Question

3. Golf Smith is a professional golfer who has just signed a $3 million contract. The terms are five annual payments of $600,000 each. Determine the present value of the contract to Mr. Smith, assuming his interest rate is 8%.

Answer 1

To find the present value of Golfer Smith's $3 million contract, each annual payment's present value is calculated and summed up, assuming an 8% interest rate. For the bond example, each payment's present value is calculated separately and then summed. If the interest rate changes to 11%, the present value is recalculated using the new rate we get $3,000.

Step-by-step explanation:

To determine the present value of Golfer Smith's $3 million contract with annual payments of $600,000 and an interest rate of 8%, we use the formula for the present value of an annuity.

The formulas used here are the same as those for calculating the present value of future cash flows from a bond.

First, calculate the present value of each annual payment separately:

1. Payment after year 1: PV = $600,000 / (1 + 0.08)^1
2. Payment after year 2: PV = $600,000 / (1 + 0.08)^2
3. Payment after year 3: PV = $600,000 / (1 + 0.08)^3
4. Payment after year 4: PV = $600,000 / (1 + 0.08)^4
5. Payment after year 5: PV = $600,000 / (1 + 0.08)^5

Then sum the present values of these payments to find the total present value of the contract.

For the bond example with a stream of payments of $240 at the end of year one and $3240 ($3000 + $240) at the end of year two, we first calculate their present values separately:

• Year 1 payment's present value: PV = $240 / (1 + 0.08)
• Year 2 payment's present value: PV = $3240 / (1 + 0.08)^2

If the discount rate increases to 11%, then we use 0.11 instead of 0.08 in the formulas above to calculate the new present values.

The initial present value of a $3,000 bond at an 8% interest rate is simply $3,000, as this is the amount the borrower receives and commits to repay.