NPV improves with increase in discount rate

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Permalink Reply by Iraj Mozaffary on June 9, 2009 at 7:00am

In case a large amount of outlays takes place on late times, or a large amount of incomes takes plase in early times, by increasing the discount rate, it can happen the Increasing of NPV.

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Permalink Reply by Ankit Kothari on June 9, 2009 at 7:53am

Hi,
I am attaching a Excel File where you can see the case where increasing WACC or COC or Discounting rates will improve the NPV but yes, there are limitation in my sheet . I have assumed constant & large outflow(in initial 5 years) than Constant inflows (in next 20 years). If your inflows is significantly lower than your outflows than this sheet will work.
Meanwhile i agree with Sacha sir.
I request you all if you will get a real exampale of the above situation pls make it available .
Note: Please read the note in attached file.

Attachments:

• Magic of Excel.xls, 19 KB

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Permalink Reply by Clark on June 9, 2009 at 12:57pm

assuming the mathematical calculations are correct, i think the NPV could increase when the discount rate increases if the cash inflows are increased to a level (to reflect real situation) that results to higher NPV.

also you may be referring to the economic NPV and, presumably taking a government's perspective, where an increase in the discount rate without paying for interest cost, could lead to the government to have greater amount of money to be appropriated for other projects that increase the net inflow and lead to an increase of the net incremental benefit, thus increasing the NPV.

i think it is important to know the reason for the increase in the discount rate. assuming that it is made to do so because of an improving economy, then it is likely that the inflows should increase.

these are just thoughts from a fresh student of economics and i hope i made sense. thanks.

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Permalink Reply by Liam Bastick on June 9, 2009 at 4:41pm

If your Excel spreadsheet is fine and you have no "hidden" associated costs of capital in your cashflows (e.g. tax paid instead of pre-financing tax paid for a post-tax enterprise value calculation), then the reason is probably mathematical. Discussions about the validity of Miller & Modigliani's propositions address one point (i.e. whether to vary the discount rate for each period or let it remain the same), but assuming that you use one constant rate throughout (which it sounds like you do) then...

(1) Are your final / later cash flows negative? A higher discount rate will reduce their effect in the overall NPV and hence increase the discount rate.

and / or

(2) Sorry to get technical, but look at your cash flows for each period. Do they keep changing sign (i.e. negative then positive then negative then positive, etc.)? Mathematically, each time it changes sign there may be another discount rate where the NPV=0 (i.e. you have an IRR). So, three changes in sign could give you three different IRRs. Between the IRRs the NPV will have to be either positive or negative. In between the IRRs local maxima and minima occur and it could be that 18% is nearer the local maximum than your 10% is), hence the higher NPV.

This second explanation doesn't make it easy to explain to non-numerate third parties but it may be the factual reason. The results would be correct albeit counter-intuitive. This is why in particular IRR (rather than NPV) can be so misleading.

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Permalink Reply by Hamid Naeem on June 10, 2009 at 4:52am

If outflows are extremely large and subsequent inflows during the life of the project are nominal, NPV (although negative) can increase with increase in discount rate.

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Permalink Reply by stefano caselli on June 12, 2009 at 10:45am

Assume that project costs are certain but project revenues are uncertain (as usually it is)

In your model you should discount costs at a risk free rate and revenues at a higher discount rate that relfects risks (es. wacc or ke)

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Permalink Reply by kemal on June 12, 2009 at 11:42am

hi Keran,

Interesting discussion, a lot of opinions from different point of views.
In my opinion, you should revisit your approach. It's ok if you want to calculate NPV with single disc.rate OR multiple disc.rate. But, you cannot compare the result. Otherwise you'll get yourself confused.

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Permalink Reply by Muhammad Aqib Zulfiqar on June 13, 2009 at 3:21am

Well, it is not possible mathematically that higher coc can result in higher positive NPV, the case under discussion can only shows improvement in NPV if the outflows in initial five year is greater than inflows over twenty year. Test it.

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Permalink Reply by Liam Bastick on June 19, 2009 at 8:14am

This is fundamentally untrue, speaking as a mathematician (please see my comment above) - consider cashflows of (100), 500 and (400) at Times 0, 1 and 2 respectively. NPV @10% = 24.0; NPV @20% = 38.9.

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Permalink Reply by Mike Adhikari on June 14, 2009 at 1:47am

Keran:
I think your math is correct. Here is my explanation why NPV increases in your case with higher discount rate. Higher discount rate means higher risk; lower discount rate means lower risk. By using higher discount rate for early years and lower discount rate for later years, you are saying that the first 5 years of negative cash flows are riskier than than the positive cash flows of later years. You are saying that the investment outlay is riskier than the probability of profits. This is opposite of most investment decisions. In most projects, the negative cash flows are the least risky cash flows. I have seen analysis where these are discounted at zero rate or at market interest rate. So, your math is most likely correct. Your approach to risk modelling may need to be revisited.

BTW, it is OK to have variable discount rate.

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Permalink Reply by Himanshu on June 21, 2009 at 6:13am

The way i have understood, is probably that the higher cash outlays ( in the beginning) can offset the effect of using higher discount rate, but we cannot expect this to happen with such a longer peroiod, if u can please post your sheet.

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Permalink Reply by T.venkataramanan on June 24, 2009 at 10:33pm

calculations are to be a checked up once again.you can put up your calculation in the web so that they can be checked.

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