Question

2. There are two bonds that a bond fund manager is considering. Bond A has a coupon rate of 5% and Bond B has a coupon rate of 8 %. Both bonds are paying interest semi-annually, have a par value of $1,000 anda maturity of 20 years. If the current YTM for both bonds is 6%, what is their current price? If the YTM changed to 7% , what would be their new current price? Which bond is more elastic to the change in interest rate? (15 pts)

Answer 1

Answer 2:

Bond A

Given that Coupon payment, $C$ = 0.05/2*1000 = 25, Yield to Maturity, $YTM$ = 6%/2 = 3%, Number of years, $n$ = 20*2 = 40 and Face value, $F$ = 1000

The current price, $P$ of bond A is calculated as follows

$P = C (PVIFA @ YTM, n) + F (PVIF @ YTM, n)$

$P = 25 (PVIFA @ 0.03, 40) + 1000 (PVIF @ 0.03, 40)$

$P = 25 \left ( \frac{1.03^{40}-1}{0.03*1.03^{40}} \right ) + 1000 (\frac{1}{1.03^{40}})$

P = 25 (23.1148) + 1000 (0.3066)

P = $884.43

Bond A

Given that Coupon payment, $C$ = 0.08/2*1000 = 40, Yield to Maturity, $YTM$ = 6%/2 = 3%, Number of years, $n$ = 20*2 = 40 and Face value, $F$ = 1000

The current price, $P$ of bond B is calculated as follows

$P = C (PVIFA @ YTM, n) + F (PVIF @ YTM, n)$

$P = 40 (PVIFA @ 0.03, 40) + 1000 (PVIF @ 0.03, 40)$

$P = 40 \left ( \frac{1.03^{40}-1}{0.03*1.03^{40}} \right ) + 1000 (\frac{1}{1.03^{40}})$

P = 40 (23.1148) + 1000 (0.3066)

P = $1231.15

When the YTM changed to 7%, the new price of the bonds are

Bond A

Given that Coupon payment, $C$ = 0.05/2*1000 = 25, Yield to Maturity, $YTM$ = 7%/2 = 3.5%, Number of years, $n$ = 20*2 = 40 and Face value, $F$ = 1000

The current price, $P$ of bond A is calculated as follows

$P = C (PVIFA @ YTM, n) + F (PVIF @ YTM, n)$

$P = 25 (PVIFA @ 0.035, 40) + 1000 (PVIF @ 0.035, 40)$

$P = 25 \left ( \frac{1.035^{40}-1}{0.035*1.035^{40}} \right ) + 1000 (\frac{1}{1.035^{40}})$

P = 25 (21.3551) + 1000 (0.2526)

P = $786.45

Bond A

Given that Coupon payment, $C$ = 0.08/2*1000 = 40, Yield to Maturity, $YTM$ = 7%/2 = 3.5%, Number of years, $n$ = 20*2 = 40 and Face value, $F$ = 1000

The current price, $P$ of bond B is calculated as follows

$P = C (PVIFA @ YTM, n) + F (PVIF @ YTM, n)$

$P = 40 (PVIFA @ 0.035, 40) + 1000 (PVIF @ 0.035, 40)$

$P = 40 \left ( \frac{1.035^{40}-1}{0.035*1.035^{40}} \right ) + 1000 (\frac{1}{1.035^{40}})$

P = 40 (21.3551) + 1000 (0.2526)

P = $1106.78

Bond B is more elastic to the change in interest rate as it's price reduces more compared to the price of bond A.