NPV in Project Management

Transcription

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. 1

2 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. 2

3 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 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% F P P = ( 1 i) n 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. 3

4 Cash Flow Table 10/9/2016 Cash Flow Representation Year Income Expense 0 $60,000 1 $33,000 $ $35,000 $ $40,000 $2000 $40,000 $35,000 $33, $1000 $1500 $2000 $60,000 Income/Benefits/Receipts/Salvage Cost/Expenditure/Disbursements 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. 4

5 NPV in Decision Making If Means Then NPV > 0 NPV < 0 NPV = 0 the investment would add value to the firm the investment would subtract value from the firm the investment would neither gain nor lose value for the firm the project may be accepted the project should be rejected 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 10 5

6 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=? F = P (1+i) n i = 8%, n = 10 F = $10000 (1+.08) 10 F = $10000 (2.1589) P = $10000 F = $ Single Payment Present Worth Factor The discount factor used to convert future values (benefits and costs) to present values. [1] 12 6

7 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. F=$10000 i = 6%, n = 5 P = F P = 7474 (1+i) n P = (1+.06) 5 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. 14 7

8 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. i = 6%, n = 5 F =? F = 900*5.637 F = $5073 A = $ 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. 16 8

9 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 F = $80000 i = 6%, n = A = 80000* A = $14192 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. 18 9

10 Uniform Series, Capital Recovery Factor Example 7 You have accumulated $ 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. A =? A =100000* A = $24389 P = $ i = 7%, n = 5 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

11 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. A = $ i = 8%, n = 5 P = 5000* 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

12 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. + + P = $25029 P = P =? i = 6%, n = 5 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

13 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. A = 500* A = $942 A = $942+$5000 = $ i = 6%, n = 5 P =? P = $ 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. Select a desirable project based on Net Present Value. End of Year Cash Flows Project A Project B Project C 0 -$ $ $

14 Investment Alternatives Example 12 NPV A = -$ $20000(P/A, 25%, 4) = -$2760 NPV B = -$ $25000(P/A, 25%, 4) = -$20950 NPV C = -$ $23000(P/A, 25%, 4) = $1326 Based on NPV, Project C is favorable. EOY Cash Flows Project A Project B Project C 0 -$ $ $ Depreciation and Taxes 28 14

15 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. 29 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 15

16 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. SD = = $ 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 $ $10500 $21000 $ $10500 $31500 $ $10500 $42000 $ $10500 $52500 $ $10500 $63000 $ $10500 $73500 $ $10500 $84000 $ $10500 $94500 $ $10500 $ $

17 The effect of Tax and Depreciation Example 15 An equipment can be purchased for $ 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 = $ 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 $6000 (AV-SV)/n B. Depreciation C = A - B C. Net Taxable Income D = C x.50 D. 50% Tax E = C - D E. Profit F = E + B F. ATCF *BTCF Before Tax Cash Flow, *ATCF After Tax Cash Flow NPV = -$ $4300 (P/A, 10%,5) + $5000 (P/F, 10%,5) NPV = -$ NPV = $

18 END OF SEMINAR Please Fill the FEEDBACK FORM and RETURN IT to the RECEPTION. 18