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Math Help - Npw nfw

  1. #1
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    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?
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  2. #2
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    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}
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  3. #3
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    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...
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  4. #4
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    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
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  5. #5
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    @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
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  6. #6
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    Quote Originally Posted by dexteronline View Post
    @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
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  7. #7
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    Quote Originally Posted by Wilmer View Post
    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
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  8. #8
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    Quote Originally Posted by dexteronline View Post
    Visiting this thread gave me the idea to create a new online NFV Calculation tool. Just went live
    What's the URL?
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  9. #9
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    Quote Originally Posted by Wilmer View Post
    What's the URL?
    Online NFV Calculation : Net Future Value Calculation
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  10. #10
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    Sample Output of NFV Calculation

    Quote Originally Posted by Wilmer View Post
    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
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  11. #11
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    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
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  12. #12
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    The changes have been implemented as per your suggestion

    Quote Originally Posted by Wilmer View Post
    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
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  13. #13
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    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
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  14. #14
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    Quote Originally Posted by Wilmer View Post
    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
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  15. #15
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    NFV Calculation

    Quote Originally Posted by dexteronline View Post
    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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