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Suppose 2 athletes sign 10-year contracts for $80 million. In one case, we're told that the $80 million will be paid in 10 equal instalments. In the other case, we're told that the $80 million will be paid in 10 instalments, but the instalments will increase by 5% per year. Who got a better deal and why?

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jepessoa

Answer:

player 2 is signing a better contract

Explanation:

the present value of an annuity (player 1) = annual payment x annuity factor

assuming that the interest rate is 10%

present value = $10 million x 6.1446 (PV annuity factor, 10%, 10 periods) = $61.446 million

player 2's contract

the present value of a growing annuity = [payment / (i - g)] x {1 - [(1 + g) / (1 + i)]ⁿ} = [$10 / (10% - 5%)] x {1 - [(1 + 5%) / (1 + 10%)]¹⁰} = $200 x 0.372 = $74.398 million

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