Question

(5 marks) sua corporation has a premium band making semiannual payments. The band pays a percent coupon, has a YTM of 7 percent and has 13 years to matunty Modighan Company has a discount bond making semiannual payments. This bond pays a 7 percent coupon, has a YTM of 9 percent, and also has 13 years lo maturity interest rates remain unchanged, what do you expect the price of these bonds to be (a) 1 year from now? (b) in 3 years? (c) in 8 years? (d) In 12 years? (e) What's going on here? (15 marks) Total (20 marks)

Answer 1

Here we are finding the YTM of semiannual coupon bonds for various maturity lengths. The Bond price equation is

P = C(PVIFA_R%,t) + $1000(PVIF_R%,t)

Kawesha Corporation Bond

Semiannual Interest Payment = ($1000*9%)2 = 45

P₀ = $45(PVIFA_3.5%,26) + $1000(PVIF_3.5%,26) = 1168.90

P₁ = $45(PVIFA_3.5%,24) + $1000(PVIF_3.5%,24) = 1160.58

P₃ = $45(PVIFA_3.5%,20) + $1000(PVIF_3.5%,20) = 1142.12

P₈ = $45(PVIFA_3.5%,10) + $1000(PVIF_3.5%,10) = 1083.17

P₁₂ = $45(PVIFA_3.5%,2) + $1000(PVIF_3.5%,2) = 1019

P13 = 1000

Modigliani Company bond

Semiannual interest payment = ($1000*7%)/2 = 35

P₀ = $35(PVIFA_4.5%,26) + $1000(PVIF_4.5%,26) = 848.53

P₁ = $35(PVIFA_4.5%,24) + $1000(PVIF_4.5%,24) = 855.05

P₃ = $35(PVIFA_4.5%,20) + $1000(PVIF_4.5%,20) = 869.92

P₈ = $35(PVIFA_4.5%,10) + $1000(PVIF_4.5%,10) = 920.87

P₁₂ = $35(PVIFA_4.5%,2) + $1000(PVIF_4.5%,2) = 981.27

P13 = 1000

(e) All else held equal, the premium over par value for a premium bond declines as maturity approaches, and the discount from par value for a discount bond declines as maturity approaches. This is called “pull to par.”

Also, notice that the price of each bond when no time is left to maturity is the par value, even though the purchaser would receive the par value plus the coupon payment immediately. This is because we calculate the clean price of the bond.