Today is January 1, 2014. Your friend Joe has just signed a contract to play for
ID: 2383367 • Letter: T
Question
Today is January 1, 2014. Your friend Joe has just signed a contract to play for the Oil Kings. He will receive $900,000 for 2014, $1,000,000 for 2015, $1,100,000 for 2016, and $1,200,000 for 2017. All payments are made at the beginning of the year. Assume 8% annual interest rate (EAR).
a. What is the present value of his contract?
b. If instead of increasing annual payments Leo wants equal dollar amount month-end cheques, how large is his monthly pay (assuming the present value remains the same)?
show all work please
step by step
do not use excel please
explain the question with words not just numbers
thanks in advance
Explanation / Answer
Solution :
a) The present value of the contract is calculated as follows :
PV = $ 900,000 / ( 1+0.08)1 + $1,000,000 / ( 1+0.08)2 + $1,100,000 / ( 1+0.08) 3 + $1,200,000 / ( 1+ 0.08) 4
PV = 833333.33 + 857338.82 + 873215.46 + 882035.82
PV = 3445923.44
b) To calculate the present value of Annuity immediate
P(PVA) = A [ ( 1+r) n -1 ] / r ( 1+r) n
3445923.44 = A [ ( 1+0.08) 4 -1 ] / 0.08 ( 1+0.08) 4
3445923.44 = A [ ( 1+0.08) 4 -1 ] / 0.1088
A [ ( 1+0.08) 4 -1 ] = 375,051.26
A = 375,051.26 / [ ( 1+0.08) 4 -1 ]
A = $ 1,040,395.96
Each monthly pay is equal to = $ 1,040,395.96 / 48
Each monthly pay is equal to = $ 21,674.91