im trying to calculate cost of debt. where did they get the 50 value from? P0 = $1,080 = $50(PVIFA,R%,46) + $1,000(PVIF,R%,46)
30 year bond, 10% semi annual. 7 years ago it was issued. current selling is 108% face value.
To calculate the cost of debt, you need to use the formula for present value of annuity factor (PVIFA) and present value factor (PVIF).
In the given equation: P0 = $1,080 = $50(PVIFA,R%,46) + $1,000(PVIF,R%,46)
The $50 represents the semi-annual coupon payment. It is consistent with the information provided that the bond pays a 10% coupon rate semi-annually on a $1,000 face value bond. The coupon payment is calculated by multiplying the face value of $1,000 by the coupon rate of 10%, and then dividing it by 2 because it is paid semi-annually.
The value of 46 represents the number of semi-annual coupon payments left until the bond reaches maturity. You mentioned that the bond has a 30-year term, which means it has a total of 60 semi-annual coupon payments (30 years multiplied by 2 since it pays semi-annually). Since the bond was issued 7 years ago, we subtract 7 from 60 to get 46 semi-annual coupon payments remaining.
By solving the equation, you can calculate the value for the interest rate (R%) using financial calculators or Excel spreadsheets, which will give you the cost of debt.