You wish to invest $45,000 and you have three choices:
(I)Buy a perpetuity that provides annual payments of $1500,first payment one year from now
(II)Receive a single payment of $60,000 in 10 years
(III)Receive a single payment of $84,600 in 20 years
Rank the three investments from best to worst,based on the internal rate of return (IRR).

Question

Quizplus · Accepted Answer

To rank the investments, we need to calculate the IRR for each one:

- Investment I: The perpetuity formula is PV = PMT / r, where PV is the present value, PMT is the annual payment, and r is the interest rate. In our case, PV = $45,000, PMT = $1,500, and r = IRR. Solving for IRR, we get 3.33%. 
- Investment II: We need to find the discount rate that makes the present value of $60,000 equal to $45,000. Using the present value formula, we get IRR = 2.72%. 
- Investment III: We need to find the discount rate that makes the present value of $84,600 equal to $45,000. Using the present value formula, we get IRR = 2.46%.

Therefore, the best choice is Investment I, as it has the highest IRR of 3.33%. Investment III is the next best choice with an IRR of 2.46%, followed by Investment II with an IRR of 2.72%.

You Wish to Invest $45,000 and You Have Three Choices