# © Chia Fah Choy 2005 Topic 2 – Investment Appraisal: Background and Techniques.

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© Chia Fah Choy 2005 Topic 2 – Investment Appraisal: Background and Techniques

© Chia Fah Choy 2005 Learning Objectives After studying this topic you will: understand the basis of long-term decision making; be able to use traditional appraisal techniques of Accounting Rate of Return and Payback; know the reasons why Discounted Cash Flow (DCF) techniques are used; be able to calculate and interpret Net Present Value (NPV); understand Internal rate of Return (IRR); know what is meant by the Excess Present Value Index; understand the effects of inflation on investment appraisal

© Chia Fah Choy 2005 Long Run Decision Making Assuming that finance is available the decision to invest will be based on three major factors: The investor’s beliefs in the future The alternative available in which to invest The investor’s attitude to risk

© Chia Fah Choy 2005 Traditional Investment Appraisal Techniques Accounting rate of return Payback

© Chia Fah Choy 2005 Accounting Rate of Return This is the ratio of average annual profits, after depreciation, to the capital invested. Alternative term: Return on Capital Employed (ROCE).

© Chia Fah Choy 2005 A firm is considering three projects each with an initial investment of \$1,000 and a life of 5 years. The profits generated by the projects are estimated to be as follows: YearProject IProject IIProject III 1200350150 2200 150 3200150 4200150200 5 150350 Total1,000 After tax and depreciation profits Calculate the accounting rate of return (ARR) on a. a.Initial capital b. b.Average capital Example 1

© Chia Fah Choy 2005 Accounting rate of return on Initial Capital Project I Project II Project III Average Profits = 1,000 5 5 5 = 200 p.a. 200 1,000 = 20% ARR is 200 1,000 = 20% 200 1,000 = 20% Example 1

© Chia Fah Choy 2005 Accounting rate of return on Average Capital Project I Project II Project III Average capital = 1,000 2 2 2 = 500 200 500 = 40% ARR is = 40% 200 500 200 500 Example 1

© Chia Fah Choy 2005 Payback A period, usually expressed in years which it takes for the project’s net cash inflows to recoup the original investment. The usual decision rules is to accept the project with the shortest payback period.

© Chia Fah Choy 2005 Calculate the payback periods for the following three projects: YearProject IProject IIProject III Cash flowCumulative cash flow Cash flowCumulative cash flow Cash flowCumulative cash flow 0-1,500 1600400300 2500 3400600400 4--300 5-- 6-- Net Cash Flow Example 2

© Chia Fah Choy 2005 Calculate the payback periods for the following three projects: YearProject IProject IIProject III Cash flowCumulative cash flow Cash flowCumulative cash flow Cash flowCumulative cash flow 0-1,500 1600-900400300 2500-400500 3400nil600400 4--300 5-- 6-- Net Cash Flow Example 2

© Chia Fah Choy 2005 Calculate the payback periods for the following three projects: YearProject IProject IIProject III Cash flowCumulative cash flow Cash flowCumulative cash flow Cash flowCumulative cash flow 0-1,500 -1500-1,500 1600-900400-1100300 2500-400500-600500 3400nil600nil400 4--300 5-- 6-- Net Cash Flow Example 2

© Chia Fah Choy 2005 Calculate the payback periods for the following three projects: YearProject IProject IIProject III Cash flowCumulative cash flow Cash flowCumulative cash flow Cash flowCumulative cash flow 0-1,500 -1500-1,500 1600-900400-1100300-1,200 2500-400500-600500-700 3400nil600nil400-300 4--300Nil 5--300 6-- 600 Net Cash Flow Pay back Periods Project I = 3 years Project II = 3 years Project III = 4 years Pay back Periods Project I = 3 years Project II = 3 years Project III = 4 years Example 2

© Chia Fah Choy 2005 Discounted Cash Flow (DCF) Net Present Value (NPV) Internal Rate of Return (IRR)

© Chia Fah Choy 2005 Net Present Value (NPV) NPV calculates the PV of expected cash inflows and outflows and finding out whether in total the present value of cash inflow is greater than the PV of cash outflows.

