Can you show steps in solving this problem Suppose you just

Can you show steps in solving this problem:

Suppose you just won the state lottery, and you have a chance between receiving $2550000 today or a 20-year annuity of $250000, with the first payment coming one year from today. What rate of return is built into the annuity? Disregard taxes.

Solution

Let the rate of return be x%

At this rate;present value of inflows=$2550000

2550000=250,000/1.0x+250,000/1.0x^2+250,000/1.0x^3+.............+250,000/1.0x^20

2550000=250,000[1/1.0x+1/1.0x^2+.............+1/1.0x^20]

[1/1.0x+1/1.0x^2+.............+1/1.0x^20]=(2550000/250,000)

=10.2

Hence x=rate of return=irr=7.49%(APPROX).