P242 A firm issues a $10 million bond with a 6% coupon rate, 4-year maturity, and annual interst payments when market interest rates are 7% 8, if the market rate changes to 8%, the book value of the bonds at the end of the first period will be: A, $9,484,581 B, $9,661,279 c, $9,737,568 D, $9,745,959 the answer is c , it said the change in interest rates is ignored. changing N from 4 to 3 ,using 7% can get the answer. But I use 8% to calculate, the answer is A. Why we can ignore the change in interest rates? I feel confused about it.
The 8% is what the market/buyers needs to be paid to buy a newly issued security, with risks, cash flow, maturity similar to the existing bond. It has nothing to do with the book value of the debt for the company that issued it one year before.
good question though.
Remember that the book value of a debt at any time is the present value of the future amount(face value and coupoon) discounted at the market rate at the time it was issued.(I will find the page for you later as i’m at work right now). So any change in the market rate does not affect the book value of the initial debt. That being said you need to discounted 10millions at 7percent to have the present value of the face value, at that amount you need to add the present value of the coupon(present value of annuity due with interest=7% N=3 10000000/(1.07)^3 + 600000(1+[1-(1/(1.07)]/0.07) the sum should equal what you have for answers c. However change in Market rate are the main motivation for companies to refinance or call a debt. hope that helps
thanks