Answer:
a) The value of one bond is $837.08.
b) The total amount Tim Horton would raise if all bonds were sold is $83,708.
Step-by-step explanation:
a) Calculate the value of one bond
This can be calculated as follows:
Annual coupon = Bond face value * Coupon interest rate = $1,000 * 6% = $60
Annual coupon discount factor = ((1 - (1 / (1 + r))^n) / r) .......... (1)
Where;
r = required semi-annual rate of return = required annual rate of return / number of semi-annual in a year = 8% / 2 = 0.08 / 2 = 0.04
n = number of semi-annuals = number of years * number of semi-annual in a year = 15 * 2 = 30
Substituting the values into equation (1), we have:
Semi-annual coupon discount factor = ((1-(1/(1 + 0.04))^30) / 0.04) = 17.2920333006645
Present value of coupon = ((Annual coupon / number of semi-annual in a year) * Semi-annual coupon discount factor) = (($60 / 2) * 17.2920333006645 = $528.76
Present value of the face value of the bond = Face value of the bond / (1 + r)^n = ($1,000 / (1 + 0.04)^30 = $308.32
Therefore, we have:
Bond value = Present value of coupon + Present value of the face value of the bond = $528.76 + $308.32 = $837.08
Therefore, the value of one bond is $837.08.
b) What is the total amount Tim Horton would raise if all bonds were sold?
Number of bonds expected to be sold = 100
Value of one bond = $837.08
Total amount that would be raised = Number of bonds expected to be sold * Value of one bond = 100 * $837.08 = $83,708
Therefore, the total amount Tim Horton would raise if all bonds were sold is $83,708.