10/9/2016

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.

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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 Money Example 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

______________________________________________________________________ Example 2- Decrease in value What is the present value of $161 to be received after 5 years if the interest rate is 10% P

F

(1i)

n

P=

161

(1+.10)

5

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 Income/Benefits/Receipts/Salvage

$40,000

Cash Flow Table

$33,000 Year

Income

0

$35,000

Expense $60,000

1

$33,000

$1000

2

$35,000

$1500

3

$40,000

$2000

0

1

$1000

2

3

$1500 $2000

Cost/Expenditure/Disbursements

$60,000

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? F= ?

Find Future Value, Given Present Value F = P (1+i)n F = $10000 (1+.08)10 F = $10000 (2.1589) F = $21589

i = 8%, n = 10

P = $10000 11

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? F=$10000

Find Present Value, Given Future Value. i = 6%, n = 5

P=

F (1+ i)n

P=

10000 (1+.06)5

P = 7474

P=? 13

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? F=?

Find Future Value, Given Annuity. i = 6%, n = 5 0

F = 900 * 5.637

F = $5073

1

2

3

A = $900

4

5

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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? F = $80000

Find Annuity, Given Future Value

i = 6%, n = 5 0

A = 80000*0.1774

A = $14192

1

2

3

4

5

A=? 17

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?

A=?

Find Annuity, Given Present Value.

0

1

2

3

4

5

i = 7%, n = 5

A =100000*0.2439 A = $24389

P = $100000 19

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.

A = $5000

Find Present Value, Given Annuity.

0

1

2

3

4

5

i = 8%, n = 5

P = 5000 *3.9927

P  $19964

P=? 21

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.

+

+

0

1

2

3

4

5

i = 6%, n = 5

P = 21062 +3967

P = $25029

P=? 23

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.

0

A = 500*1.8836

2

1

A = $942 A = $942 + $5000 = $5942

3

4

5

i = 6%, n = 5 P=?

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 Year

Select a desirable project based on Net Present Value.

Cash 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

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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

Based on NPV, Project C is favorable.

EOY

Cash 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

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Depreciation and Taxes

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Depreciation

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.

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Computation Methods

STRAIGHT LINE METHOD For an asset with useful life n years, the annual depreciation in year j is

SD =

adjusted cost n

( j = 1,2,3,…..,n )

Adjusted cost = Asset Value – Salvage Value 30

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Straight Line Method

Example 13 A 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.

120000 -15000 SD = = $10500 10

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Straight Line Method Year

Example 14

Determine the straight-line depreciation schedule for example 5.1

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 15 An 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 33

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 + 3104 NPV = $1405 34

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END OF SEMINAR Please Fill the FEEDBACK FORM and RETURN IT to the RECEPTION.

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