© Chia Fah Choy 2005 An investment is being considered for which the net cash flows have been estimated as follows: What is the NPV if the discount rate is 20%? Is the project acceptable? Year 0Year 1Year 2Year 3Year 4 -9,5003,0004,7004,8003,200 Example 3

© Chia Fah Choy 2005 An investment is being considered for which the net cash flows have been estimated as follows: What is the NPV if the discount rate is 20%? Is the project acceptable? Year 0Year 1Year 2Year 3Year 4 -9,5003,0004,7004,8003,200 Example 3

© Chia Fah Choy 2005 3,2004 AmountYear -95000 4,8003 4,7002 3,0001 Example 3

© Chia Fah Choy 2005 3,2004 PVAmountYear -95000 4,8003 4,7002 3,0001 Example 3

© Chia Fah Choy 2005 0.4823,2004 0.579 0.694 0.833 1.000 PVAmountYear -95000 4,8003 4,7002 3,0001 Example 3

© Chia Fah Choy 2005 1,5420.4823,2004 0.579 0.694 0.833 1.000 PVAmountYear -9,500-95000 2,7794,8003 3,2624,7002 2,4993,0001 Example 3

© Chia Fah Choy 2005 1,5420.4823,2004 0.579 0.694 0.833 1.000 PVAmountYear -9,500-95000 582 2,7794,8003 3,2624,7002 2,4993,0001 Example 3

© Chia Fah Choy 2005 Meaning of NPV Amount owing b/fwd Year’s interest Year’s cash flow Balance o/s c/fwd End Year 19,500 End Year 2 End Year 3 End Year 4 Example 3

© Chia Fah Choy 2005 Meaning of NPV Amount owing b/fwd Year’s interest Year’s cash flow Balance o/s c/fwd End Year 19,5001,900 End Year 2 End Year 3 End Year 4 Example 3

© Chia Fah Choy 2005 Meaning of NPV Amount owing b/fwd Year’s interest Year’s cash flow Balance o/s c/fwd End Year 19,5001,9003,000 End Year 2 End Year 3 End Year 4 Example 3

© Chia Fah Choy 2005 Meaning of NPV Amount owing b/fwd Year’s interest Year’s cash flow Balance o/s c/fwd End Year 19,5001,9003,0008,400 End Year 2 End Year 3 End Year 4 Example 3

© Chia Fah Choy 2005 Meaning of NPV Amount owing b/fwd Year’s interest Year’s cash flow Balance o/s c/fwd End Year 19,5001,9003,0008,400 End Year 28,400 End Year 3 End Year 4 Example 3

© Chia Fah Choy 2005 Meaning of NPV Amount owing b/fwd Year’s interest Year’s cash flow Balance o/s c/fwd End Year 19,5001,9003,0008,400 End Year 28,4001,6804,7005,380 End Year 3 End Year 4 Example 3

© Chia Fah Choy 2005 Meaning of NPV Amount owing b/fwd Year’s interest Year’s cash flow Balance o/s c/fwd End Year 19,5001,9003,0008,400 End Year 28,4001,6804,7005,380 End Year 35,3801,0764,8001,656 End Year 4 Example 3

© Chia Fah Choy 2005 Meaning of NPV Amount owing b/fwd Year’s interest Year’s cash flow Balance o/s c/fwd End Year 19,5001,9003,0008,400 End Year 28,4001,6804,7005,380 End Year 35,3801,0764,8001,656 End Year 41,6563313,2001,213 Example 3

© Chia Fah Choy 2005 Meaning of NPV Amount owing b/fwd Year’s interest Year’s cash flow Balance o/s c/fwd End Year 19,5001,9003,0008,400 End Year 28,4001,6804,7005,380 End Year 35,3801,0764,8001,656 End Year 41,6563313,2001,213 Net Terminal Value has a present value of 1,213 x 0.482 = 585 Example 3

© Chia Fah Choy 2005 Internal Rate of Return Discount rate which gives zero NPV Alternative names: –DCF yield –Marginal efficiency of capital –Trial and error method –Discounted yield –Actuarial rate of return

