Discover the answers you need at Westonci.ca, a dynamic Q&A platform where knowledge is shared freely by a community of experts. Connect with a community of experts ready to provide precise solutions to your questions on our user-friendly Q&A platform. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.
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
Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. We're dedicated to helping you find the answers you need at Westonci.ca. Don't hesitate to return for more.
