Question

Miller Corporation has a premium bond making semiannual payments. The bond has a coupon rate of 11 percent, a YTM of 9 percent, and 11 years to maturity. The Modigliani Company has a discount bond making semiannual payments. This bond has a coupon rate of 9 percent, a YTM of 11 percent, and also has 11 years to maturity. Both bonds have a par value of $1,000.

(a) What is the price of each bond today?
(b) If interest rates remain unchanged, what do you expect the price of these bonds to be 1 year from now? In 2 years? In 6 years? In 10 years? In 11 years?

Answer 1

a.

Miller Corporation Bond

Payment mode = Semiannually

Par Value = $1000

Coupon Rate = 11%

Coupon Payment = (11%/2)*1000 = $55

Time to Maturity = 11 years

YTM = 9%

Price of Bond = 55(P/A,4.5%,22) + 1000(P/F,4.5%,22)

Price of Bond = 55*13.7844 + 1000*0.3797

Price of Bond = $1137.842

Modigliani Company Bond

Payment mode = Semiannually

Par Value = $1000

Coupon Rate = 9%

Coupon Payment = (9%/2)*1000 = $45

Time to Maturity = 11 years

YTM = 11%

Price of Bond = 45(P/A,5.5%,22) + 1000(P/F,5.5%,22)

Price of Bond = 45*12.583 + 1000*0.3079

Price of Bond = $874.135

b.

1 year from now

Price of Miller Bond = 55(P/A,4.5%,20) + 1000(P/F,4.5%,20) = $1129.98

Price of Modigliani Bond = 45(P/A,5.5%,20) + 1000(P/F,5.5%,20) = $880.45

2 years from now

Price of Miller Bond = 55(P/A,4.5%,18) + 1000(P/F,4.5%,18) = $1149.06

Price of Modigliani Bond = 45(P/A,5.5%,18) + 1000(P/F,5.5%,18) = $887.47

6 years from now

Price of Miller Bond = 55(P/A,4.5%,10) + 1000(P/F,4.5%,10) = $1079.09

Price of Modigliani Bond = 45(P/A,5.5%,10) + 1000(P/F,5.5%,10) = $924.60

10 years from now

Price of Miller Bond = 55(P/A,4.5%,2) + 1000(P/F,4.5%,2) = $1018.70

Price of Modigliani Bond = 45(P/A,5.5%,2) + 1000(P/F,5.5%,2) = $981.483

11 years from now

Price of Miller Bond = 55 + 1000 = $1055

Price of Modigliani Bond = 45 + 1000 = $1045