Question

Both Bond Sam and Bond Dave have 9 percent coupons, make semiannual payments, and are priced at par value. Bond Sam has 5 years to maturity, whereas Bond Dave has 18 years to maturity.

1) If interest rates suddenly rise by 4 percent, what is the percentage change in the price of Bond Sam?

2) If interest rates suddenly rise by 4 percent, what is the percentage change in the price of Bond Dave?

3) If rates were to suddenly fall by 4 percent instead, what would the percentage change in the price of Bond Sam be then?

4) If rates were to suddenly fall by 4 percent instead, what would the percentage change in the price of Bond Dave be then?

Answer 1

Solution: Part a: Bond Sam calculation of price at YTM of 13% (i.e 9+4%) Par value semi annual coupon rate = 9%/2 semi annual yield to maturity = 13%/2 Number of payments = 5*2 1000 4.50% 6.50% PV of bond = PV of interest + PV of maturity PV of interest Semi annual interest = 1000*4.5% X PVIFA(6.5%,10)** PV of interest 45.00 7.18883 323.50 PV of maturity value Par value X PVIF(6.5%, 10)** PV of maturity value 1,000.00 0.53273 532.73 PV of bond/Price of bond 856.22 7.18883 **PVIFA(6.5%,10) formula |(1-(1.0651-10/0.065 (1-(1+r)^-n/r 1/(1.065410) 0.53273 ***PVIF(6.5%,10) formula = 1/(1+r)^n -14.38% % change in price (856.22-1000)/1000

Bond Dave calculation of price at YTM of 13% (i.e 9+4%) Par value semi annual coupon rate = 9%/2 semi annual yield to maturity = 13%/2 Number of payments = 18*2 1000 4.50% 6.50% 36 PV of bond = PV of interest + PV of maturity PV of interest Semi annual interest = 1000*4.5% 45.00 13.79057 PV of interest 620.58 PV of maturity value Par value X PVIF(6.5%,36)** PV of maturity value 1,000.00 0.10361 103.61 PV of bond/Price of bond 724.19 13.79057 **PVIFA(6.5%,36) formula (1-(1.0651-36)}/0.065 (1-(1+r)^-n)/ 1/(1.065436) 0.10361 ***PVIF(6.5%,36) formula = 1/(1+r)^n -27.58% % change in price (724.19-1000)/1000

Part b: Bond Sam calculation of price at YTM of 5% (i.e 9-4%) Par value semi annual coupon rate = 9%/2 semi annual yield to maturity = 5%/2 Number of payments = 5*2 1000 4.50% 2.50% 10 PV of bond = PV of interest + PV of maturity PV of interest Semi annual interest = 1000*4.5% X PVIFA(2.5%,10)** PV of interest 45.00 8.75206 393.84 PV of maturity value Par value X PVIF(2.5%, 10)** PV of maturity value 1,000.00 0.78120 781.20 PV of bond/Price of bond 1,175.04 | 8.75206 **PVIFA(2.5%, 10) formula (1-(1.0254-10))/0.025 (1-(1+r)^-n)/r 1/(1.025410) 0.78120 ***PVIF(2.5%,10) formula = 1/(1+r)^n 17.50% % change in price (1175.04-1000/1000

Bond Dave calculation of price at YTM of 5% (i.e 9-4%) Par value semi annual coupon rate = 9%/2 semi annual yield to maturity = 5%/2 Number of payments = 18*2 1000 4.50% 2.50% PV of bond = PV of interest + PV of maturity PV of interest Semi annual interest = 1000*4.5% x PVIFA(2.5%,36)** PV of interest 45.00 23.55625 1,060.03 PV of maturity value Par value X PVIF(2.5%,36)** PV of maturity value 1,000.00 0.41109 411.09 PV of bond/Price of bond 1,471.13 **PVIFA(2.5%,36) | 23.55625 (1-(1.0254-36)}/0.025 (1-(1+r)^-n)/r 1/(1.025436) 0.41109 ***PVIF(2.5%,36) formula = 1/(1+r)^n 47.11% % change in price (1471.13-1000/1000