J&J Manufacturing just issued a bond with a $1,000 face value and a coupon rate of 8%. If the bond has a life of 20 years, pays annual coupons, and the yield to maturity is 7.5%, what percent of the bond’s total price is represented by the present value of the coupons?
- A) 7%
- B) 1%
- C) 6%
- D) 2%
E) 100.0%
Answer: C
Response:
Using the TVOM keystrokes above, you get the price of around $1,051.
Now, in this problem, you must calculate the value of the annuity stream (the interest payments or coupons) and divide that into the bond price. Recall that the total bond value is comprised of the PV of the coupons plus the PV of the maturity payoff of $1000.
Keystrokes for the PV of the coupons? 80 PMT, 7.5 I/Y, 20 N, CPT PV = -815.56. Divide that into 1051 and you get $815.56 / 1,050.97 = 77.6%.
