NPV Question

I was solving the Wiley Qbank when I came across this " For an investment that has inflows in the early stages and outflows in the later stages, the use of a higher discount rate makes the NPV higher."

Therefore I took a random set of figures, $1200 as inflows for Year 1,2,3 and outflos of 479,584 and 784 for Year 4,5,6 respectively and when I increased the discounting rate the NPV decreased.Why is this the case?

take year 1 to 3 as earnings (inflows), these will give you the positive side of the NPV computation.

The cash outflows occurs in the later years, which means that with higher discount rate, it will make the negative side of the NPV smaller.

Thus the NPV will increase with higher discount rate.

Using BAii plus, you should be keying in CFo: 1200(positive), C01: 1200(positive), F01: 2, C02: (-)479584 negative, F02: 3, C03: (-)784(negative), F03: 3

NPV for discount 10 percent = -983592, NPV for discount 12 percent = -916111,

NPV for higher discount rate is indeed higher NPV. Im thinking its the negative signs and all that you are mixed up with.

  1. When you consider higher discount rate,If cash outflows are happening in later years, the present value of those would be lower as such compared to outflows that happen in earlier years because of larger discounting periods, so that contributes to higher NPV (lower value of cash outflows)

  2. Now if you increase the discount rate, it further reduces the PV of cash outflows (higher discount rate - lower PV) again a positive result for NPV compared to lower discount rate, combine the two and you will get your answer

As a scenario, I am giving the below.

  1. CF0 = -1,000,000; CF1 to CF5 = +300,000; Discount Rate = 6% and NPV = 248,782

CF0 = -1,000,000; CF1 to CF5 = +300,000; Discount Rate = 12% and NPV = 72,708

  1. CF0 to CF4 = +300,000; CF5 = -1,000,000 Discount Rate = 6% and NPV = 558,749

CF0 to CF4 = +300,000; CF5 = -1,000,000 Discount Rate = 12% and NPV = 574,802

In Scenario I the NPV decreases because of increasing the discount rate as the outflow is in the earlier years

In Scenario II the NPV increases because of increasing the discount rate as the outflow is in the later years

This is a misleading question. It tries to convey the message that the further away in time a cash flow the smaller its value when discounted back to present. So a bigger discount will make cash outflows in Y4-Y6 even smaller and hence increase NPV. However it neglects the fact that with increasing discount rates ALL cash flows will reduce in value, including cash inflows.

I would say, no.

This question is about deferring outflows later in the life of the project so as to take advantage of the opportunity cost of using those funds now for a more productive use. The discount rate resembles more like the return that you can earn on those funds (outside of the project i.e. similar to opportunity cost of letting go of the investment opportunity of investing in this capital project).

High the return required (discount rate) on the outflow, lower the PV of the outflow and higher the NPV, because by deferring the investments into the project you are able to achieve higher return (from more productive use of those funds now.)

About your second question, about the “PV of inflows getting lower as well”, the net impact is in favor of outflow because outflows are happening later in the life of the project and hence it has greater no. of discounting periods as well (thats why i said, think of it as the benefit of holding onto those funds and investing more productively out of the project), so this combination leads to lowest discounted value of the outflow and not as low discounted value of the inflows. Overall result - Increase in NPV

You must be really dumb not to refer to the graph which depicts my point that NPV as a function of discount rate is ambiguous. Go back to the original post: “ For an investment (not two investments) that has inflows in the early stages and outflows in the later stages, the use of a higher discount rate makes the NPV higher.” Except it doesn’t…

If you like to think differently fair enough. That’s what I said. The questions is misleading and ambiguous, subject to different interpretations.

You point is not taken.

