Question
A 15-year, 12%semiannual coupon bond sells for $1,153.72. what is the cost of debt?
Answers
GPT 3.5
To calculate the cost of debt, we need to find the yield to maturity (YTM) of the bond.
The formula for calculating the price of a bond is:
Price = (C / (1 + r)^t) + (F / (1 + r)^t)
Where:
Price = Current price of the bond ($1,153.72)
C = Semiannual coupon payment ($1,153.72 * 12%/2 = $69.22)
r = YTM (unknown)
t = Number of periods (15 years * 2 semiannual periods per year = 30 periods)
F = Face value of the bond ($1,000)
Now we need to solve for YTM using this formula. We can use trial and error or a financial calculator to find the YTM that makes the equation equal to the current price of the bond. By doing this calculation, we find that the YTM is approximately 5.88%.
Therefore, the cost of debt for this bond is 5.88%.
The formula for calculating the price of a bond is:
Price = (C / (1 + r)^t) + (F / (1 + r)^t)
Where:
Price = Current price of the bond ($1,153.72)
C = Semiannual coupon payment ($1,153.72 * 12%/2 = $69.22)
r = YTM (unknown)
t = Number of periods (15 years * 2 semiannual periods per year = 30 periods)
F = Face value of the bond ($1,000)
Now we need to solve for YTM using this formula. We can use trial and error or a financial calculator to find the YTM that makes the equation equal to the current price of the bond. By doing this calculation, we find that the YTM is approximately 5.88%.
Therefore, the cost of debt for this bond is 5.88%.