# NPV/Payback Period

YR 1 cost \$570,356,918 NPV \$125 million Generating \$85 million each year in after tax cash flow What’s the payback period? 4.11 4.7 5.24 6.06

85 * 6.06 = ~ 570M so 6.06 is the payback period.

I was being lazy, let me just write the whole Q: Project with NPV \$125M Lasts 10 years Generate \$85M in after tax Cash flow Cost of cap is 8% What’s the payback period 4.11 4.7 5.24 6.06 BTW D is wrong.

C

Correct. Can you explain? I don’t understand why you take away NPV before dividing by 85M

Okay, I just threw numbers in, I guess I did it right, LOL PV \$570,356,918 FV = 125MM PMT = 85MM Compute N = 5.24

does the question say, payback period or discounted payback period ? payback = 570/85 = 6.7

You first calculated the PV of the 85mil flow from the project. If you have an NPV of 125, it means the initial investment in the project was 125mil lower than the PV of the flow. Deduct that from the PF of cash flow, that would be an initial investment of 445.36mil (more or less). If you have a BAII Plus professional, after you calculate the NPV using: CF0=-445.36mil , CF1=85 for F1=10, CPT NPV, introduce the cost of capital I=8, at a couple of arrows down you get the payback. Or, simply, divide 445.36mil /85 = 5.2395~5.24

that’s what I kept getting you need to take away the NPV but I don’t understand why So you get (570 - 125)/85 I just don’t get why it’s -125? Can someone explain?

How did my calculation work then?

Because of the positive the NPV, there is an extra flow of cash to your project, beyond your initial investment. You need to find the period your initial investment gets recouped.

amberpower Wrote: ------------------------------------------------------- > How did my calculation work then? You had 125 in FV

map1 Wrote: ------------------------------------------------------- > amberpower Wrote: > -------------------------------------------------- > ----- > > How did my calculation work then? > > > You had 125 in FV So that deducted it? Would my way work each time? Seems an awful lot easier.

I think it would work each time, but only for payback period, not for discounted payback period. For discounted payback period you have to deduct the NPV upfront from the initial investment, since you would use the cost of capital to discount the flows.

Got it, thanks. I was going to initially go the CF way but I didn’t know what to use for time periods, how did you know it was 10? Or you just knew to go at least 10 to see where the payback time period would fall?

I have my BAII Plus professional, a real plus plus:) he tells me the payback, the discounted payback, duration and all this sweet stuff:) I just made sure I got the NPV of 125 with the cost of 8, for the project duration (author reposted supplementary data - the duration of 10):))

Well that would have helped! LOL

C

C, assuming it is DISCOUNTED PAYBACK it asks for, normally, you just take 570/85 = 6.75 b/c they give you all the extra info, we are supposed to know it wants discounted ??? tricky bastards

amberpower Wrote: ------------------------------------------------------- > Okay, I just threw numbers in, I guess I did it > right, LOL > > PV \$570,356,918 > FV = 125MM > PMT = 85MM > Compute N = 5.24 I do this and I get 6