16 Time Value and Project Viability Indicators

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TIME VALUE OF MONEY AND PROJECT VIABILITY INDICATORS Prepared by Norman R. Ramos LGU Finance Advisor, ADB TA 7451-PHI Support to Local Government Financing November 2011

TIME VALUE OF MONEY: 

TIME VALUE OF MONEY TIME VALUE OF MONEY Is the opportunity cost of foregoing the use of your funds to some future date such as the loss of purchasing power that occurs over time as a result of inflation. If you invest your one peso today, you expect to receive in return more than one peso a year from now. INFLATION – is an increase in average prices over time.

SIMPLE INTEREST: 

SIMPLE INTEREST SIMPLE INTEREST - is the amount of interest earned on the principal amount stated. The PRINCIPAL AMOUNT STATED is the base amount that we borrow or save. I = P r t I = (P1,000)(.08)(3) = P240 w here: I = Interest P = Principal r = Rate t = Time

SIMPLE INTEREST : 

SIMPLE INTEREST SIMPLE INTEREST - used in many short-term (less than one year) transactions and is computed initially based on original principal amount, interest rate, and time span. It is added onto the principal to determine the total amount owed or due. P + I = S where S = Total amount due (maturity amount)

COMPOUND INTEREST: 

COMPOUND INTEREST COMPOUND INTEREST – interest earned or charged on both the principal amount and on the accrued interest that has been previously earned or charged. With compound interest, we earn interest both on the principal amount and on the interest that has already accrued. Interest for year 1 = (P1,000)(.08)(1) = P80 Interest for year 2 = (P1,080)(.08)(1) = P86.40 Interest for year 3 = (P1,166.40)(0.08)(1) = P93.31

QUOTED VS EFFECTIVE RATE: 

QUOTED VS EFFECTIVE RATE Interest rates take on 2 dimensions: a) rate that is stated or quoted by the lending institution, and b) actual or effective rate that is earned or charged. STATED or QUOTED RATE – is the rate of interest that is listed, normally on an annual basis, and it disregards compounding. EFFECTIVE ANNUAL RATE – is the actual rate that is paid by the borrower or earned by the investor when compounding is taken into consideration.

DISCOUNT RATE: 

DISCOUNT RATE Discount Rate or the interest rate in present value calculations may be represented by: a) Company’s opportunity cost of capital b) Investors’ opportunity cost of capital c) Risk adjusted discount rate

EFFECTIVE ANNUAL RATE: 

EFFECTIVE ANNUAL RATE Effective Annual Rate = (1+i) n - 1 w here: i = Interest rate per period (found by dividing the quoted rate by the number of compounding periods) n = Number of compounding periods per year Example : Using 8% compounded quarterly for one year gives an effective annual rate of : (1+ .08 / 4 ) 4 -1 = (1.02) 4 = 1.0824 –1 = 0.0824 or 8.24%

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9 Investment cost, income and expenses for capital investment projects are earned and spent over a period of time, usually reckoned in terms of years. Cash inflows and outflows for projects or any investment proposition are therefore generated and spent over a number of years. The concept of the discounted cash flow (DCF) recognizes that cash inflows and outflows for projects are generated through time. Computing for the estimated return for each project has to recognize the timing of these cash inflows and outflows to determine the acceptability of the project. DISCOUNTED CASH FLOW (DCF)

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10 DCF methods may be applied in the analysis of : investment decisions financing decision choosing the best alternative decision There are 2 variations of the DCF method: a) the Internal Rate of Return (IRR) b) the Net Present Value (NPV) The IRR method computes for the estimated annual return from the net cash flows generated by the project over its useful life. If the IRR is equal to or higher than the minimum desired rate of return, then the project should be accepted . DISCOUNTED CASH FLOW (DCF)

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11 The NPV method starts with a desired ROI and determines the NPV of the project’s net cash flows over time discounted at the desired ROI. The initial capital investment is then subtracted from the NPV of cash flows. If the resulting sum (i.e., the difference between the NPV of cash flows and initial capital investment) is zero or positive, the project should be accepted. Generally, both the IRR and NPV approaches result in the same accept or reject the project decision. In some cases, however, the use of one approach is preferable to the other. Comparing rates of return of projects which involve different capital outlays and different life spans is better analyzed using the NPV approach. DISCOUNTED CASH FLOW (DCF)

DISCOUNTED CASH FLOW (DCF): 

Income and Expense Items to Be Considered When Using the DCF Method in Analyzing Investment Alternatives a. Initial and Subsequent Capital Investment Outlays - The initial capital outlay is equivalent to the estimated project cost. b. Operating Inflows and Outflows – Income or savings generated by the project (inflows) and operating costs (outflows) should be determined. These information can be lifted or picked up from the projected income statements of the project. DISCOUNTED CASH FLOW (DCF)

DISCOUNTED CASH FLOW (DCF): 

Income and Expense Items to Be Considered When Using the DCF Method in Analyzing Investment Alternatives c. Economic Life of Project – If the project is deemed to have an economic life of 10 years, the analysis should also have a ten-year horizon. If the operations has reached full capacity by the 5 th year, operating inflows and outflows may be kept constant until the end of the project’s life. d. Future Disposal/Salvage/Residual Values - At the end of a project’s useful life, the disposal or salvage value of project assets should be estimated and included as an inflow. e. Minimum Desired Rate of Return – To determine the acceptability of a project, the desired rate of return or discount rate should be set by the creditor or investor. DISCOUNTED CASH FLOW (DCF)

TIME VALUE OF MONEY METHODS: 

