a bond that has a $ 1,000 par value ((face value)) and a coupon interest rate of 10.1% the bonds have a current market value of $1,127 and will mature in 10 years the firm's marginal tax rate is 34% the cost of capital from this debt is %
a bond that has a $1,000 par value (face value)and a coupon interest rate of 10.1% the bonds have a current market of $1,127 and will mature in 10 years the firm marginal tax rate is 34% the cost of capital from this debt is
To find the cost of capital from this debt, we need to calculate the yield to maturity (YTM).
The yield to maturity is the total return anticipated on a bond if it is held until it matures. It takes into account the bond's current market value, par value, coupon payment, and time to maturity.
First, let's calculate the annual coupon payment using the coupon interest rate and the par value:
Coupon payment = Coupon interest rate * Par value
Coupon payment = 10.1% * $1,000
Coupon payment = $101
Next, we need to determine the number of coupon payments remaining until maturity. Since the bond will mature in 10 years and pays coupons annually, the number of coupon payments remaining is also 10.
The yield to maturity can be calculated using a financial calculator or spreadsheet software. However, if you do not have access to these tools, you can use an approximation method called trial and error.
1. We assume a YTM value.
2. Calculate the bond price using the assumed YTM value.
3. Compare the calculated bond price with the market value.
- If the calculated bond price is higher than the market value, reduce the assumed YTM value.
- If the calculated bond price is lower than the market value, increase the assumed YTM value.
4. Repeat steps 2 and 3 until the calculated bond price is very close to the market value.
Let's start with an assumed YTM value of 10% and see if it gets us close to the market value.
Using the assumed YTM of 10%, we can calculate the present value of the future cash flows:
PV = Coupon payment / (1 + YTM)^1 + Coupon payment / (1 + YTM)^2 + ... + Coupon payment / (1 + YTM)^n + Par value / (1 + YTM)^n
PV = $101 / (1 + 10%)^1 + $101 / (1 + 10%)^2 + ... + $101 / (1 + 10%)^10 + $1,000 / (1 + 10%)^10
Calculating this equation will give us the present value (PV) of the bond.
Now, we compare the calculated present value (PV) with the market value ($1,127).
If the calculated PV is higher than the market value, we need to reduce our assumed YTM value and repeat these steps. If the calculated PV is lower than the market value, we need to increase our assumed YTM value and repeat these steps.
We repeat this trial and error process until we get the calculated present value (PV) very close to the market value ($1,127).
Finally, once we have the YTM value, we can use it as the cost of capital from this debt.