Question

Firm X has a beta of 1.3 and a debt-to-equity ratio of 0.7 .
It has deb with a coupon of 8%, face value of $1,000 and yield-to-maturity of 12%. It has chosen firm P as a proxy company for a new project it is considering in a totally different line of business from its present one. Firm P has a beta of 1.6 and debt-to-equity ratio of 0.4 and a bond with yield-to-maturity of 10%, a coupon of 12% and face value of $1,000.
Both firms are in the 40 percent marginal tax bracket. The expected return on the S&P is 13% and the rate on 90-day Treasury bill is 3%.
Find the required return on the new project that Firm X is considering. Show all formulae, steps and calculations neatly and in the proper sequence.

Answer 1

This question requires to calculate the required rate of return for a new project that Firm X wants to undertake. For this purpose, Firm X is using another Firm P as proxy. It is required that we calculate:

1. The Cost of Equity for Firm P
2. The Cost of Debt for Firm P
3. Finally, calculate Weighted Average Cost of Capital (WACC) using 1 and 2 above.

Step 1: Cost of Equity for Firm P: This will be calculated using Capital Asset Pricing Formula (CAPM) formula, which is:

Cost of Equity = Risk Free Rate (Rf) + Beta *(Market Rate of Return (Rm) - Risk Free Rate (Rf))

With reference to this question,

Beta = Beta of Firm P = 1.6

Risk Free Rate (Rf) = 90-day Treasury bill Rate as provided in question= 3% or 0.3

Market Rate of Return (Rm) = Expected return on the S&P as provided in question = 13% or 0.13

Using the CAPM formula and all the values above, the cost of equity is:

Calculation:

Cost of Equity = 0.03+ 1.6(.13-.03) = .19            i.e. 19%

Therefore, Cost of Equity = 19%

Step 2: Cost of Debt for Firm P:

The question provides the Coupon Rate that Firm P pays to the bond holders, which effectively is Cost of Debt.

Therefore, Cost of Debt = 12%

Step 3: Calculation of Weighted Average Cost of Capital (WACC).

To calculate WACC, the below formula is used:

Calculation for Market Value of Debt =

Assuming the debt is for 1 year maturity. The formula to calculate Market Value of Debt =

Coupon Rate (As provided in the question) = 0.12 i.e. 12%

Yield to Maturity (As provided in the question) = 0.1 i.e. 10%

Time Period = 1 year

Market Value of Debt = {0.12 / (1+0.1)^1} * 1000 = 0.1091*1000 = $ 1091

Therefore, Market Value of Debt = $ 1091

Calculation of Market Value of Equity =

Debt to Equity Ratio for Firm P = 0.4

Market Value of Equity = 1091 / 0.4 = $ 2727.5

Now we are ready with all the inputs to calculate WACC –

Cost of Equity = from Step 1: 19% or 0.19

Cost of Debt = from Step 2: 12% or 0.12

Market Value of Equity = $2727.5 (from above)

Market Value of Debt = $1091 (from above)

Market Value of Equity + Market Value of Debt = $2727.5 + $1091 = $3818.5

Corporate tax Rate = 40% or 0.4

Input all the values into the formula to calculate WACC:

Hence, The Required Rate of Return from new Project which Firm X wants to start = 15.63%