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3 September, 15:15

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?

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  1. 3 September, 18:49
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    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
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