Question

Bond X is a premium bond making semiannual payments. The bond pays a coupon rate of 10 percent, has a YTM of 8 percent, and has 14 years to maturity. Bond Y is a discount bond making semiannual payments. This bond pays a coupon rate of 8 percent, has a YTM of 10 percent, and also has 14 years to maturity. The bonds have a $1,000 par value. What is the price of each bond today? If interest rates remain unchanged, what do you expect the price of these bonds to be one year from now? In four years? In nine years? In 13 years? In 14 years? (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.)

Answer 1

BOND X

current price of bond X:

PV of face value = $1,000 / (1 + 4%)²⁸ = $333.48

PV of coupon payments = $50 x 16.66306 (PV annuity factor, 4%, 26 periods) = $833.15

market price = $1,166.63

price of bond X in 1 year:

PV of face value = $1,000 / (1 + 4%)²⁶ = $360.69

PV of coupon payments = $50 x 15.98277 (PV annuity factor, 4%, 28 periods) = $799.14

market price = $1,159.83

price of bond X in 4 years:

PV of face value = $1,000 / (1 + 4%)²⁰ = $456.39

PV of coupon payments = $50 x 13.59033 (PV annuity factor, 4%, 20 periods) = $679.52

market price = $1,135.91

price of bond X in 9 years:

PV of face value = $1,000 / (1 + 4%)¹⁰ = $675.56

PV of coupon payments = $50 x 8.11090 (PV annuity factor, 4%, 10 periods) = $405.55

market price = $1,081.11

price of bond X in 13 years:

PV of face value = $1,000 / (1 + 4%)² = $924.56

PV of coupon payments = $50 x 1.88609 (PV annuity factor, 4%, 2 periods) = $94.30

market price = $1,018.86

price of bond X in 14 years:

$1,000 + $50 =$1,050

BOND Y

current price of bond Y:

PV of face value = $1,000 / (1 + 5%)²⁸ = $255.09

PV of coupon payments = $40 x 14.89813 (PV annuity factor, 5%, 26 periods) = $595.93

market price = $851.02

price of bond Y in 1 year:

PV of face value = $1,000 / (1 + 5%)²⁶ = $281.24

PV of coupon payments = $40 x 14.37519 (PV annuity factor, 5%, 28 periods) = $575.01

market price = $856.25

price of bond Y in 4 years:

PV of face value = $1,000 / (1 + 5%)²⁰ = $376.89

PV of coupon payments = $40 x 12.46221 (PV annuity factor, 5%, 20 periods) = $498.49

market price = $875.38

price of bond Y in 9 years:

PV of face value = $1,000 / (1 + 5%)¹⁰ = $613.91

PV of coupon payments = $40 x 7.72173 (PV annuity factor, 5%, 10 periods) = $308.87

market price = $922.78

price of bond Y in 13 years:

PV of face value = $1,000 / (1 + 5%)² = $907.03

PV of coupon payments = $40 x 1.85941 (PV annuity factor, 5%, 2 periods) = $74.38

market price = $981.41

price of bond Y in 14 years:

$1,000 + $40 =$1,040