Question

An athlete signs a five-year endorsement deal with a prominent sponsor. Under this deal, the athlete will receive $5,000 each year for the first three years and $6,500 each year for the final two years. What is the present value of the total deal if the payments are discounted 6%

Answer 1

To calculate the present value of the endorsement deal, we need to discount each future payment using the given discount rate of 6%. We calculate the present value of the payments for the first three years and for the final two years separately, and then sum them up. The present value of the total deal is approximately $24,674.91.

Step-by-step explanation:

To calculate the present value of the total endorsement deal, we need to discount each future payment using the given discount rate of 6%. Since the payments are different for the first three years and the final two years, we need to calculate the present value for each set of payments separately and then sum them up.

For the first three years, the athlete will receive $5,000 per year. To calculate the present value of these payments, we can use the present value formula:

PV = CF / (1 + r)^t

Where PV is the present value, CF is the cash flow (payment), r is the discount rate, and t is the number of years. Substituting the values, we get:

PV = $5,000 / (1 + 0.06) + $5,000 / (1 + 0.06)² + $5,000 / (1 + 0.06)³

Calculating this, we find that the present value of the payments for the first three years is approximately $13,336.78.

For the final two years, the athlete will receive $6,500 per year. Using the same formula, we have:

PV = $6,500 / (1 + 0.06)⁴ + $6,500 / (1 + 0.06)⁵

Calculating this, we find that the present value of the payments for the final two years is approximately $11,338.13.

Now, we can sum up the present values of both sets of payments to find the total present value of the endorsement deal:

Total PV = $13,336.78 + $11,338.13 = $24,674.91

Therefore, the present value of the total deal is approximately $24,674.91.

Answer 2

PV= $23,370.85

Step-by-step explanation:

Giving the following information:

Cash flow (1-3)= $5,000

Cash flow (4-5)= $6,500

Discount rate= 6%

To calculate the present value, first, we need to calculate the final value:

FV= {A*[(1+i)^n-1]}/i

A= annual cash flow

Year 1-3:

FV= {5,000*[(1.06^3) - 1] / 0.06

FV= 15,918

Year 4-5:

FV= {6,500*[(1.06^2) - 1]} / 0.06

FV= 13,390

Now, the present value:

PV= FV/(1+i)^n

PV= 15,918/(1.06^3)= 13,365.06

PV= 13,390/(1.06^5)= 10,005.79

PV= $23,370.85