Steve Hawks is a big football star who has been offered contracts by two differe

Question

Steve Hawks is a big football star who has been offered contracts by two different teans, The payment (in millions of dollars) under the two contracts are shown below: Team A- Yr 0, Cash payment is $8; Yr 1 CP $4; Yr 2 is $4; Yr 3 is $4; Yr 4 is $4; Team B; Yr 0 Cash Payment is $2.5; Yr 1 is $4; Yr 2 is $4; Yr 3 is $8; Yr 4 is $8; Steve plans to accept the contract that provides him with the highest net present value. At what discount rate would he be indifferent between the two contracts? a. 10.85% B. 11.35% C. 12.66% D. 13.98%

Explanation / Answer

NPV for a year is calculated by R(t)/(1+i)^t Here R(t) is the payment, t is the year number, i = discount rate Total NPV is sum of this for all the years considered In case of Team A: Year 0 = 8/(1+i)^0 = 8 Year 1 = 4/(1+i)^1 = 4/(1+i) Year 2 = 4/(1+i)^2 Year 3 = 4/(1+i)^2 Year 4 = 4/(1+i)^2 Thus Total NPV = 8 + 4((1+i)^-1 + (1+i)^-2+ (1+i)^-3+ (1+i)^-4) Similarly for Team B Total NPV = 2.5 + 4((1+i)^-1) + 4((1+i)^-2) + 8((1+i)^-3) + 8((1+i)^-4) As he must be indifferent to both the contracts, The NPV of both must be equal => 8 + 4((1+i)^-1 + (1+i)^-2+ (1+i)^-3+ (1+i)^-4) = 2.5 + 4((1+i)^-1) + 4((1+i)^-2) + 8((1+i)^-3) + 8((1+i)^-4) => 5.5 = 4 ((1+i)^-3) + (1+i)^-4) On solving the above equation, or substitute option B in the place of i (i.e i = 0.1085) you will get LHS = RHS Thus Option B is the option

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