© Chia Fah Choy 2005 1,3120.4103,2004 0.512 0.640 0.800 1.000 PVAmountYear -9,500-95000 -322 2,4584,8003 3,0084,7002 2,4003,0001 r = 25% Example 3

© Chia Fah Choy 2005 -200 -400 200 400 600 0 NPV 5%10%15%20%25%30%35%40% Discount rate NPV @ 20% = 582 NPV @ 25% = -322 IRR = 20% +5% (582/904)=23.2% Example 3

© Chia Fah Choy 2005 Decision rule using IRR Where the calculated IRR is greater than the company’s cost of capital then the project is acceptable.

© Chia Fah Choy 2005 NPV and IRR compared Accept/reject decisions Absolute and relative measures Mutually exclusive projects

© Chia Fah Choy 2005 Accept/reject decisions Accept ProjectReject Project NPVPositive NPVNegative NPV IRRIRR above cost of capital IRR below cost of capital

© Chia Fah Choy 2005 Absolute and relative measures NPV is an absolute measure of the return on a project IRR is a relative measure relating the size and timing of the cash flows to the initial investment

© Chia Fah Choy 2005 Assume a project has the following cash flows: Project acceptable by both methods – assuming 10% is the cost of capital. Year 0Year 5 Project x-20,00040,241 NPV@10%4,990 IRR15% Now assume that the project is scaled up by a factor of 10. Year 0Year 5 Project 10x-200,000402,410 NPV@10%49,900 IRR15% The NPV method clearly discriminates between Project X and Project 10X whereas the IRR remains unchanged at 15%. Example 4

© Chia Fah Choy 2005 Mutually exclusive projects Only one of several alternative projects can be chosen

© Chia Fah Choy 2005 Mutually exclusive projects of differing scale A property company wishes to develop a site it owns. Three sizes of property are being considered and the costs and revenues are as follows: Year 0 Expenditure Year 1 to perpetuity Rentals p.a. Small development20.6 Medium development 41 Large development61.35 The cost of capital is 10% and it is required to rank the projects by NPV and IRR and to select the most profitable. The projects are mutually exclusive because the building of one size of development excludes the others. Example 5

© Chia Fah Choy 2005 ExpenditureP.V. of rentals NPVIRR % Small26430 Medium410625 Large613.57.522.5 Incremental expenditure Incremental rental Incremental IRR Stage 1 (small) 20.630 Stage 2 (medium - small) 20.420 Stage 3 (large - medium) 20.3517.5 Example 5 Ranking of NPV and IRR Incremental IRR

© Chia Fah Choy 2005 Mutually exclusive projects, same scale Two mutually exclusive investments have cash flows as follows: Year 0Year 1Year 2Year 3 Project A-24,0008,00012,00016,000 Project B-24,00016,00010,0008,000 The cost of capital is 10% and it is required to rank the projects by NPV and IRR and to select the most profitable. Example 6

© Chia Fah Choy 2005 Mutually exclusive projects, same scale The NPV and IRR of these projects are as follows: NPV @10%IRR % Project A5,20020.65 Project B4,81222.8 The ranking differ and, assuming that 10% is the appropriate discount rate, the ranking given by the NPV, i.e. Project A being preferred, gives the maximum wealth to the company. Example 6

© Chia Fah Choy 2005 Non-conventional cash flows

© Chia Fah Choy 2005 Examples of Non-Conventional Cash-Flow Patterns Year 0Year 1Year 2 Project X-2,0004,700-2,750 Project Y2,000-4,0004000 Project X has 2 outflows and is thus non- conventional Project Y has an outflow in a year’s time instead of initially and is thus non- conventional When a project has non-conventional cash flows it may have – –One IRR – –Multiple IRRs – –No IRR Example 7

© Chia Fah Choy 2005 Examples of Non-Conventional Cash-Flow Patterns Year 0Year 1Year 2 Project X-2,0004,700-2,750 Project Y2,000-4,0004000 Present Value Profile of Project X Multiple IRRs Example 7

