A basketball player is offered the following contract today, Jan. 1, 2012: $2 million immediately, $2.40 million in 2012, $2.90 million in 2013, $3.60 million in 2014, and $3.80 million in 2015. Assume all payments other than the first $2 million are paid at the end of the year. If the appropriate discount rate is 10 percent per year, what is the present value of the deal?

The answer is $11.24 million Explanation:

Using the formula

Present worth = x / (1+R/100) ∧n

R = 10%

Year 2012

2.40 / (1+10/100) ∧1

= 2.40 / (1+0.1) ∧1

= 2.40 / (1.1) ∧1

2.40/1.1

= 2.18

Year 2013

2.90 / (1+10/100) ∧2

= 2.90 / (1+0.1) ∧2

= 2.90 / (1.1) ∧2

2.90/1.21

= 2.396

Year 2014

3.60 / (1+10/100) ∧3

= 3.60 / (1+0.1) ∧3

= 3.60 / (1.1) ∧3

3.60/1.331

= 2.70

Year 2015

To determine the present value

2+3.80 / (1+10/100) ∧4

= 5.8 / (1+0.1) ∧4

5.8 / (1.1) ∧4

5.8/1.4641

= 3.96

Therefore the present value, add together the value from year 1 to year 4

2.18 + 2.396 + 2.70 + 3.96

= 11.236

= 11.24 Approximately

Therefore the present value is $11.24 millions