# Math Help - Npw nfw

1. ## Npw nfw

Projects Cash Flow

n A B
1 -$17,500$-15,900
1 $13,610$13,210
2 $14,930$13,720
3 $14,300$13,500
Consider two mutually exclusive investment projects, each with MARR=12%.
(a) on the basis of the NPW criterion, which alternative would be selected?

(b) on the basis of the NFW criterion, which alternative would be selected?

2. For (a) simply compute the NPW of each project. A project's NPW is given by:

${NPV}_x = \sum_{t=1}^3 z_t (1+i)^{-(t-1)}$

Where $x \in {A,B}$ is your project and $t$ is the variable to denote a period. Since we compute the NPV for periode one and not for zero we have to correct this in the formula. With $i = 0.12$ you denote the interest rate. $z_t$ is the project's cash flow in some period.

You will choose the project with the highest NPV.

For (b) you will get the same result since the NFV is just the ${NFV}_x^t = {NPV}_x \mdot (1+i)^{t-1}$. Therefore if ${NPV}_A > {NPV}_B$ then ${NPV}_A \cdot (1+i)^{t-1} > {NPV}_B \cdot (1+i)^{t-1}$

3. NPV A: -17510 + 13610 + 14930/1.12 + 14300/1.12^2 = ~20840.23

NPV B: -15900 + 13210 + 13720/1.12 + 13500/1.12^2 = ~20322.12

As Raphw said, doing the NFV is redundant...

4. NPV Calculations for part a) are as following, I run this through an online NPV Calculation tool. Can't mention the link I think as we are not allowed to put web links here. Project A has higher NPV thus it should be the preferred one

PROJECT A

Net Cash Flows
CF0 = -17500
CF1 = 13610
CF2 = 14930
CF3 = 14300

Discounted Net Cash Flows
DCF1 = 13610/(1+0.12)^1 = 13610/1.12 = 12151.79
DCF2 = 14930/(1+0.12)^2 = 14930/1.2544 = 11902.1
DCF3 = 14300/(1+0.12)^3 = 14300/1.40493 = 10178.46

NPV Calculation
NPV = 12151.79 + 11902.1 + 10178.46 -17500
NPV = 34232.35 -17500
NPV = $16,732.35 PROJECT B Net Cash Flows CF0 = -15900 CF1 = 13210 CF2 = 13720 CF3 = 13500 Discounted Net Cash Flows DCF1 = 13210/(1+0.12)^1 = 13210/1.12 = 11794.64 DCF2 = 13720/(1+0.12)^2 = 13720/1.2544 = 10937.5 DCF3 = 13500/(1+0.12)^3 = 13500/1.40493 = 9609.03 NPV Calculation NPV = 11794.64 + 10937.5 + 9609.03 -15900 NPV = 32341.17 -15900 NPV =$16,441.17

5. @raphw

We discount each of the net cash flows at time t not at time t-1

Correct me on this one, as I been using discounted cash flow techniques for a while now and I would disagree with the assertion that you would discount the net cash flow at time t-1 instead of discounting it at time t

6. Originally Posted by dexteronline
@raphw We discount each of the net cash flows at time t not at time t-1
This is the given schedule:
1 -$17,500$-15,900
1 $13,610$13,210
2 $14,930$13,720
3 $14,300$13,500
If at time t, then schedule would be:
0 -$17,500$-15,900
1 $13,610$13,210
2 $14,930$13,720
3 $14,300$13,500

7. Originally Posted by Wilmer
This is the given schedule:
1 -$17,500$-15,900
1 $13,610$13,210
2 $14,930$13,720
3 $14,300$13,500
If at time t, then schedule would be:
0 -$17,500$-15,900
1 $13,610$13,210
2 $14,930$13,720
3 $14,300$13,500
Hi Wilmer

Thanks for pointing it out
Visiting this thread gave me the idea to create a new online NFV Calculation tool. Just went live

8. Originally Posted by dexteronline
Visiting this thread gave me the idea to create a new online NFV Calculation tool. Just went live
What's the URL?

