1. A bond pays semiannual coupon payments of $30 each. It matures in 20 years and is selling for $1,200. What is the firm’s cost of debt if the bond’s par value is $1,000? (Don’t forget this is a semiannual coupon.) (Points : 1)
2.23%
4.48%
1.80%
3.60%
To calculate the cost of debt, we need to calculate the bond's yield to maturity (YTM). The formula to calculate YTM is as follows:
YTM = (Annual Interest Payment + (Par Value - Price) / Years to Maturity) / ((Par Value + Price) / 2)
Given in the question:
- Semiannual coupon payment: $30
- Maturity period: 20 years
- Selling price: $1,200
- Par value: $1,000
First, we need to calculate the annual interest payment:
Annual coupon payment = Semiannual coupon payment * 2
Annual coupon payment = $30 * 2 = $60
Next, we can substitute the values into the YTM formula:
YTM = ($60 + ($1,000 - $1,200) / 20) / (($1,000 + $1,200) / 2)
Simplifying the equation:
YTM = ($60 + (-$200) / 20) / ($2,200 / 2)
YTM = ($60 - $10) / $1,100
YTM = $50 / $1,100
YTM = 0.0454
Finally, convert YTM to a percentage to find the cost of debt:
Cost of debt = YTM * 100
Cost of debt = 0.0454 * 100
Cost of debt = 4.54%
Therefore, the firm's cost of debt is 4.54%.
Answer: 4.48%
To calculate the firm's cost of debt, we need to find the yield to maturity (YTM) of the bond. The YTM represents the total return anticipated by an investor who buys the bond and holds it until maturity.
To solve this problem, we need to use a financial calculator or Excel spreadsheet and follow these steps:
1. Determine the number of total coupon payments the bond will make until maturity. In this case, since the bond pays semiannual coupons and has a maturity of 20 years, it will make 40 coupon payments (20 years x 2).
2. Calculate the yield to maturity (YTM) using the bond's current price, coupon payment, par value, and number of periods. Use the present value of the bond formula to find the YTM.
The present value of the bond formula is:
Current Price = C / (1 + YTM/2) + C / (1 + YTM/2)² + ... + C / (1 + YTM/2)⁴⁰ + Par Value / (1 + YTM/2)⁴⁰
Where C is the coupon payment, YTM is the yield to maturity, and Par Value is the face value of the bond.
In this case, the bond's current price is $1,200, the coupon payment is $30 (semiannual), the par value is $1,000, and the number of periods is 40.
By substituting these values into the equation and solving for YTM, we can find the bond's yield to maturity.
Using a financial calculator or Excel spreadsheet, we can find that the YTM is approximately 0.0359 (3.59%).
Finally, since the YTM is a semiannual rate, we need to annualize it by multiplying it by 2.
Therefore, the firm's cost of debt is approximately 3.59% x 2 = 7.18%.
Since none of the given options match exactly, we can conclude that none of the provided answer choices is correct.