My Math Forum Two Questions (NPV and 2 IRRs)
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 September 23rd, 2014, 12:30 PM #1 Newbie   Joined: Sep 2014 From: Denmark Posts: 3 Thanks: 0 Two Questions (NPV and 2 IRRs) So I've got 2 assignments that I think I'm not really getting. (My first language isn't English so apologize beforehand for odd sentences). Assignment 1(translated from Danish): A listed Danish life insurance company is considering offering a life insurance policy in the following terms: All 80 year olds can by immediate payment of a single amount of 100.000kr receive 250.000kr on their 90th birthday if they are at this time alive. Alternatively, the insurance premium on 100.000kr is lost. For the Danes in general it is assumed that 40% of the 80 year olds will be alive at the age of 90, and the interest rate is zero in all relevant future. Discuss if this life insurance company should offer life insurance at these specified terms. Okay, now to some basic math: So if we assume 100 people pay this sum, it's: 100x100.000 = 10.000.000, which is the amount the insurance company will recieve. The amount the insurance company will have to pay is 100x40%x250.000 = 10.000.000. So we're at a 'break even' point here, 10million go in and 10million go out..... But surely, this can't be everything there is to this assignment, or?? I'm thinking it has something to do with NPV, but the assignment says to assume the interest rate is zero. Assignment 2 Discuss the following statement: "If you are considering one and only one investment project Z, which has two internal interests(2 internal rates of return?), Z is disadvantageous if the required return for the project is higher than the lowest IRR and less than the highest IRR. So it has 2 IRRs because of asymmetrical cash flows, right? it is an investment, so the first cash flow is a negative, followed by positives and one negative, making it graph like the graph in link below. http://www.unistudyguides.com/images...FINS161347.jpg So from the assignment text, we know the required rate of return is located between the lower and higher IRR, where the NPV is positive. Therefore, "Z is disadvantageous if the required return for the project is higher than the lowest IRR and less than the highest IRR" is false. It is advantageous because the NPV is positive, or am I just not getting this all? Much appreciated if someone could point me in the right direction with this assignment, thanks!
 September 24th, 2014, 10:48 AM #2 Newbie   Joined: Sep 2014 From: Denmark Posts: 3 Thanks: 0 Maybe they want me to mention "The Time Value Of Money" and "Adverse selection" in assignment 1?
September 24th, 2014, 08:04 PM   #3
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 Originally Posted by Anonyd Assignment 2 Discuss the following statement: "If you are considering one and only one investment project Z, which has two internal interests(2 internal rates of return?), Z is disadvantageous if the required return for the project is higher than the lowest IRR and less than the highest IRR. So it has 2 IRRs because of asymmetrical cash flows, right? it is an investment, so the first cash flow is a negative, followed by positives and one negative, making it graph like the graph in link below. http://www.unistudyguides.com/images...FINS161347.jpg So from the assignment text, we know the required rate of return is located between the lower and higher IRR, where the NPV is positive. Therefore, "Z is disadvantageous if the required return for the project is higher than the lowest IRR and less than the highest IRR" is false. It is advantageous because the NPV is positive, or am I just not getting this all? Much appreciated if someone could point me in the right direction with this assignment, thanks!
The 2 IRR values on this investment are false

The cash flows from your accompanying graph shows the following there cash flows

Code:
-100 230 -132
The net present value of these cash flows is given by

Code:
NPV = -100 +230 (1+i)^-1 -132 (1+i)^-2
and the net future value of these cash flows is given by

Code:
NFV = -100 (1+i)^2 +230 (1+i)^1 -132
If the interest rate were to be 10% or 20% the investment will have a NPV and NFV of zero

In between these two values is the positive NPV and NFV

But if you just look at the three cash flows and check the un-discounted sum or simply the net value then it is negative

NV = -2

So the investor has lost kr. 2 on her investment thus any positive IRR values of 10% and 20% are giving her false hope of profits.

P.S. The required rate of return (WACC) in irrelevant in this context

 September 25th, 2014, 01:40 AM #4 Newbie   Joined: Sep 2014 From: Denmark Posts: 3 Thanks: 0 The graph I linked was just some graph I found online which I thought what an investment graph with two IRRs would look. There was no graph to assignment 2, only the text i posted.
 September 25th, 2014, 08:02 PM #5 Member     Joined: May 2014 From: Rawalpindi, Punjab Posts: 69 Thanks: 5 If there are multiple IRR values (oxymoron itself) then you would have to at first check the net worth of the investment at 0% discount rate If the net worth is positive at 0% then if the required rate of return is lower than the first IRR, Investment Z makes sense But IRR as you have seen from the sample investment is itself mired in complexity My own theory is that there are no multiple IRR value even when there are multiple IRR values There is always either one IRR or no IRR values The problem is tied to the way IRR equation is defined as the sum of discounted cash flows The real problem is the discount factor itself that results in formation of a N-degree polynomial based on the IRR equation Solving for a polynomial higher than degree 4 is currently not possible using any formulas But if you fix the way a single dollar is discounted, one can easily find the "real" IRR using a closed form formula no matter how many cash flows one has or whether such cash flows are in uniform or in uneven amounts Someone I know is working of such a formula to discount the dollar and I will keep you posted if He succeeds
 May 25th, 2017, 03:11 PM #6 Newbie   Joined: May 2017 From: Overland Park Posts: 3 Thanks: 0 AbrahamA seems like a very smart guy and I agree with him, two IRRs cannot both make NPV equal 0. Either one will and the other won't, or vice versa. It would be possible of course on different time scales but I can't understand how IRR could be two different numbers. Also, I would not advise using a formula like the one mentioned above to solve IRR. It will take a very long time depending on how many cash flows and how many different cash flows there are. It would be better to use a program of some kind. AbrahamA, did any one build the formula you speak of?
 May 26th, 2017, 07:26 AM #7 Senior Member   Joined: May 2008 Posts: 297 Thanks: 81 Beer soaked reply follows. You may have to wait for a long time before our friend Abraham replies. He's been having some financial difficulties.

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