# NPV question

https://i.imgur.com/k6y1jYG.png

Been working through this for a while and im unsure about how to get to the conclusion?

Best thing is to draw a timeline for the 2 alternatives:

0: 120 // 200

1: 120 // 80

2: 120 // 80

3: 120 // 80

4: 120 // 80

5: 120 // 80

Now start to calculate the NPVs of each alternative. Bear in mind that the payments are made at the beginning of each period. So you either change your calculator to BGN mode or multiply the initial result with (1+r) as I’ve done here.

For the first option: N = 5; I/Y = 9; PMT = 120; FV = 0 --> CPT PV = 466,759.15

This is the result assuming end year payments. To get the NPV for beginning of period payments multiply this result with (1+0,09) and you get NPV option 1 = 508,766.39

For the second option you can use the CF worksheet: CF0 = 200; C01 = 80; F01 = 4 --> CPT NPV; I = 9; NPV option 2 = 459,177.59

As you start with CF0 for the first payment of 200 no additional adjustment for beginning of period payments is needed for the second option using the CF worksheet.

The resulting delta is 49,588.80 in line with answer C.

Oscar

Nice one Oscar, justice done.

P1 - pay 80K more, and P2 thro P5 pay 40K less

So

CF0 = -80, CF1-4 = +40

NPV @ 9% => 49.589

That’s a good one! That way is far more elegant than the one proposed by me above!

Thanks!

Yep, cpk123 used incremental cash flow method, kind of speak.

Just checking the numbers of the problem you can learn that option B can never be chosen, so if you are in trouble on the exam, at least take out 1 option, so you have 50/50. Most known as “educated guessing”. Always try to apply it.