3.Let’s examine the most glaring issue with IRR via an example. A friend offers

Question

3.Let’s examine the most glaring issue with IRR via an example. A friend offers you an "investment." He knows that every year there is one day when some lottery numbers are fixed. Based on his insider knowledge, if you invest $2 with him, he will return you $100 at the end of each of the next two years by matching lottery numbers.

a. Calculate the IRR for this project.

b. Next, calculate how much you might expect to earn from this project (i.e, the future value). Let's assume you're an ordinary investor and can, under normal circumstances, earn an interest rate of 5% on cash you have on hand.

c. Let's say you find an awesome bank account that offers 1000% interest. If you put your $2 into this account, how much will you have at the end of 2 years?

d. In the module, it was discussed that, generally, if the discount rate is less than the IRR then a project should be accepted. And yet, even though our IRR from part (a) is greater than 1000%, the amount earned in part (c) is more than in part (b). Why the rule of thumb doesn't apply, and why IRR is not a perfect measure of an investment.

Explanation / Answer

Q. 3)

a) Internal rate of return (IRR):-

Sice the cash flows are equal in all the years, then the Present value (P.V.) factor is calculated by dividing the initial investment by annual cash inflow, as

P/V Factor = Intial investment/ Annual Cash inflows

   = 2 / 100

   = 0.02

By looking the present value table against two year the P/V factor 0.02 and we will find it against 5000 %, Thus, IRR = 5000 % .

Alternatively, IRR may be calculated by Trial and Error method which is as follows:-

Take two rates. One rate at which P.V. of cash inflow is greater than the P.V. of cash outflow and vice-versa.

At 4900 %

P.V. of cash inflow = 100 * Cumulative P.V. factor for two years @ 4900 %

   = 100 * 0.0204 = $ 2.04

At 5200 %

P.V. of cash inflow = 100 * Cumulative P.V. factor for two years @ 5200 %

   = 100 * 0.0192 = $ 1.92

Thus, IRR (by inter-polation) = 4900 + (2.04 - 2) * (5200 - 4900) / (2.04 - 1.92)

   = 4900 + 0.04 * 300 / 0.12

   = 4900 + 12 / 0.12

   = 4900 + 100

   = 5000 %

Q. 3 C) Amount = Principal ( 1 + Rate of interest / 100)Time

   = 2 ( 1 + 1000 / 100)2

  = 2 ( 1 + 10 )2

= 2 * (11)2   = $ 242

Conclusion:- We will have at the end of 2 years = $ 242

Q. 3 ) d) IRR is not a perfect measure of an investment because IRR measures only the quality of investment. IRR does not take into account the scale of investement. IRR just provides a relative measure of value. Further it is assumed in IRR method that all fund earn rate equal to internal rate of return which is not correct. Further, the objective of financial management is to maximize sharehoder's wealth, thus IRR can not be treated as perfect measure of an investment.

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