NPV in Project Management - 3FOLD Education...
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10/9/2016 1 NPV in Project Management FREE PROFESSIONAL DEVELOPMENT SEMINAR The Basics • Most people know that money you have in hand now is more valuable than money you collect later on. • That’s because you can use it to make more money by running a business, or buying something now and selling it later for more, or simply putting it in the bank and earning interest. • Future money is also less valuable because inflation erodes its buying power. This is called the time value of money.
Transcript of NPV in Project Management - 3FOLD Education...
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NPV in Project ManagementFREE PROFESSIONAL DEVELOPMENT SEMINAR
The Basics
• Most people know that money you have in hand now is more valuable than money you collect later on.
• That’s because you can use it to make more money by running a business, or buying something now and selling it later for more, or simply putting it in the bank and earning interest.
• Future money is also less valuable because inflation erodes its buying power. This is called the time value of money.
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The Basics
• But how exactly do you compare the value of money now with the value of money in the future?
• That is where net present value comes in.
What is Net Present Value?
• Net present value (NPV) or net present worth (NPW) is a measurement of the profitability of an undertaking that is calculated by subtracting the present values (PV) of cash outflows (including initial cost) from the present values of cash inflows over a period of time.
• Incoming and outgoing cash flows can also be described as benefit and cost cash flows, respectively.
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Example of Time Value of MoneyExample 1 - Increase in value
What will be the future value of $100, 5 years from now if the interest rate is 10%
F = P (1+i)n | F = $100 (1.10)5 | F = $100 x 1.610 | F = $161
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Example 2- Decrease in value
What is the present value of $161 to be received after 5 years if the interest rate is 10%
)1( in
FP
P =
1615
(1+.10) P = $100
Cash Flow
• Cash flow is the difference between total cash inflow and outflows for a given period of time.
• It is an important concept in evaluating investment opportunities, projects, etc.,
• Cash flow diagram is an excellent technique to visualize and solve several cash flow problems.
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Cash Flow Representation
Year Income Expense
0 $60,000
1 $33,000 $1000
2 $35,000 $1500
3 $40,000 $2000
$60,000
$33,000
$1000$1500
$35,000
$40,000
$2000
0 1 2 3
Cost/Expenditure/Disbursements
Income/Benefits/Receipts/Salvage
Cas
h F
low
Tab
le
NPV in Decision Making
• NPV is an indicator of how much value an investment or project adds to the firm. In financial theory, if there is a choice between two mutually exclusive alternatives, the one yielding the higher NPV should be selected.
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NPV in Decision Making
If… Means… Then…
NPV > 0 the investment would add value to the firm
the project may be accepted
NPV < 0 the investment would subtract value from the firm
the project should be rejected
NPV = 0 the investment would neither gain nor lose value for the firm
We should be indifferent in the decision whether to accept or reject the project.
Single Payment – Compound Amount Factor
The future worth of a sum invested (or loaned) at compound interest.[1]
F = P ( 1 + i )n
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Single Payment – Compound Amount Factor
Example 3
If you invest $10000 in a fixed deposit that pays an interest of 8%, compounded
annually, what will be the maturity value at the end of year 10?
Find Future Value, Given Present Value
F = P (1+i)n
F = $10000 (1+.08)10
F = $10000 (2.1589)
F = $21589 11
P = $10000
F= ?
i = 8%, n = 10
Single Payment – Present Worth Factor
The discount factor used to convert future values (benefits and costs) to present values.[1]
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Single Payment – Present Worth Factor
Example 4
A bank pays 6% interest rate per year for fixed deposit. If you want a maturity
value of $10000 in 5 years, how much you should initially deposit in the bank?
Find Present Value, Given Future Value.
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P = 7474P =F
(1+ i)nP =
10000
(1+.06)5 P = ?
F=$10000
i = 6%, n = 5
Uniform Series, Compound Amount Factor
Takes a uniform series and moves it to a single value at the time of the last payment in the series.
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Uniform Series, Compound Amount Factor
Example 5
If you plan to deposit $900 each year in a savings account for 5 years and if the
bank pays 6% per year, compounded annually, how much money will have
accumulated at EOY 5?
Find Future Value, Given Annuity.
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F = ?
i = 6%, n = 5
0 1 2 3 4 5
A = $900F = $5073F = 900*5.637
Uniform Series, Sinking Fund Factor
Takes a single payment and spreads into a uniform series over N earlier periods. The last payment in the series occurs at the same time as F.
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Uniform Series, Sinking Fund Factor
Example 6
How much you should deposit per year for 5 years to accumulate $80000 at the EOY 5 if
the bank pays 6% interest per year compounded annually?
Find Annuity, Given Future Value
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F = $80000
i = 6%, n = 5
0 1 2 3 4 5
A = ? A = $14192A=80000*0.1774
Uniform Series, Capital Recovery Factor
Takes a single payment and spreads it into a uniform series over N later periods. The first payment in the series occurs one period later than P.
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Uniform Series, Capital Recovery Factor
Example 7
You have accumulated $100000 in a savings account that pays 7% per year, compounded
annually. Suppose you wish to withdraw a fixed sum of money at the end of each year for
5 years, what is the maximum amount that can be withdrawn?
Find Annuity, Given Present Value.
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i = 7%, n = 5
0 1 2 3 4 5
A = ?
