Suppose a company will issue new 5 year debt with a face value of $1000 and a coupon rate of 8 percent, paid annually.If the issuing price is $1080 and the tax rate is 40 percent.what is the after-tax cost of debt?If the expected rate of return of the company’s common stock is 18 percent and the company’s target capital structure is 3:7. What is the firm’s WACC?

To calculate the after-tax cost of debt, we first need to find the after-tax cost of interest payments. The formula to calculate this is:

After-tax cost of debt = Coupon rate × (1 - Tax rate)

Given that the coupon rate is 8% and the tax rate is 40%, we can calculate the after-tax cost of debt:

After-tax cost of debt = 0.08 × (1 - 0.40) = 0.08 × 0.60 = 0.048 or 4.8%

Next, to calculate the firm's Weighted Average Cost of Capital (WACC), we need to consider the weight of debt and equity in the capital structure.

Given that the target capital structure is 3:7 (debt to equity ratio), we can calculate the weights as follows:

Weight of debt = 3 / (3 + 7) = 0.3 or 30%
Weight of equity = 7 / (3 + 7) = 0.7 or 70%

The cost of debt is already calculated as 4.8%. The cost of equity is given as 18%.

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

WACC = (0.3 × 0.048) + (0.7 × 0.18)
WACC = 0.0144 + 0.126
WACC = 0.1404 or 14.04%

Therefore, the firm's Weighted Average Cost of Capital (WACC) is 14.04%.

To determine the after-tax cost of debt, we need to first calculate the interest expense and then apply the tax rate.

1. Interest expense:
The coupon rate of the debt is 8%, which means the company will pay $80 as interest each year ($1000 * 8%).

2. Tax savings:
The interest expense is tax-deductible, so the company will save taxes on the interest payment. The tax savings can be calculated as: Tax savings = Interest expense * Tax rate.
In this case, the tax rate is 40%, so the tax savings would be $32 ($80 * 0.4).

3. After-tax cost of debt:
To calculate the after-tax cost of debt, we subtract the tax savings from the issuing price and divide it by the face value:
After-tax cost of debt = (Issuing price - Tax savings) / Face value.
In this scenario, the issuing price is $1080, and the face value is $1000.
After-tax cost of debt = ($1080 - $32) / $1000 = $1048 / $1000 = 1.048, or 10.48%.

Moving on to the calculation of the firm's weighted average cost of capital (WACC):

1. Cost of equity:
The cost of equity is the expected rate of return on the company's common stock, which is given as 18%.

2. Cost of debt:
We have already calculated the after-tax cost of debt, which is 10.48%.

3. Weighted average cost of capital (WACC):
The WACC is calculated using the target capital structure, which is the proportion of debt and equity in the company's capital structure.
In this case, the target capital structure is 3:7, which means the weight of debt is 3/10 and the weight of equity is 7/10.

WACC = (Weight of debt * Cost of debt) + (Weight of equity * Cost of equity).
WACC = (3/10 * 10.48%) + (7/10 * 18%).

Calculating this equation will give you the firm's WACC, which represents the average rate of return required by the company's investors to finance its operations and investments.