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Chapter seven

Chapter seven. Net present value and other investment criteria. Chapter objectives. LO7.1 Understand the reasons why the net present value criterion is the best way to evaluate proposed investments. LO7.2 Understand the payback rule and some of its shortcomings.

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Chapter seven

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  1. Chapter seven Net present value and other investment criteria

  2. Chapter objectives LO7.1 Understand the reasons why the net present value criterion is the best way to evaluate proposed investments. LO7.2 Understand the payback rule and some of its shortcomings. LO7.3 Understand the discounted payback rule and some of its shortcomings. continued

  3. Chapter objectives LO7.4 Understand accounting rates of return and some of the problems with them. LO7.5 Understand the internal rate of return criterion and its strengths and weaknesses. LO7.6 Understand the profitability index and its relation to net present value.

  4. Chapter organisation • Net present value • The payback rule • The discounted payback rule • The accounting rate of return • The internal rate of return • The present value index • The practice of capital budgeting • Summary and conclusions

  5. Net present value (NPV) • Net present value (NPV) is the difference between an investment’s market value (in today’s dollars) and its cost (also in today’s dollars). • An investment is worth undertaking if it creates value for its owners. • Value is created by identifying an investment that is worth more in the marketplace than it costs to acquire. NPV provides a measure of how much value is created by undertaking an investment.

  6. NPV • Recall that the important elements in making financial decisions are: • the cash flows • the timing of the cash flows • the risk of the cash flows. • Estimation of these elements is important in the calculation of the NPV. continued

  7. NPV Steps in calculating NPV: • Estimate the expected future cash flows. • Estimate the required return for projects of this risk level. • Find the present value of the cash flows and subtract the initial investment.

  8. NPV illustrated 0 1 2 Initial outlay Revenues $2000 Revenues $1000 ($1100) Expenses 1000 Expenses 500 $500 Cash flow $1000 Cash flow – $1100.00 1 $500 x 1.10 +454.55 1 $1000 x 1.10 2 +826.45 +$ 181.00 NPV continued

  9. NPV illustrated • Suppose the cash revenues from our fertiliser business will be $200 000 per year. Cash costs (including taxes) will be $140 000 per year. We will wind down the business in 8 years. Estimated salvage value (net of taxes) of the project is $20 000. The project costs $300 000 to launch. We require a 15% return on the project. continued

  10. NPV illustrated • We have two types of cash inflows. • Operating cash inflows which are $60,000 each year for 8 years. • To find the PV of these cash flows we can use the PV of ordinary annuity formula. • In the terminal year you get $20,000 as a lump-sum. • To find the PV of this we have to use the PV of a single amount formula. continued

  11. NPV illustrated NPV = PV of cash inflows – initial outlay = $ 275,777 – $300,000 = – $24,223 Is this a good investment?

  12. Implications of NPV • An investment should be accepted if the NPV is positive, and rejected if it is negative. • NPV is a direct measure of how well the investment meets the goal of financial management—to increase owners’ wealth. • A positive NPV means that the investment is expected to add value to the firm.

  13. Decision criteria test—NPV • Does the NPV rule account for the time value of money? • Does the NPV rule account for the risk of the cash flows? • Does the NPV rule provide an indication about the increase in value? • Should we consider the NPV rule for our primary decision rule?

  14. Payback period • Payback period is the amount of time required for an investment to generate cash flows to recover its initial cost. • Steps in estimating the payback period are: • Estimate the cash flows. • Accumulate the future cash flows until they equal the initial investment. • Work out how long this takes to happen. • An investment is acceptable if its calculated payback is less than some prescribed number of years.

  15. Payback period illustrated Initial investment = –$1000 Year Cash flow 1 $200 2 400 3 600 Accumulated Year cash flow 1 $200 2 600 1200 3 2 years Payback period = 2 + 400/600 = ⅔

  16. Decision criteria test—payback • Does the payback rule account for the time value of money? • Does the payback rule account for the risk of the cash flows? • Does the payback rule provide an indication about the increase in value? • Should we consider the payback rule for our primary decision rule?

  17. Evaluation of payback period • Advantages: • Easy to understand. • Adjusts for uncertainty of later cash flows. • Biased towards liquidity. • Disadvantages: • Time value of money and risk ignored. • Ignores cash flows beyond the cut-off date. • Biased against long-term and new projects. • Arbitrary determination of acceptable payback period.

  18. Discounted payback period • Discounting payback period is the length of time required for an investment’s discounted cash flows to equal its initial cost. • Takes into account the time value of money. • More difficult to calculate. • An investment is acceptable if its discounted payback is less than some prescribed number of years.

  19. Example—Discounted payback Initial investment = –$1 000 R = 10% PV of Year Cash flow cash flow 1 $200 $182 2 400 331 3 700 526 4 300 205 continued

  20. Example—Discounted payback Accumulated Year discounted cash flow 1 $182 2 513 3 1039 4 1244 Discounted payback period is just under three years.

