Question

PLEASE SHOW WORK. THANK YOU!

Bond A has the following terms:
•  Coupon rate of interest: 10 percent

•  Principal: $1,000

•  Term to maturity: 8 years

Bond B has the following terms:
•   Coupon rate of interest: 5 percent
•   Principal: $1,000
•   Term to maturity: 8 years

a. What should be the price of each bond if interest rates are 10 percent?
b. What will be the price of each bond if, after five years have elapsed, interest rates are 10 percent?
c. What will be the price of each bond if, after eight years have elapsed, interest rates are 8 percent?

Answer 1

The solution to Part a)

The price of a bond is the sum total of present values of all coupon payments and present value of maturity value.

Hence,

Bond A price at t₀ = PV of all coupon payments + PV of maturity value

PV of all coupon payments = (coupon payments) * cumulative discount factor for 8 years at the Interest rate (R) 10%

= (Principal Value * Coupon Rate ) * ( (1-1/(1+R)^N) / R )

= $ 100.00 * ((1- 1/(1+10%)⁸)/10%)

= $ 100.00 * 5.3349

= $ 533.49

PV of maturity value = Principal Value * discount factor for 8^th year at the Interest rate (R) 10%

= $ 1000 * (1/(1+R)^N)

= $ 1000 * (1/(1+10%)⁸)

= $ 1000 *   0.4665

= $ 466.51

Bond A price at t₀ = PV of all coupon payments + PV of maturity value

= $ 533.49 + $ 466.51 = $ 1000.00

Likewise,

Bond B price at t₀ = PV of all coupon payments + PV of maturity value

PV of all coupon payments = (coupon payments) * cumulative discount factor for 8 years at the Interest rate (R) 10%

= (Principal Value * Coupon Rate ) * ( (1-1/(1+R)^N) / R )

= $ 50.00 * ((1- 1/(1+10%)⁸)/10%)

= $ 50.00 * 5.3349

= $ 266.75

PV of maturity value = Principal Value * discount factor for 8^th year at the Interest rate (R) 10%

= $ 1000 * (1/(1+R)^N)

= $ 1000 * (1/(1+10%)⁸)

= $ 1000 *   0.4665

= $ 466.51

Bond B price at t₀ = PV of all coupon payments + PV of maturity value

= $ 266.75 + $ 466.51 = $ 733.25

The solution to Part B)

Now, the remaining life of Bond A & B will be 3 years as 5 years have lapsed

& R = 10%

Hence,

Bond A price at t₅ = PV of all coupon payments + PV of maturity value

PV of all coupon payments = (coupon payments) * cumulative discount factor for 3 years at the Interest rate (R) 10%

= (Principal Value * Coupon Rate ) * ( (1-1/(1+R)^N) / R )

= $ 100.00 * ((1- 1/(1+10%)³)/10%)

= $ 100.00 * 2.4869

= $ 248.69

PV of maturity value = Principal Value * discount factor for 3^rd year at the Interest rate (R) 10%

= $ 1000 * (1/(1+R)^N)

= $ 1000 * (1/(1+10%)³)

= $ 1000 *   0.7513

= $ 751.31

Bond A price at t₅ = PV of all coupon payments + PV of maturity value

= $ 248.69 + $ 751.31 = $ 1000.00

Likewise,

Bond B price at t₅ = PV of all coupon payments + PV of maturity value

PV of all coupon payments = (coupon payments) * cumulative discount factor for 3 years at the Interest rate (R) 10%

= (Principal Value * Coupon Rate ) * ( (1-1/(1+R)^N) / R )

= $ 50.00 * ((1- 1/(1+10%)³)/10%)

= $ 50.00 * 2.4869

= $ 124.34

PV of maturity value = Principal Value * discount factor for 3^rd year at the Interest rate (R) 10%

= $ 1000 * (1/(1+R)^N)

= $ 1000 * (1/(1+10%)³)

= $ 1000 *   0.7513

= $ 751.31

Bond B price at t₅ = PV of all coupon payments + PV of maturity value

= $ 124.34 + $ 751.31 = $ 875.65