Tim Horton wants to raise funds to open a branch of their coffee shop in Trinidad. To raise the funds, Tim Horton would sell bonds 100 $1,000 par value with a coupon interest rate of 6%. The bonds would mature in 15 years and interest would be paid semi-annually. The required rate of return is expected to be 8%. Requirement:
a) Calculate the value of one bond
b) What is the total amount Tim Horton would raise if all bonds were sold?

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.

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.

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