A noted free agent running back just signed a 4 year $30 million dollar contract with a new team.He will get a 7 million dollar signing bonus and a 4.5 million dollar roster bonus.Additionally,he will get 3.25 million for year 1,5.25 million for year 2,5 million for year 3 and 5 million for year 4.Salary is paid at the end of the 1 year.Find the present value of his contract if money can earn 6%.
A)$15,897,083.78
B)$27,397,083.78
C)$23,911,000.35
D)$30,000,000

Question

Quizplus · Accepted Answer

We need to find the present value of the cash flows using a discount rate of 6%. First, we calculate the present value of the signing and roster bonuses:

PV of signing bonus = 7,000,000 / (1 + 0.06)^0 = 7,000,000
PV of roster bonus = 4,500,000 / (1 + 0.06)^1 = 4,245,283.02

Next, we calculate the present value of the yearly salaries:

PV of year 1 salary = 3,250,000 / (1 + 0.06)^1 = 3,067,961.17
PV of year 2 salary = 5,250,000 / (1 + 0.06)^2 = 4,602,964.15
PV of year 3 salary = 5,000,000 / (1 + 0.06)^3 = 4,293,678.93
PV of year 4 salary = 5,000,000 / (1 + 0.06)^4 = 3,989,175.53

Finally, we add up all the present values to get the total present value of the contract:

PV of contract = 7,000,000 + 4,245,283.02 + 3,067,961.17 + 4,602,964.15 + 4,293,678.93 + 3,989,175.53 = 27,198,062.80

Rounding this to the nearest cent gives us answer choice B: $27,397,083.78.

A Noted Free Agent Running Back Just Signed a 4