47 HW Question 2 of 6 You did not receive full cre 1000 poin

47 HW Question 2 (of 6) You did not receive full cre 10.00 points Bond X is a premium bond making semiannual payments. The bond pays a coupon rate of 11 percent, has a YTM of 9 percent, and has 17 years to maturity. Bond Y is a discount bond making semiannual payments. This bond pays a coupon rate of 9 percent, has a YTM of 11 percent, and also has 17 years to maturity The bonds have a $1,000 par value. What is the price of each bond today? (Do not round intermediate calculations. Round your answers to 2 decimal places, e.g., 32.16.) Price of Bond X Price of Bond Y If interest rates remain unchanged, what do you expect the price of these bonds to be one year from now? In nine years? In 12 years? In 14 years? In 17 years? (Do not round intormediate calculations. Round your answers to 2 decimal places, o.g., 32.16.) Price of bond One year Nine years 12 years 14 years 17 years Bond X Bond Y Hints References eBook & Resources Hint #2

Solution

Bond X
Par value of Bond = $1000
Coupon rate = 11%, semi annual = 11%/ 2 = 5.5%
YTM = 9%, semi annual = 9%/2 = 4.5%
Years to maturity (n) = 17 year, semi annual = 17*2 = 34
Price of bond = Par value * PVIFA (r, nth ) + Interest * PVF (r,n )
Price of Bond X = $ 1000 * PVIFA( 5.5%, 34th) + $1000*4.5% * PVF(5.5%, 34 years)
= $1000 * 0.161963 + 45 * 15.23703
= $847.63

Bond Y
Par value of Bond = $1000
Coupon rate = 9%, semi annual = 9%/ 2 = 4.5%
YTM = 11%, semi annual = 11%/2 = 5.5%
Years to maturity (n) = 17 year, semi annual = 17*2 = 34
Price of bond = Par value * PVIFA (r, nth ) + Interest * PVF (r,n )
Price of Bond X = $ 1000 * PVIFA( 4.5%, 34th) + $1000*5.5% * PVF(4.5%, 34 years)
= $1000 * 0.223896 + 55 * 17.24676
= $1172.47

2.

Bond X
Price of bond = Par value * PVF (r, nth ) + Interest * PVIFA (r,n )

Price of Bond X

P₁= $ 1000 * ( PVIFA 5.5%, 32th) + $1000*4.5% * (PVIF 5.5%, 32 years)
P₁ = $1000 * 0.180269 + 45 * 14.9042
= $850.96

P₉= $ 1000 * ( PVIFA 5.5%, 16th) + $1000*4.5% * (PVIF 5.5%, 16 years)
P₉ = $1000 * 0.424581 + 45 * 10.46216
= $895.38

P₁₂= $ 1000 * ( PVIFA 5.5%, 10th) + $1000*4.5% * (PVIF 5.5%, 10 years)
P₁₂ = $1000 * 0.585431 + 45 * 7.537626
= $924.63

P₁₄ = $ 1000 * ( PVIFA 5.5%, 6th) + $1000*4.5% * (PVIF 5.5%, 6 years)
P₁₄ = $1000 * 0.725246 + 45 * 4.99553
= $950

P₁₇= $1000

Bond Y
Price of bond = Par value * PVF (r, nth ) + Interest * PVIFA (r,n )

Price of Bond Y

P₁= $ 1000 * ( PVIFA 4.5%, 32th) + $1000*5.5% * (PVIF 4.5%, 32 years)
P₁ = $1000 * 0.2445 + 55 * 16.78889
= $ 1167.89

P₉= $ 1000 * ( PVIFA 4.5%, 16th) + $1000*5.5% * (PVIF 4.5%, 16 years)
P₉ = $1112.34

P₁₂= $ 1000 * ( PVIFA 4.5%, 10th) + $1000*5.5% * (PVIF 4.5%, 10 years)
P₁₂ = 1079.12

P₁₄ = $ 1000 * ( PVIFA 4.5%, 6th) + $1000*5.5% * (PVIF 4.5%, 6 years)
P₁₄ = $ 1051.58

P₁₇= $1000

	Price of bond
Price of Bond X	847.63
Price of Bond Y	1172.47