Compute the cost of the capital for the firm for the following:?

a. A bond that has a $1,000 par value (face value) and a contract or coupon interest rate of 11.6%. The bonds have a current market value of $1,124 and will mature in 10 years. The firms marginal tax rate is 34%.
b. if the firms bonds are not frequently traded, how would you go about determining a cost of debt for this company?
c. A new common stock issue that paid a $1.74 dividend last year. The par value of the stock is $ 16, and the firm’s dividends per share have grown at a rate of 8.8% per year. This growth rate is expected to continue into the foreseeable future.
d. A bond selling to yield 12.4% for the purchaser of the bond. The borrowing firm faces a tax rate of 34%.

a. To compute the cost of capital for the bond, you need to calculate the yield to maturity (YTM) of the bond. YTM represents the total return anticipated on a bond if held until it matures, taking into account the bond's current market price, coupon payments, and time to maturity. In this case, the bond has a $1,000 par value, a coupon interest rate of 11.6%, a current market value of $1,124, and will mature in 10 years.

The formula to calculate YTM can be a bit complex, but fortunately, there are financial calculators or spreadsheet functions that can do the math for you. One common function used is the YIELD function in Excel or Google Sheets.

To calculate the YTM using the YIELD function in Excel or Google Sheets, you can use the following formula:

`=YIELD(settlement, maturity, rate, pr, redemption, frequency, [basis])`

where:
- `settlement`: The date the bond was purchased or settled.
- `maturity`: The maturity date of the bond.
- `rate`: The coupon interest rate of the bond.
- `pr`: The price or the current market value of the bond.
- `redemption`: The par value or the face value of the bond.
- `frequency`: The number of coupon payments per year.
- `[basis]` (optional): The day count basis or method for calculating the number of days between settlement and maturity.

In this case, you would input the following values into the YIELD function:

`=YIELD(settlement date, maturity date, coupon rate, price, par value, number of coupon payments per year)`

For example:
`=YIELD("01/01/2022", "01/01/2032", 11.6%, 1124, 1000, 1)`

After getting the YTM value from the YIELD function, you multiply it by (1 - tax rate) to account for the tax shield benefit of the interest expense. In this case, the tax rate is 34%, so you would multiply the YTM by (1 - 0.34) or 0.66 to get the after-tax cost of debt.

b. If the firm's bonds are not frequently traded, determining the cost of debt becomes a bit challenging. One approach to estimate the cost of debt in such a scenario is by comparing the yield on similar bonds from other companies in the same industry that are publicly traded or have recently issued bonds. The yield on those bonds can serve as a proxy for the cost of debt for the company you're analyzing.

Alternatively, another method involves estimating the credit spread over risk-free bonds that the company would have to pay due to its creditworthiness. This would require analyzing the company's financial statements, credit rating, and other available data to assess its credit risk and determine an appropriate credit spread.

c. To compute the cost of capital for the new common stock issue, you need to calculate the cost of equity. The cost of equity represents the return required by the company's equity investors (shareholders) to compensate them for the risk of investing in the stock.

One common method to estimate the cost of equity is by using the dividend growth model, also known as the Gordon Growth Model. The formula for the Gordon Growth Model is:

`Cost of Equity = (Dividend per Share / Stock Price) + Growth Rate of Dividends`

In this case, you are given the dividend per share ($1.74) and the growth rate of dividends (8.8%). To complete the calculation, you would divide the dividend per share by the stock price and add the growth rate of dividends.

For example, if the stock price is $16, the calculation would be as follows:

Cost of Equity = ($1.74 / $16) + 8.8%

d. To compute the cost of capital for the bond selling at a yield of 12.4%, you need to calculate the after-tax cost of debt. The after-tax cost of debt takes into account the tax shield benefit from deducting interest expense.

The formula to calculate the after-tax cost of debt is:

`After-tax Cost of Debt = Yield to Maturity × (1 - Tax Rate)`

In this case, the bond is selling to yield 12.4%, and the tax rate is 34%. To find the after-tax cost of debt, you would multiply the yield to maturity (12.4%) by (1 - 0.34) or 0.66.