Question

QUESTION 15 Acme issues a $300,000 bond with a 5% coupon payment with a maturity of 20 years. The bond is issued at 97%, but callable after five years at 103. Assuming it is called after five years at 103, what is the total interest expense for the bond issue? O a. $309,000 b. $93,000. O c. $90,750 d. $75,000.

Answer 1

15.

The bond is sold at a discount oof 97% i.e. 97% of $300000 = $291000

Therefore , Discount given = $300000 -$291000 =$9000

Each year from year 1-5 there is a coupon payment of 5% of face value = 5% of $300000 = $15000 for five years

Finally, the bond is called at 103 i.e. 103% of $300000 = $309,000

Premium paid for calling = $309000-$300000= $9000

Therefore, total interest expense in five years

= discount given + interest payments + premium paid for calling

= 9000+ 5*15000 + 9000 = $93000 (option b)

For Benson bond (assuming a par value of $1000 ) with 1% coupon payment paid semiannually for 22 years, we get 44 coupon payments of $ 5 spaced 6 months apart and $1000 redemption value at end of 22 years. Discount rate for 6 month period is half of YTM ie. 3.5%/2 = 1.75%

Therefore the Value of the bond can be ascertained as equal to the present value of the future cash flows

V = PV of 1st cash flow+ PV of 2nd cash flow +....+ PV of 44th Cashflow + PV of Redemption value

= 5/(1+0.0175)¹ + 5/(1+0.0175)²+.....+5/(1+0.0175)⁴⁴+ 1000/(1+0.0175)⁴⁴

Applying sum of GP formula   

= 5/0.0175 * (1- (1/1.0175)⁴⁴) + 1000/1.0175⁴⁴

= 152.54 + 466.11

= $618.65 (option d)