A = $24389A=100000*0.2439 P = $100000
Uniform Series, Present Worth Factor
Takes a single payment and spreads it into a uniform series over N later periods. The first payment in the series occurs one period later than P.
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Uniform Series, Present Worth Factor
Example 8
If you decide to withdraw $5000 from your savings account at the end of each year for 5
years, how much money you should have in the bank now, if the bank pays 8% interest
rate compounded annually.
Find Present Value, Given Annuity.
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i = 8%, n = 5
0 1 2 3 4 5
A = $5000
19964$PP = 5000*3.9927 P = ?
Arithmetic Gradient – Present Worth Factor
Takes a arithmetic gradient series and moves it to a single payment two periods earlier than the first nonzero payment of the series.
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Arithmetic Gradient – Present Worth Factor
Example 9
How much money must initially be deposited in a savings account paying 6% per year, compounded annually, to
provide for 5 withdrawals that starts at $5000 and increase by $500 each year?
Find Present Value, Given Annuity and Gradient.
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i = 6%, n = 5
0 1 2 3 4 5
P = $25029P = 21062+3967 P = ?
+
+
Arithmetic Gradient – Uniform Series Factor
Takes a arithmetic gradient series and converts it to a uniform series. The two series cover the same interval, but the first payment of the gradient
series is 0.
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Arithmetic Gradient – Present Worth Factor
Example 10
How much money must initially be deposited in a savings account paying 6% per year, compounded annually, to
provide for 5 withdrawals that starts at $5000 and increase by $500 each year?
Find Present Value, Given Annuity and Gradient.
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A = $942A= 500*1.8836i = 6%, n = 5
0 1 2 3 4 5
P = ?
A= $942+$5000 = $5942
P = $25029
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Investment Alternatives
Example 11
The XYZ manufacturing company is currently earning an average before-tax return of 25% on its total investment.
The board of directors of XYZ is considering three project as given in the below table.
End of YearCash Flows
Project A Project B Project C
0 -$50000 -$80000 -$53000
1 20000 30000 23000
2 20000 30000 23000
3 20000 30000 23000
4 20000 30000 23000
Select a desirable project based on Net Present Value.
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Investment Alternatives
Example 12
NPVA = -$50000 + $20000(P/A, 25%, 4) = -$2760
NPVB = -$80000 + $25000(P/A, 25%, 4) = -$20950
NPVC = -$53000 + $23000(P/A, 25%, 4) = $1326
EOYCash Flows
Project A Project B Project C
0 -$50000 -$80000 -$53000
1 20000 30000 23000
2 20000 30000 23000
3 20000 30000 23000
4 20000 30000 23000
Based on NPV, Project C is favorable.
Depreciation and Taxes
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DEPRECIATION
(1) Decline in value of a capitalized asset.
(2) A form of capital recovery applicable to a property with a life span of more than one year, in which an appropriate portion of the asset's value is periodically charged to current operations.
Depreciation
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STRAIGHT LINE METHOD
For an asset with useful life n years, the annual depreciation in year j is
Computation Methods
SD =adjusted cost
n( j = 1,2,3,…..,n )
Adjusted cost = Asset Value – Salvage Value
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Straight Line Method
Example 13A new machine costs $120,000, has a useful life of 10 years, and can be sold for $15,000 at the end of
its useful life. Determine the annual straight-line depreciation amount for this machine.
SD =120000 -15000
10= $10500
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Straight Line Method
Example 14
Determine the straight-line
depreciation schedule for
example 5.1
Year Depreciation Charge per year
Accumulated Depreciation,
Book Value at End of Year
1 $10500 $10500 $109500
2 $10500 $21000 $99000
3 $10500 $31500 $88500
4 $10500 $42000 $78000
5 $10500 $52500 $67500
6 $10500 $63000 $57000
7 $10500 $73500 $46500
8 $10500 $84000 $36000
9 $10500 $94500 $25500
10 $10500 $105000 $15000
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The effect of Tax and Depreciation
Example 15An equipment can be purchased for $18000. The operating costs will be $10000 per year,
and the useful life is expected to be 5 years, with $5000 salvage value that time. The
present annual sales volume should increase by $16000 as a result of acquiring the
equipment. The company’s tax rate is 50%. Using straight-line depreciation technique with
10% MARR, calculate Net Present Worth of this investment.
Solution
Straight Line Depreciation per year = Asset Value – Salvage Value / n
Straight Line Depreciation per year = ($18,000 - $5000)/5 = $2600
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The effect of Tax and Depreciation
Calculation Description Year 1 Year 2 Year 3 Year 4 Year 5
Income - Expense A. BTCF $6000 $6000 $6000 $6000 $6000
(AV-SV)/n B. Depreciation -2600 -2600 -2600 -2600 -2600
C = A - B C. Net Taxable Income 3400 3400 3400 3400 3400
D = C x .50 D. 50% Tax -1700 -1700 -1700 -1700 -1700
E = C - D E. Profit 1700 1700 1700 1700 1700
F = E + B F. ATCF 4300 4300 4300 4300 4300*BTCF – Before Tax Cash Flow, *ATCF – After Tax Cash Flow
NPV = -$18000 + $4300 (P/A, 10%,5) + $5000 (P/F, 10%,5)NPV = -$18000 + 16301 + 3104NPV = $1405
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END OF SEMINARPlease Fill the FEEDBACK FORM and RETURN IT to the RECEPTION.
