.