10. Which of the following payment terms should a professional athlete prefer in
ID: 1190806 • Letter: 1
Question
10. Which of the following payment terms should a professional athlete prefer in a “ten million dollar” five-year contract if the athlete wants to obtain the greatest present value of income?
A) Receive $2 million each of the next five years.
B) Receive $6 million next year and then receive $1 million in each of the subsequent four years.
C) Receive $1 million in each of the next four years and then receive $6 million in the subsequent year.
D) All of the above have the same present value of income.
Explanation / Answer
For this question we need to calculate three different present values for the three different possibilities. Let us assume the discount rate is 5%.
1) Present Value when yearly payments are $2,000,000 for 5 years at 5%.
PV of annuity = PMT * [{1 – (1 + I/Y)-N} / I/Y]
Where PMT is the yearly constant payment, I/Y is the interest rate per year and N is number of years.
PV of the annuity = $2,000,000 * [{1 – (1 + 0.05)-5} / 0.05]
PV = $8,658,953.34
2) Present Value when $6 million are received in the first year and $1 million thereafter for each year.
PV of the cash flow: PMT1/(1 + r)1 + …….. + PMTn / (1 + r)n
Where PMT is the yearly cash flow, R is the rate per year and N is number of year.
Solving for the present value of the cash flows we have: PV = $9,091,381.43
3) Present Value when $1 million are received in the first four years and $6 million in the last year.
PV of the cash flow: PMT1/(1 + r)1 + …….. + PMTn / (1 + r)n
Where PMT is the yearly cash flow, R is the rate per year and N is number of year.
Solving for the present value of the cash flows we have: PV = $8,247,107.50
As we can conclude, option B provides the highest PV hence it must be chosen to receive $6 million in the first year and $1 million thereafter for the next four years.
I hope my solution solves your query.
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