a. The value of a $1000 par value McDonald's Corporation bond for 10% required rates of return is approximately $914.43.
b. The value of a $1000 par value McDonald's Corporation bond for 8.875% required rates of return is approximately $1,000.00.
c. The value of a $1000 par value McDonald's Corporation bond for 6% required rates of return is approximately $1,279.22.
Explanation:
Note: This question is note complete. The complete question is therefore provided before answering the question as follows:
McDonald's Corporation has 8
% (8.875%) bonds that mature in 15 years. What is the value of a $1000 par value McDonald's Corporation bond for each of the following required rates of return assuming the investor will hold the bond to maturity assume the coupon is paid annually?
a. 10%
b. 8.875%
c. 6%
The explanation to the answer is now given as follows:
a. The value at 10% annual required rate
Annual coupon = Bond face value * Coupon rate = $1000 * 8.875% = $88.75
Annual coupon discount factor = ((1 - (1 / (1 + r))^n) / r) .......... (1)
Where;
r = Annual required interest rate = 10%, or 0.10
n = number of years = 15
Substituting the values into equation (1), we have:
Annual coupon discount factor = ((1-(1/(1 + 0.10))^15) / 0.10) = 7.60607950630837
Present value of coupon = (Annual coupon * Annual coupon discount factor) = $88.75 * 7.60607950630837 = $675.039556184868
Present value of the face value of the bond = Face value / (1 + r)^n = $1,000 / (1 + 0.10)^15 = $239.392049369163
Therefore, we have:
Current bond value = Present value coupon + Present value of the face value of the bond = $675.039556184868 + $239.392049369163 = $914.431605554031
Approximating to 2 decimal places, we have:
Current bond value = $914.43
Therefore, the value of a $1000 par value McDonald's Corporation bond for 10% required rates of return is approximately $914.43.
b. The value at 8.875% annual required rate
Annual coupon = Bond face value * Coupon rate = $1000 * 8.875% = $88.75
Annual coupon discount factor = ((1 - (1 / (1 + r))^n) / r) .......... (1)
Where;
r = Annual required interest rate = 8.875%, or 0.08875
n = number of years = 15
Substituting the values into equation (1), we have:
Annual coupon discount factor = ((1-(1/(1 + 0.08875))^15) / 0.08875) = 8.12051595946604
Present value of coupon = (Annual coupon * Annual coupon discount factor) = $88.75 * 8.12051595946604 = $720.695791402611
Present value of the face value of the bond = Face value / (1 + r)^n = $1,000 / (1 + 0.08875)^15 = $279.304208597388
Therefore, we have:
Current bond value = Present value coupon + Present value of the face value of the bond = $720.695791402611 + $279.304208597388 = $999.999999999999
Approximating to 2 decimal places, we have:
Current bond value = $1,000.00
Therefore, the value of a $1000 par value McDonald's Corporation bond for 8.875% required rates of return is approximately $1,000.00.
c. The value at 6% annual required rate
Annual coupon = Bond face value * Coupon rate = $1000 * 8.875% = $88.75
Annual coupon discount factor = ((1 - (1 / (1 + r))^n) / r) .......... (1)
Where;
r = Annual required interest rate = 6%, or 0.06
n = number of years = 15
Substituting the values into equation (1), we have:
Annual coupon discount factor = ((1-(1/(1 + 0.06))^15) / 0.06) = 9.712248987741
Present value of coupon = (Annual coupon * Annual coupon discount factor) = $88.75 * 9.712248987741 = $861.962097662014
Present value of the face value of the bond = Face value / (1 + r)^n = $1,000 / (1 + 0.06)^15 = $417.26506073554
Therefore, we have:
Current bond value = Present value coupon + Present value of the face value of the bond = $861.962097662014 + $417.26506073554 = $1,279.22715839755
Approximating to 2 decimal places, we have:
Current bond value = $1,279.23
Therefore, the value of a $1000 par value McDonald's Corporation bond for 6% required rates of return is approximately $1,279.22.
