Question

Mr. Alessandro Silva is a soccer player who plays as an attacking midfielder for Agostini FC, a top ranked first division soccer team. Mr. Silva has decided to invest his annual bonus in an investment account, which offers 7 percent interest per year. Mr. Silva’s annual bonus, based on his current contract with the team, is $7,950,000 this year. Mr. Silva is confident that his bonus will increase at a constant rate of 6 percent per year over the next 5 years. Agostini FC pays players bonuses at the end of each year. Mr. Silva must pay a flat tax rate of 28 percent.

1) If Mr. Silva does not withdraw any money from the investment account, how much money after tax he can accumulate in the investment account at the end of year 5?

2) If Mr. Silva decides to donate the balance of the investment account (at the end of year five) to Youth Soccer League Association(YSLA), starting year 6 and going through infinity, how much could he afford to pay, at maximum, to YSLA per year.

Answer 1

1.We need to find the Future Value---- FV at end of 5 yrs.of the 6% growing after-tax annuity of 7950000*(1-28%)= 5724000--- will be at 7% interest per year

Using FV of growing annuity formula,

FV(ga)=Annuity amt.*((1+r)^n-(1+g)^n)/(r-g)

ie. 5724000*((1+0.07)^5-(1+0.06)^5)/(0.07-0.06)

36820290

2..

Here, we need to calculate the perpetuity whose PV or Present Value is the above $ 36820290 at 7%

using the formula for PV of perpetuity= Perpetuity/r

ie. 36820290=Perpetuity/7%

so, the Perpetuity=36820290*7%=

2577420

ANSWER:

The Maximum he afford to pay to YSLA per year= $ 2577420