Question

The market value of XYZ Corporation's common stock is $40 million and the market value of its risk-free debt is $60 million. The beta of the company's common stock is 0.8, and the expected market risk premium is 10%. If the Treasury bill rate is 6%, what is the firm's cost of capital? (Assume no taxes.)

Answer 1

To calculate the firm's cost of capital, we use the Capital Asset Pricing Model to find the cost of equity and the risk-free rate for the cost of debt. With the weights of debt and equity calculated from their market values, the weighted average cost of capital (WACC) for XYZ Corporation is determined to be 9.2%.

Step-by-step explanation:

To determine the firm's cost of capital for XYZ Corporation, which has a market value of common stock at $40 million and risk-free debt at $60 million, we can use the Capital Asset Pricing Model (CAPM) for the equity portion and the risk-free rate for the debt portion. Since there are no taxes, the weight of debt does not need to be adjusted for tax benefits. The formula for CAPM for equity cost is:

Cost of Equity = risk-free rate + (beta × market risk premium)

For XYZ Corporation:

• Cost of Equity = 6% + (0.8 × 10%)
• Cost of Equity = 6% + 8%
• Cost of Equity = 14%

Since the debt is risk-free, its cost is simply the Treasury bill rate:

• Cost of Debt = 6%

We know the market values of debt and equity, so we can calculate their respective weights:

• Weight of Equity = $40 million / ($40 million + $60 million)
• Weight of Equity = 40%
• Weight of Debt = $60 million / ($40 million + $60 million)
• Weight of Debt = 60%

Finally, we can calculate the weighted average cost of capital (WACC):

• WACC = (Weight of Equity × Cost of Equity) + (Weight of Debt × Cost of Debt)
• WACC = (0.4 × 14%) + (0.6 × 6%)
• WACC = 5.6% + 3.6%
• WACC = 9.2%

Therefore, the firm’s cost of capital is 9.2%.

Answer 2

Answer: The cost of capital is 9.2%

Step-by-step explanation:

Given:

Common stock = $40 million

Market value = $60 million

Beta = 0.8

Market risk premium = 10%

Treasury bill rate = 6%

Here , we'll use the following formula to evaluate the firm's cost of capital:

Cost of capital = (Cost of debt × Weight of debt) + (Cost of equity × Weight of equity)

∵ Cost of equity = Risk - Rate + (Beta × Premium)

Cost of equity = 6 + (0.8×10)

Cost of equity = 0.14

Cost of equity = 14%

∵ Weight of equity =
`(Total\ equity)/(Total\ debt + Total\ Equity)`

Weight of equity =
`(40)/(60 + 40)`

Weight of equity = 0.40

∵ Weight of debt =
`(Total\ debt)/(Total\ debt + Total\ Equity)`

Weight of debt =
`(60)/(60 + 40)`

Weight of debt = 0.60

Putting these three variable in the above given equation:

Cost of capital = (6×0.60) + (14×0.40)

Cost of capital = 0.36 + 0.56

∴ Cost of capital = 0.092

∴ Cost of capital = 9.2%