© Chia Fah Choy 2005 Examples of Non-Conventional Cash-Flow Patterns Year 0Year 1Year 2 Project X-2,0004,700-2,750 Project Y2,000-4,0004000 Not a real number! No IRR Example 7

© Chia Fah Choy 2005 A labour saving machine costs \$60,000 and will save \$24,000 p.a. at current wage rates. The machine is expected to have a 3 year life and nil scrap value. The firm’s cost of capital is 10%. Calculate the project’s NPV a. a.With no inflation b. b.With general inflation of 15% which wage rates are expected to follow (i.e. synchronised inflation). c. c.With general inflation of 15% and wages rising at 20% p.a. (i.e. differential inflation). Example 8

© Chia Fah Choy 2005 NPV – No inflation Project unacceptable as it has a negative NPV at company’s cost of capital.

© Chia Fah Choy 2005 General Inflation 15%, wages increasing at 15% Wage saving p.a. with no inflation Wage saving p.a. with 15% inflation 24,00027,600 24,00031,740 24,00036,501 YearCash flow26 ½% Discount factors Present value 0-60,0001.000-60,000 127,6000.79221,859 231,7400.62419,806 336,5010.49418,031 NPV-304 With a 15% inflation rate, the discount rate is 1.10 (1.15) – 1 = 0.265 = 26 ½ %

© Chia Fah Choy 2005 YearWage saving p.a. with 20% rising 124,000(1.20) 1 28,800 224,000(1.20) 2 34,560 324,000(1.20) 3 41,472 YearCash flow26 ½% Discount factors Present value 0-60,0001.000-60,000 128,8000.79222,810 234,5600.62421,565 341,4720.49420,487 NPV4,862 General Inflation 15%, wages increasing at 20%

© Chia Fah Choy 2005 Money and Real Discount Rates

© Chia Fah Choy 2005 General inflation of 15% and wages rising at 20% p.a. YearMoney cash flow General inflation 15% discount factors Real cash flows Real discount factors 10% Present values 0-60,0001.000-60,0001.000-60,000 128,8000.87025,0560.90922,776 234,5600.75626,1270.82621,581 341,4720.65827,2890.75120,494 NPV4,851

© Chia Fah Choy 2005 Summary Investment decisions are long run decisions where consumption and investment opportunities are balanced over time. The decision to invest is based on many factors including: the investor’s beliefs in the future, the alternatives available and his attitude to risk. The ‘traditional’ investment appraisal techniques are the accounting rate of return and payback. Discount Cash Flow (DCF) techniques use cash flows rather than profits and take account of the time value of money.

© Chia Fah Choy 2005 Summary The formula for Net Present Value is and given the assumption of the basic model, a project is acceptable if it has a positive NPV at the firm’s cost of capital. NPV can be interpreted as the potential increase in consumption made possible by the project valued in present day terms.

© Chia Fah Choy 2005 Summary Internal Rate of Return (IRR) is the discount rate which gives zero NPV and can be found graphically or by linear interpolation. With conventional projects IRR and NPV give the same accept or reject decision. NPV is an absolute measure whereas IRR is a relative one. NPV is a more appropriate measure for choosing between mutually exclusive projects and in general is technically superior to IRR.

© Chia Fah Choy 2005 Summary The discount rate used in DCF calculations is known as the cost of capital. Specific inflation is of more direct concern in investment appraisal and differential inflation is commonly encountered. The general treatment of inflation in investment appraisal means distinguishing between money and real cash flows The amount and timing of tax payment and other tax effects must be considered

© Chia Fah Choy 2005 Points to note!! Successful investment appraisal is entirely dependent on the accuracy of cost and revenue estimates. No appraisal technique can overcome significant inaccuracies in the estimates.

© Chia Fah Choy 2005 Learning Objectives After studying this topic you will: understand the basis of long-term decision making; be able to use traditional appraisal techniques of Accounting Rate of Return and Payback; know the reasons why Discounted Cash Flow (DCF) techniques are used; be able to calculate and interpret Net Present Value (NPV); understand Internal rate of Return (IRR); know what is meant by the Excess Present Value Index; understand the effects of inflation on investment appraisal