Question

Please explain basics of solving equations for IRR.

Question:

You have the opportunity to buy a piece of land for $10,000. You are sure that five years from now it will be worth $20,000. If you can earn eight per cent per year by investing your money in the bank is this investment in land worthwhile? Answer this question by calculating the internal rate of return of the investment.

Answer: Solving for the internal rate of return

20,000 /(1+ i)5 = 10,000 20,000 = 10,000(1+i)^5 20000/10,000 = (1+i)^5 (2)^1/5 – 1 = I

I will appreciate if you explain how to solve this equation, because although I have the answer I cannot understand how it was done.

Answer 1

Cost of Land = $10,000
Cash Flow in 5 years = $20,000
Period = 5 years

Let IRR be i%

Cost of Land * (1 + IRR)^Period = Cash Flow in 5 years
$10,000 * (1 + i)^5 = $20,000
(1 + i)^5 = $20,000 / $10,000
(1 + i)^5 = 2
1 + i = (2)^(1/5)
1 + i = 1.1487
i = 0.1487 or 14.87%

IRR of Investment = 14.87%

Yes, you should invest in this investment as you can earn higher return than 8.00%