Question

A sports star can sign a 6-year contract that starts at $12M with increases of $3M each year for his expected playing career of 6 years. It is also possible to sign a contract that starts at $8M for the first year and then increases at $2M each year for 10 years. (note some income is deferred until after he retires). If his interest rate for the time value of money is 8%, what is the value of each choice? Contributed by Hamed Kashani, Saeid Sadri, and Baabak Ashuri, Georgia Institute of Technology

Answer 1

$\small PV = \frac{FV}{(1+r)^n}$ (Present value formula)

Value of choice 1:

$\small = 12+\sum_{i=1}^{6}\frac{3}{(1+0.08)^i} = 12 +3\sum_{i=1}^{6}\frac{1}{(1.08)^i} = 12 +3\sum_{i=1}^{6}0.93^i$

$\small = 12 +3(0.93+0.87+0.80+0.75+0.70+0.65)=26.1M$

Value of choice 2:

$\small = 8+\sum_{i=1}^{10}\frac{2}{(1+0.08)^i} = 8 +2\sum_{i=1}^{10}\frac{1}{(1.08)^i} = 8 +2\sum_{i=1}^{10}0.93^i$

$\small = 8 +2(0.93+0.87+0.80+0.75+0.70+0.65+0.60+0.56+0.52+0.48)=21.72M$