Why does a IRR calculation produce a positive return when the final periods create an overall deficit?

Question

If payment 0 = -1,000,000, then you have 83 periods of 100,000 and one last period of -9,000,000. this give s a positive % return but has actually created a loss of 1,700,000. Try it in excel and explain it to me why this is so>

Answer 1

The basic premise of finance is that money now is worth more than money in the future. At 10% interest, that 9MM payment you have to make in 84 years is only worth about three or four thousand now. In other words, you could put aside a few thousand of that first hundred thousand dollar payment you get in a year, invest it at 10% and have more than enough to make that last payment.

If you don't like thinking of it in present value terms, think of it in future value terms. IRR makes the implicit assumption that you can reinvest money you get at the same rate. If you reinvest that first $100,000 payment at 10% for the remaining 83 years, it will be worth over $270MM -- way more than you need to pay off the $9MM

Answer 2

There is something wrong with the question. IRR stands for Interna Rate of Return. It is the interest rate that equates the cash inflows to the outflow with time value considerations.
So you should have an initial investment and a future stream of cash flows, including the final payment. Then the IRR is figured out and there won't be any surplus or deficit.
1000000=100000/(1+irr)+
100000/(1+irr)^2+.......+100000/(1+irr)^83-9000000/(1+irr)^83
This is easily calculated as
1000000=100000x(PVIFA)83,IRR-9000000x(PVIFA)83,IRR
From this interpolate for the IRR from the discount table and plug in you Excel and there won't be a surplus or deficit.
PVIFA is present value interest factor of an annuity from the discount table.

Answer 3

If I understand you correctly, you are simply summing up the payments/withdrawals to get the loss of 1,700,000 (depositing $1M at the beginning, withdrawing a total of $8.3M, then depositing $9M at the end).

Internal Rate of Return is the interest rate at which the present value of inflows equals the present value of outflows. Obviously, the present value of your first payment is $1M. The present value of your $9M payment will be quite small due to the 83 periods between your first payment and your last.

Think about it elementarily. If you can deposit $1M and withdraw $8.3M over the next 83 months (or years...whatever time frame the period is) before you even deposit anymore money, would you think that's a good investment?