TIME VALUE OF MONEY METHODS 1. FUTURE VALUE OF A LUMP SUM 2. PRESENT VALUE OF A FUTURE LUMP SUM 3. FUTURE VALUE OF AN ORDINARY ANNUITY 4. FUTURE VALUE OF AN ANNUITY DUE 5. PRESENT VALUE OF AN ORDINARY ANNUITY 6. PRESENT VALUE OF AN ANNUITY DUE

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15 1 . FUTURE VALUE OF A LUMP SUM FV = PV (1+i) n where FV = Future value PV = Present value i = Interest rate n = Number of periods (1+i) n = FVF (Future value factor) Compute for FVF or refer to the Future Value of a lump sum table FUTURE VALUE OF A LUMP SUM

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16 2. PRESENT VALUE OF A FUTURE LUMP SUM 1 PV = FV ------- (1+i) n Where the term in the square brackets is known as the present value factor (PVF). Compute for PVF or refer to a Present Value of a future lump sum table . PRESENT VALUE OF A FUTURE LUMP SUM

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17 3. FUTURE VALUE OF AN ORDINARY ANNUITY Assume that money is invested at the end of each period. (1+i) n - 1 FV = A ----------- i Compute for FVOA or refer to the Future Value of an ordinary annuity table. FUTURE VALUE OF AN ORDINARY ANNUITY

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18 4. FUTURE VALUE OF AN ANNUITY DUE Assume : Money is invested at the beginning of each period. (1+i) n+1 -1 FV = A ----------- - 1 i Compute for the FVAD or refer to the Future Value of an annuity due table. FUTURE VALUE OF AN ANNUITY DUE

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19 5. PRESENT VALUE OF AN ORDINARY ANNUITY (1+i) n - 1 PV = A ------------- I (1+i) n Compute for the PVOA or refer to the Present Value of an ordinary annuity table. PRESENT VALUE OF AN ORDINARY ANNUITY

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20 6. PRESENT VALUE OF AN ANNUITY DUE (1+i) n-1 -1 PV = A -------------- + 1 i (1+i) n-1 Compute for the PVAD or refer to the Present Value of an annuity due table. PRESENT VALUE OF AN ANNUITY DUE

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21 Payback Period Accounting Rate of Return Net Present Value Internal Rate of Return Profitability Index PROJECT VIABILITY INDICATORS

PAYBACK PERIOD: 

PAYBACK PERIOD Payback = ___ Investment___ = ___ P40 Mil___ = 5.33 years Period Annual cash inflow P7.5Mil per year Measures the number of years required to recover the initial investment . Rough measure of investment risk - the longer it takes to recoup an original investment, the greater the risk. Deficiency : 1. Ignores timing of cash flows. 2. Insensitive to all cash flows occurring beyond the payback date.

ACCOUNTING RATE OF RETURN: 

ACCOUNTING RATE OF RETURN Accounting Rate of Return = Average annual cash inflow Total cash outflow = ([(7.5 x 9 + 17) /10]/40) = 21.13% The accounting rate of return (AROR) relates the profits provided by a project to its average investment. This measure is easy to calculate but not as accurate as the IRR. Does not consider the Time Value of Money. Rates of return provided are not realistic because it is based on the average value of the investment over its life, rather than original cost. It uses average income without discounting cash flows to PV. Deficiency - Insensitive to the timing of cash flows

NET PRESENT VALUE : 

Criteria for capital budgeting Net Present Value (NPV) method focuses on all cash flows generated by a project and capitalizes them at a market-determined discount rate. NPV = PV of Inflows – PV of Outflows Where the present values of cash inflows and outflows are determined by discounting the cash flows at a market-determined opportunity cost of capital. The NPV rule accepts projects with positive NPVs and rejects projects with negative NPVs. NET PRESENT VALUE

INTERNAL RATE OF RETURN: 

The Internal Rate of Return (IRR) is the discount rate that makes the NPV or excess market value of a project equal to zero. A project is accepted or rejected by comparing its IRR with its required rate of return, which is the opportunity cost of capital. INTERNAL RATE OF RETURN

PROFITABILITY INDEX: 

Criteria for capital budgeting The Profitability Index (PI) is a different way of presenting the same information that the NPV provides. PI = PV of inflows PV of outflows The PI rule accepts projects of PI>1 and rejects projects if PI<1. Advantage of PI – Easy to calculate , explain, provides clear picture of cost benefit analysis. Disadvantages of PI – May give a false sense of security for a project if interest rate estimates are too low or cash flow estimates are too high. PROFITABILITY INDEX

EXAMPLE 1 : 

The LGU is contemplating construction of a container loading pier. The LGU’s best estimate of cash flows associated with constructing and operating the pier for a 10-year period appears in the following table. The LGU expects to salvage the pier for P9.5 Mil at the end of its useful life, bringing the 10th year cash flow to P17Mil : Following figure presents the same information in the form of a cash flow diagram : 1 2 3 4 5 6 7 8 9 10 7.5 17 40 EXAMPLE 1

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28 Example 1: NPV, IRR, PI

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29 Example 1: NPV, IRR, PI

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30 The Philippine Government is issuing a bond. Hereunder are the features of the bond issuance: 1. Face Value/Amount -P 10 Bil 2. Term - 10 years 3. Interest Rate - 10% p.a. fixed payable yearly (end of year) 4. Repayment of Principal - Lump sum upon maturity 5. Price - 90% (or 10% discount against face value) From the point of view of the investor: 1. Provide the amortization schedule of the bond float 2. Compute for the NPV at the discount rates of 10% and 12% 3. Estimate the IRR of the Bond. EXAMPLE 2

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31 EXAMPLE 2: AMORTIZATION SCHEDULE, NPV, IRR

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32 NPV at discount rates of 10% and 12%; IRR EXAMPLE 2: AMORTIZATION SCHEDULE, NPV, IRR