An investor has two bonds in her portfolio, Bond C and Bond Z. Each bond matures in 4 years, has a face value of $1,000, and has a yield to maturity of 9.1%. Bond C pays a 11.5% annual coupon, while Bond Z is a zero coupon bond. Required:
Assuming that the yield to maturity of each bond remains at 9.1% over the next 4 years, calculate the price of the bonds at each of the following years to maturity.

Years to Maturity                Bond C Price            Bond Z Price  

             4                                  $1,077.58                  $705.83

             3                                  $1,060.64                  $770.06

             2                                  $1,042.16                   $840.14

             1                                   $1,022.00                  $916.59

             0                                  $1,000.00               $1,000.00

Explanation:

Note: The complete requirement of this question is to calculate the price of the bonds at each of the following years to maturity:

Years to Maturity                Bond C Price                   Bond Z Price

4

3

2

1

0

The explanation of the answer is now given as follows:

Step 1: Calculations of Bond C Prices for each Years to Maturity

a. Calculation of Bond A Price for 4 Years to Maturity                

Annual coupon = face value * Annual coupon rate = $1,000 * 11.5% = $115

Annual coupon discount factor = ((1-(1/(1 + r))^n)/r)

Where;

r = yield to maturity = 9.1%, or 0.091

n = number of period or years to maturity = 4

Annual coupon discount factor = ((1-(1/(1 + 0.091))^4)/0.091) = 3.23262156846014

PV of coupon = Annual coupon * Annual coupon discount factor = $115 * 3.23262156846014 = $371.751480372917

PV of the face value of the bond = Face value / (1 + r)^n = $1000 / (1 + 0.091)^4 = $705.831437270127

Therefore, we have:

Price of Bond C in Year 4 = PV of coupon + PV of the face value of the bond = $371.751480372917 + $705.831437270127= $1,077.58

b. Calculation of Bond C Price for 3 Years to Maturity               

Annual coupon = face value * Annual coupon rate = $1,000 * 11.5% = $115

Annual coupon discount factor = ((1-(1/(1 + 0.091))^3)/0.091) = 2.52679013119002

PV of coupon = Annual coupon * Annual coupon discount factor = $115 * 2.52679013119002 = $290.580865086852

PV of the face value of the bond = Face value / (1 + r)^n = $1000 / (1 + 0.091)^3 = $770.062098061708

Therefore, we have:

Price of Bond C in Year 3 = PV of coupon + PV of the face value of the bond = $290.580865086852 + $770.062098061708 = $1,060.64

c. Calculation of Bond C Price for 2 Years to Maturity               

Annual coupon = face value * Annual coupon rate = $1,000 * 11.5% = $115

Annual coupon discount factor = ((1-(1/(1 + 0.091))^2)/0.091) = 1.75672803312831

PV of coupon = Annual coupon * Annual coupon discount factor = $115 * 1.75672803312831= $202.023723809756

PV of the face value of the bond = Face value / (1 + r)^n = $1000 / (1 + 0.091)^2 = $840.137748985324

Therefore, we have:

Price of Bond C in Year 2 = PV of coupon + PV of the face value of the bond = $202.023723809756 + $840.137748985324 = $1,042.16

d. Calculation of Bond C Price for 1 Year to Maturity                

Annual coupon = face value * Annual coupon rate = $1,000 * 11.5% = $115

Annual coupon discount factor = ((1-(1/(1 + 0.091))^1)/0.091) = 0.916590284142987

PV of coupon = Annual coupon * Annual coupon discount factor = $115 * 0.916590284142987 = $105.407882676444

PV of the face value of the bond = Face value / (1 + r)^n = $1000 / (1 + 0.091)^1 = $916.590284142988

Therefore, we have:

Price of Bond C in Year 1 = PV of coupon + PV of the face value of the bond = $105.407882676444 + $916.590284142988 = $1,022.00

e. Calculation of Bond A Price for 0 Years to Maturity               

Price of Bond C in Year 0 = Bond face value = $1,000

Step 2: Calculations of Bond Z Prices for each Years to Maturity

Since Bond Z is a zero coupon bond, we have:

f. Calculation of Bond Z Price for 4 Years to Maturity              

Price of Bond Z in Year 4 = Face value / (1 + r)^n = $1000 / (1 + 0.091)^4 = $705.83

g. Calculation of Bond Z Price for 3 Years to Maturity                

Price of Bond Z in Year 3 = Face value / (1 + r)^n = $1000 / (1 + 0.091)^3 = $770.06

h. Calculation of Bond Z Price for 2 Years to Maturity                

Price of Bond Z in Year 2 = Face value / (1 + r)^n = $1000 / (1 + 0.091)^2 = $840.14

i. Calculation of Bond Z Price for 1 Year to Maturity                

Price of Bond Z in Year 1 = Face value / (1 + r)^n = $1000 / (1 + 0.091)^1 = $916.59

j. Calculation of Bond Z Price for 0 Years to Maturity                

Price of Bond Z in Year 0 = Bond face value = $1,000