  1. In NPV calculation (when outflow is in later stage and inflow is in early stage)

  2. If we increase the discount rate,

  3. The PV of inflows fall less when compared to the PV of outflow(s) resulting in increase in NPV

  4. The above statement regarding outflow is justified because, we are putting money into the project at a later stage (we get to use those funds and earn returns, why is that ambiguous?. A discount rate(WACC) justifies the cost of the fund for the project. This is represented by project WACC. Now if the risk of the project has gone up, as represented by higher project WACC (which is also the higher discount rate that you are referring to) then are you not better off if your investments into the project are not locked up from day 1? (of course you are). By putting money into the project at a later date, you are reducing the uncertainties, earning additional return on the funds that you are holding.

  5. All I am saying is that, usually the benefit from putting funds into a project at a later date (in case the interest rate is increased) far outweighs the disadvantage of cash in-flows discounted at higher rates (because there is an advantage also that you are getting in-flows at an early stage of the project. This negates to some extent the disadvantage of the higher discount rate)

I feel, thus that using higher discount rate just depicts that the riskiness of the project is more and the required return is more, i don’t find any ambiguity in this.

An no need to be rude here, if i am wrong then i am well equipped in my brain to accept it. Just prove me wrong, and i will accept the defeat.

As such by knowing two cents more than me you are not going to conquer the world. If you are , then all credit to me for being so close.

BTW i could not really see the graph that you had posted earlier(some error was coming instead of the graph), anyways I still stand by what i said earlier.

I suppose what your interpretation is,

When all else remaining same how can the project’s NPV increase if Discount rate increases? or How can the NPV increase when the WACC is increasing(in the special situation where cash inflows into the project are at later stage)?

so to answer this and eliminate all confusion, lets define something

inflow means -> the funds invested by co. into the project

outflow means -> cash flows generated by the project

Now lets imagine, the inflow as something which the co. borrows from a bank, and bank charges WACC as the interest taking into consideration riskiness of the project. The benefit of having inflow at the later stage of the project is to defer borrowing at a later stage and save the interest. If the WACC increases, the Bank will fund at a higher rate, by deferring the funding at a later stage, you are drawing more and more interest benefits, you need to pay to the bank only at a later stage (the benefit also increases because of WACC increasing)

The outflow out of the project come at a earlier stage though. The benefit of deferring the inflow outweighs the disadvantage of discounting of outflows out of the project on relative terms. This relative advantage increases further as discount rate goes up (WACC).

Vgmalu. Just to prove your point wrong. Change your discount rate to for example 25% in your scenario 2 and your NPV will be lower ($544,640 compared to $558,749).

Thanks for proving me wrong in saying that an increase in discount rate always leads to increase in NPV, i accept that it can reduce the NPV also.

However this only proves that the benefit is outweighed by the outflows getting reduced because of the higher discount rate. It does not prove “changing the Interest rate leads to ambiguity in assessment of the project NPV” as suggested by the water croc above.

Changing the Interest rate leading to increase / decrease of NPV has its rationale is my point.

I assume the “For an investment that has inflows in the early stages and outflows in the later stages, the use of a higher discount rate makes the NPV higher” was a question and the answer was true. If that is the case, it is a very poorly written question and I think the answer should be that it can increase or decrease NPV depending on the variables used.

Lets all help one another and not be rude to each other!!!

I see you are a long time member here, surprised you haven’t developed predatory instincts and immunity to rude language. Sorry about that.

I see a major confusion here. Cash inflow is universal language in finance to mean the cash coming in. So cash outflow is what you spend, inflow is what you receive.

So with a little tongue in cheek, I hope August 9 will be a good day for you…

Really if you felt that my reply was rude, i am sorry. My English is not that good, being an Indian, i studied in a Regional school (not English medium). We don’t have enough facilities here unlike the wwestern ppl.

I have no knowledge of English grammar. I have developed my intuition about English language just by reading newspapers. I come from a relatively poor background, and i am proud of what i have achieved.

I never meant to be arrogant.

I was just referring to croc’s remark that “The discount rate is ambiguous in judging the riskiness of the project i.e. discounting the CF at WACC” is flawed as a concept. Maybe i misinterpreted.

Actually Vgmalu, I thought Crocks reply to you was rude…