Question

Problem 6.34 Tirade Owens, a professional athlete, currently has a contract that will pay him a large amount in the first year of his contract and smaller amounts thereafter. He and his agent have asked the team to restructure the contract. The team, though reluctant, obliged. Tirade and his agent came up with a counteroffer Year Current Contract Team's Offer Counter offer $4,720,300 $7,671,420 $3,437,100 $2,922,920 $7,262,000 3,558,380 53,891,300 $3,642,300 $4,080,700 $3,706,000 $2,565,000 $1,898,000 What is the present values of Current Contract using a 14 percent discount rate? (Round answer to 2 decimal places, e.g. 15.25.) Present value LINK TO TEXT INTERACTIVE TUTORIAL What is the present values of Team's Offer using a 14 percent discount rate? (Round answer to 2 decimal places, e.g. 15.25.) Present value INTERACTIVE TUTORIAL

Answer 1

There are 2 ways to solve the above question: 1st one requires manual efforts and can be done with the help of a normal calculator and 2nd one uses a direct formula and can be done only with the help of a financial calculator.

Let's see the 1st method:

We need to calculate the present value of 4 future payments. Discount rate is given as 14%

Suppose if we get $1 at the end of 1st year, its value today will be 1/1.14 = 0.88 (Formula is (1/(1+discount rate)^n), where n denotes time period)

If we get $1 at the end of 2nd year, its value today will be 1/(1.14*1.14) = 0.77

Similarly for 3rd year, PV = 1/(1.14*1.14*1.14) =0.67 and for 4th year = 1/(1.14*1.14*1.14*1.14) = 0.59

Now let's calculate PV of Current offer. It will be 0.88* 7262000 + 0.77*3706000 + 0.67*2565000+0.59*1898000 = 12,076,892.40

Calculation for team and counter offer are shown in the excel screenshot below:

Team = 10,990638.18 and Counter = 14,094,070.51

Counter contract has highest present value

Team 3558380 3891300 3643000 4080700 Counter 4720300 7671420 3437100 2922920 Year Current 7262000 3706000 2565000 1 4 4 6 Solution 1 using long calculation 7 Discount rate 14% Formula Used 0.877192982 1/Power(1.14,1) 2 0.769467528 1/Power(1.14,2) 3 0.674971516 1/Power(1.14,3) 40.592080277 1/Power(1.14,4) 10 12 13 14 15 16 17 18 19 Current Team Counter 3121385.96 414 2994228.99 5902908.59 2458921.23 2319 416101.99 1730603.28 1 6370175.44 2851646.66 1731301.94 0614.04 944.60 4 12,076,892.40 10,990,638.18 14,094,070.51

2nd Method:

Directly use the formula = NPV(discount rate, FV at end of Year 1, FV at end of Year 2, FV at end of Year 3, FV at end of Year 4)

Excel solution is as below:

Year Current 7262000 3706000 2565000 1898000 14% Team 3558380 3891300 3643000 4080700 Counter 4720300 7671420 3437100 2922920 1 4 4 7 Discount rate 21 Solution 2 using NPV formula NPV(B7,B2,B3,B4,B5) NPV(B7,C2,C3,C4,C5) NPV(B7,D2,D3,D4,B5) 14,094,070.51 23 24 12,076,892.40 10,990,638.18

Hope the solution helps you. Please let me know if you face any difficulty.