Question

Finance 325: Chapter 7 Homework All bonds are semi-annual. All yield measures are stated as annual percentage rates. 6. Suppose you buy a 30 year bond that pays a 6% coupon for the first 15 years and a 8% coupon for the last 15 years. The YTM of this bond is 7%. What is the price of the bond?

Answer 1

Present Value of coupons for first 15 years = Coupon * PVAF (3.5%, 30 periods)

Coupon = 6% /2 = 3% * 1000 = 30

YTM semi annual = 7% /2 = 0.035

periods = 15 years * 2 = 30

= 30 * 18.3920454089

= 551.761362267

Present Value of coupons for last 15 years = Coupon * PVAF (3.5%, 30th - 60th periods)

Coupon = 8% /2 = 4% * 1000 = 40

YTM semi annual = 7% /2 = 0.035

periods = 15 years * 2 = 30

= 40 * 6.55268870336

= 262.107548134

Present Value of Face value after 30 years = 1000 / (1+r)^n

r = 0.035

n = 30 years * 2 = 60

= 1000 / (1+0.035)^60

= 126.93430573

Total value of Bond =  551.761362267 + 262.107548134 + 126.93430573 = 940.80

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