# NPV question

if a project has IRR of 10%, and the NPV for the project is -\$250,000 using required rate of return of 11%, what is the change in NPV if required rate of return is now 12%? the choices are A decrease more than 250,000, B decrease less than 250,000, C increase more than 250,000, D increase less than 250,000 This is real question from dec 2007, what is your answer and why? Thanks

my answer is B. 0=CF0+CF1/(1+10%)+… -250=CF0+CF1/(1+11%)+… ?=CF0+CF1/(1+12%)+… since all dominators are >1, every additional 1%'s affect to the whole number will becoming less, like diminishing margin. so decrease less than 250,000 or test it with actual number, a=100/1.1=90.909 b=100/1.11=90.090 c=100/1.12=89.286 b-a=-0.819 c-b=-0.804 |c-b|

annexguy I think you’ve forgotten that CF0 is a negative number, so any diminishing of subsequent cash flows will lead to decrease of NPV more than 250,000. Required rate of return is the cost of capital: the greater it is, the smaller is the NPV; if RRR is an infinite number, NPV will equal CF0. I’d say the answer is A.

The answer is B. There is a convex relationship between NPV and Discount Rate. As Discount rate rises, the slope of the curve becomes less steep. The relationship is the same as the bond price / yield curve.

Hi, Would like to ask freewin3k. How did you manage to find questions to the 2007 dec exam? I myself would like to try question from the latest level 1 exam. Thanks

wyantis - inverse relationship exists in case of conventional cash flow (initial outflow and subsequent inflows). If cash flows are not conventional, NPV profile can take numerous shapes. But given the amount of information I’d guess it B Also how did u get the old question papers. I remember someone in this forum put the pdf link to all questions of 2007 couple months ago. Can’t find that thread now. Some one please repost.

The answer is A Just run a NPV with ROR 11% and 12.

kocunni69, How did you calculate the NPV without knowing the cash flows?? I think the answer is B based on the limited information provided.

Lets forget about the actual value of NPV and run the following cf0 = -100 cf1 = 90 I = 11 NPV = -18.92 cf0 = -100 cf1 = 90 I = 12 NPV = -19.64 So we say that NPV decresed more than 18.92

kochunni69, I think the question meant that the difference in NPV is more than \$250,000 or not? In your case the NPV for 12% discount rate should be atleast -18.92-18.92=-37.84. OR may be I took it wrong…

Another way to look at is: IRR is the discount rate at which the NPV = 0 Here the IRR is 10. When discount rate increased by a point, the present value of future cash flows decreased by 250,000. If the discount rate increases further, the present value of future cash flows is going to decrease further. So there is an inverse relationship between ROR and NPV.

You are reading this wrong. We know it will decrease, but will it decrease by an ADDITIONAL amount greater than 250,000? In your example NPV decreased by an additional .72.

It seems that the question is not about the cumulative change. Rather it is about additional change, as wyantjs stated.

If its not about the cumulative NPV, the answer could be either A or B depending on the size and timing of the cashflow. just try this example: CF0 = 27,750,000 CF1 = 30,525,000 You will get the answer B, Then consider a cashflow series where the cash inflow is higher on later years, you may find a different Answer (I think). I leave that for you to workout. freewin3k, you should tell us the correct answer and explanation after above discussion, and where you got the last year paper. thanks! Annex

I dont have the answer… i got the question from another forum. ppl were comparing answers after dec 2007 exam.

The question is wrongly framed or the choices are wrongly framed. Since freewin tells he has written what was discussed, i think the question has been framed wrongly by hearsay. “What is the “change” in NPV” is the question. We cannot calculate the change. The only info which is inferable is that NPV will become -260000 or -270000 or whatever once ROR is 12%. Hence NPV will decrease. We cannot figure out how much it will change by without cash flows. The options are not perfect. What does “decrease more than 250,000”. It means NPV decreases more than 250000 or becomes something like -520,000. What does “decrease less than 250,000” mean. It means NPV becomes something like -480,000. In fact if say B is the answer then it means “Change in NPV is decreased less than 250,000” I don’t think it makes sense. Others chip in.

Which is that forum Freewin?