PROBLEM:

5.    LMN Ltd. has issued a bond with a face value of $500,000 and a coupon rate of 8%. The bond matures in 5 years and the prevailing market rate of interest is 10%. Calculate the present value of the bond.

Solution:

PV of bond = ($40,000 x [(1 - (1 + 10%)^-5) / 10%]) + ($500,000 / (1 + 10%)^5) = $415,319.08

Note: $40,000 is the annual interest payment ($500,000 x 8%).

To calculate the present value of the bond, we first need to calculate the present value of the annuity payments, which is the interest payments of $40,000 per year for 5 years. We can use the present value of annuity formula to do this:

PV of annuity = PMT x [(1 - (1 + r)^-n) / r]

where PV is the present value of the annuity, PMT is the amount of the annuity payment, r is the interest rate, and n is the number of periods.

In this case, the PMT is $40,000, the interest rate is 10%, and the number of periods is 5 years. Substituting these values into the formula, we get:

PV of annuity = $40,000 x [(1 - (1 + 10%)^-5) / 10%]

Simplifying the equation, we get:

PV of annuity = $40,000 x [3.79079]

PV of annuity = $155,941.76

Next, we need to calculate the present value of the face value of the bond, which is $500,000. We can use the present value formula to do this:

PV = FV / (1 + r)^n

where PV is the present value, FV is the future value, r is the interest rate, and n is the number of periods.

In this case, the FV is $500,000, the interest rate is 10%, and the number of periods is 5 years. Substituting these values into the formula, we get:

PV of $500,000 = $500,000 / (1 + 10%)^5

PV of $500,000 = $259,377.32

Finally, we can calculate the total present value of the bond by adding the present value of the annuity payments and the present value of the face value of the bond:

PV of bond = $155,941.76 + $259,377.32

PV of bond = $415,319.08

Therefore, the present value of the bond is $415,319.08.