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Sagot :
Answer:
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
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