Question

Suppose you are the agent for a baseball pitcher. Suppose he is offered the following contract by the New York Yankees: a signing bonus of $3,000,000 (to be received immediately), a first year’s salary of $6,000,000 (to be received one year from today), a second year’s salary of $7,000,000 (to be received two years from today), and a third year’s salary of $8,000,000 (to be received three years from today). Suppose he is offered the following contracts by the San Francisco Giants: a signing bonus of $6,000,000, a first year’s salary of $5,500,000, a second year’s salary of $6,000,000, and a third year’s salary of $6,000,000.

If you believe the interest rate is 10%, which offer would you advise the pitcher to accept?
Would your advice change if you believed the interest rate were 5%?

Answer 1

Results are below.

Step-by-step explanation:

Giving the following information:

New York Yankees:

Signing bonus= $3,000,000

Cf1= $6,000,000

Cf2= $7,000,000

Cf3= $8,000,000

San Francisco Giants:

Signing bonus= $6,000,000

Cf1= $5,500,000

Cf2= $6,000,000

Cf3= $6,000,000

The best option is the one with the higher Present Value.

To calculate the present value, we need to use the following formula on each cash flow:

PV= Cf/(1+i)^n

a) New York Yankees:

Cf0=3,000,000

Cf1= 6,000,000/1.1= 5,454,545.45

Cf2= 7,000,000/1.1^2= 5,785,123.97

Cf3= 8,000,000/1.1^3= 6,010,518.41

Total PV= $20,250,187.83

San Francisco Giants:

Cf0= 6,000,000

Cf1= 5,500,000/1.1= 5,000,000

Cf2= 6,000,000/1.1^2= 4,958,677.69

Cf3= 6,000,000/1.1^3= 4,507,888.81

Total PV= $20,466,566.5

At an interest rate of 10%, the contract of San Francisco Giants is the more profitable.

b) i= 5%

New York Yankees:

Cf0=3,000,000

Cf1= 6,000,000/1.05= 5,714,285.71

Cf2= 7,000,000/1.05^2= 6,349,206.35

Cf3= 8,000,000/1.05^3= 6,910,700.79

Total PV= $21,974,192.85

San Francisco Giants:

Cf0= 6,000,000

Cf1= 5,500,000/1.05= 5,238,095.24

Cf2= 6,000,000/1.05^2= 5,442,176.87

Cf3= 6,000,000/1.05^3= 5,183,025.59

Total PV= $21,863,297.7

At an interest rate of 5%, the contract of New York Yankees is the more profitable.