9. Originally Posted by Wilmer
What's the URL?
Online NFV Calculation : Net Future Value Calculation

10. ## Sample Output of NFV Calculation

Originally Posted by Wilmer
What's the URL?
Here is a sample output from the Online NFV Calculation tool

Net Cash Flows
CF0 = -15000
CF1 = 6500
CF2 = 5500
CF3 = 4500
CF4 = 3500

Compounded Net Cash Flows
CCF1 = 6500 x (1+0.12)^3 = 6500 x 1.40493 = 9132.03
CCF2 = 5500 x (1+0.12)^2 = 5500 x 1.2544 = 6899.2
CCF3 = 4500 x (1+0.12)^1 = 4500 x 1.12 = 5040
CCF4 = 3500 x (1+0.12)^0 = 3500 x 1 = 3500

NFV Calculation
NFV = 9132.03 + 6899.2 + 5040 + 3500 -15000x(1+0.12)^4
NFV = 24571.23 -15000x1.57351936
NFV = 24571.23 -23602.7904
NFV = 968.44

11. I'd simplify it some:
Code:
Compounded Net Cash Flows
CCF0 = -15000 x (1+0.12)^4 = -23602.79
CCF1 =   6500 x (1+0.12)^3 =   9132.03
CCF2 =   5500 x (1+0.12)^2 =   6899.20
CCF3 =   4500 x (1+0.12)^1 =   5040.00
CCF4 =   3500 x (1+0.12)^0 =   3500.00
=======
NFV  =                          968.44

12. ## The changes have been implemented as per your suggestion

Originally Posted by Wilmer
I'd simplify it some:
Code:
Compounded Net Cash Flows
CCF0 = -15000 x (1+0.12)^4 = -23602.79
CCF1 =   6500 x (1+0.12)^3 =   9132.03
CCF2 =   5500 x (1+0.12)^2 =   6899.20
CCF3 =   4500 x (1+0.12)^1 =   5040.00
CCF4 =   3500 x (1+0.12)^0 =   3500.00
=======
NFV  =                          968.44
The changes have been implemented as per your suggestion, See the link
Online NFV Calculation : Net Future Value Calculation

13. I saw this:
"You need to make sure that the first cash flow is a negative amount
or else the program won't be able to show NFV Calculation."

That seems like an erroneous statement:
there's no reason preventing the flows to be like (as example):
6000, -7000, 2000, -3000, 4000

14. Originally Posted by Wilmer
I saw this:
"You need to make sure that the first cash flow is a negative amount
or else the program won't be able to show NFV Calculation."

That seems like an erroneous statement:
there's no reason preventing the flows to be like (as example):
6000, -7000, 2000, -3000, 4000
Yup that is fixed now, yet you do need to recall that here we are finding NFV in context of Capital Budgeting thus the first cash flow will be compounded at time period n-1, where as if we were to find NFV of an ordinary annuity with streams of cash receipts or payments we would compound the first cash flow at time period n.

See this page for two versions of my NPV Calculation tool Online NPV Calculation : Net Present Value Calculation

The first one on top permits finding NPV in the context of Capital Budgeting where the first cash flow is discounted at time period t=0 then have a look the bottom of the page for another version of the NPV Calculation tool that permits finding NPV of an annuity with streams of receipts or payments, here I am discounting the first cash flow at time period t=1. This latter version functions like MS Excel NPV formula.

So I guess I better create another version of the NFV Calculation tool as well for Calculating Net Future Value of an ordinary annuity

15. ## NFV Calculation

Originally Posted by dexteronline
yet you do need to recall that here we are finding NFV in context of Capital Budgeting thus the first cash flow will be compounded at time period n-1, where as if we were to find NFV of an ordinary annuity with streams of cash receipts or payments we would compound the first cash flow at time period n.

Sorry about the wrong interpretation of NFV Calculation for an annuity, it seems the calculator would work in both contexts as for Capital Budgeting and for an annuity. Just tested it with an ordinary annuity of \$10,000 per year for 5 years at 12% rate, and it produces the correct answer as listed below. You got to remember, my mind sometimes doesn't work right though it does work in some instances

Compounded Net Cash Flows

CCF0 = 10000 x (1+0.12)^4 = 15735.19
CCF1 = 10000 x (1+0.12)^3 = 14049.28
CCF2 = 10000 x (1+0.12)^2 = 12544
CCF3 = 10000 x (1+0.12)^1 = 11200
CCF4 = 10000 x (1+0.12)^0 = 10000
NFV = 63528.47

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