The Nutrex Corporation wants to calculate its weighted average cost of capital. Its target capital structure weights are 40 percent long-term debt and 60 percent common equity. The before tax cost of debt is estimated to be 10 percent and the company is in the 40 percent tax bracket. The expected return on the market is 13 percent and the firm's stock beta is 1.8.
a. What is Nutrex's cost of debt?
b. Estimate Nutrex's expected return on common equity using the security market line.
c. Calculate the after-tax weighted average cost of capital.
To answer these questions, we need to calculate the cost of debt (a), the expected return on common equity (b), and the after-tax weighted average cost of capital (c).
a. Cost of Debt:
The cost of debt is the before-tax cost of debt adjusted for taxes.
Formula:
Cost of Debt = Before-tax cost of debt * (1 - Tax rate)
Given:
Before-tax cost of debt = 10%
Tax rate = 40%
Calculation:
Cost of Debt = 10% * (1 - 0.40)
Cost of Debt = 10% * 0.60
Cost of Debt = 6%
So, the cost of debt for Nutrex Corporation is 6%.
b. Expected Return on Common Equity:
To estimate the expected return on common equity, we will use the Capital Asset Pricing Model (CAPM) and the given information about the expected return on the market (13%) and the firm's stock beta (1.8).
Formula:
Expected Return on Common Equity = Risk-Free Rate + Beta * (Expected Return on Market - Risk-Free Rate)
Given:
Expected Return on Market = 13%
Risk-Free Rate is not provided.
Beta = 1.8
We are missing the Risk-Free Rate in the formula. Typically, the risk-free rate is the yield on a government bond, such as a 10-year Treasury bond. However, since this information is not provided, we cannot calculate the expected return on common equity accurately.
c. After-tax Weighted Average Cost of Capital:
Weighted Average Cost of Capital (WACC) is the weighted average of the cost of debt and the cost of equity, adjusted for taxes.
Formula:
WACC = Weight of Debt * Cost of Debt * (1 - Tax rate) + Weight of Equity * Expected Return on Equity
Given:
Weight of Debt = 40%
Weight of Equity = 60%
Cost of Debt = 6% (calculated in part a)
Expected Return on Equity is not provided.
We are missing the Expected Return on Equity in the formula. Without this information, we cannot calculate the after-tax WACC accurately.