  21. Ordinary and discounted payback Initial investment = –$300 R = 12.5% • What is the ordinary payback period? • What is the discounted payback period?

  22. Decision criteria test—discounted payback • Does the discounted payback rule account for the time value of money? • Does the discounted payback rule account for the risk of the cash flows? • Does the discounted payback rule provide an indication about the increase in value? • Should we consider the discounted payback rule for our primary decision rule?

  23. Evaluation of discounted payback • Advantages • Includes time value of money. • Easy to understand. • Does not accept negative estimated NPV investments. • Biased towards liquidity. • Disadvantages • May reject positive NPV investments. • Arbitrary determination of acceptable payback period. • Ignores cash flows beyond the cut-off date. • Biased against long-term and new products.

  24. Accounting rate of return (ARR) • An investment’s average net income divided by its average book value. • A project is accepted if ARR > target average accounting return.

  25. Example—ARR Year 1 2 3 Sales $440 $240 $160 Expenses 220 120 80 Gross profit 220 120 80 Depreciation 80 80 80 Taxable income 140 40 0 Taxes (30%) 42 12 0 Net profit $ 98 $28 $0 Assume initial investment = $240 continued

  26. Example—ARR continued

  27. Example—ARR

  28. Evaluation of ARR • Advantages • Easy to calculate and understand. • Accounting information almost always available. • Disadvantages • The measure is not a ‘true’ reflection of return. • Time value is ignored. • Arbitrary determination of target average return. • Uses profit and book value instead of cash flow and market value.

  29. Decision criteria test—ARR • Does the ARR rule account for the time value of money? • Does the ARR rule account for the risk of the cash flows? • Does the ARR rule provide an indication about the increase in value? • Should we consider the ARR rule for our primary decision rule?

  30. Internal rate of return (IRR) • IRR is the discount rate that equates the present value of the future cash flows with the initial cost. • A project is accepted if: IRR > the required rate of return • The IRR on an investment is the required return that results in a zero NPV when it is used as the discount rate.

  31. Example 1—IRR Initial investment = –$200 Year Cash flow 1 $ 50 2 100 3 150 • Find the IRR such that NPV = 0 50 100 150 0 = –200 + + + (1+IRR) (1+IRR) (1+IRR) 1 2 3 50 100 150 200 = + + (1+IRR) (1+IRR) (1+IRR) 1 2 3 continued

  32. Example 1—IRR Trial and error Discount rates NPV 0% $100 5% 68 10% 41 15% 18 20% –2 IRR is just under 20%—about 19.44%

  33. Example 2—NPV profile Net present value 120 Year Cash flow 0 –$275 100 1 100 2 100 80 3 100 4 100 60 40 20 0 – 20 Discount rate – 40 2% 6% 10% 14% 18% 22% IRR

  34. Advantages of IRR • Popular in practice. • Does not require a discount rate. • The IRR appears to provide a simple way of communicating information about a proposal.

  35. Problems with IRR • Multiple rates of return • Occurs if more than one discount rate makes the NPV of an investment zero. • This will happen when there is more than one negative cash flow (non-conventional cash flows). • Mutually exclusive investment decisions • Project is not independent  mutually exclusive investments. Highest IRR does not indicate the best project.

  36. Multiple rates of return Assume you are considering a project for which the cash flows are as follows: Year Cash flows 0 –$60 1 155 2 –100 continued

  37. Multiple rates of return • To find the IRR on this project NPV is calculated at various rates: at 10%: NPV = –$1.74 at 20%: NPV = –0.28 NPV crosses zero at 30%: NPV = 0.06 at 40%: NPV = –0.31 • Two questions: 1. What is going on here? 2. How many IRRs can there be?

  38. NPV profile

  39. IRR and non-conventional cash flows • When the cash flows change sign more than once, there is more than one IRR. • When you solve for IRR you are solving for the root of an equation, and when you cross the x axis more than once, there will be more than one return that solves the equation. • If you have more than one IRR, you cannot use any of them to make your decision.

  40. IRR, NPV andmutually-exclusive projects Net present value Year 0 1 2 3 4 160 140 Project A: – $350 50 100 150 200 120 Project B: – $250 125 100 75 50 100 80 60 40 Crossover Point 20 0 – 20 – 40 – 60 – 80 Discount rate – 100 0 2% 6% 10% 14% 18% 22% 26% IRR IRR B A

  41. Decision criteria test—IRR • Does the IRR rule account for the time value of money? • Does the IRR rule account for the risk of the cash flows? • Does the IRR rule provide an indication about the increase in value? • Should we consider the IRR rule for our primary decision criteria?

  42. Present value index (PVI) • The present value index is the present value of an investment’s future cash flows divided by its initial cost. • The PVI is also known as the benefit/cost ratio. • Accept a project with a PVI > 1.0.

  43. Net present value index (NPVI) • The net present value index is the net present value of the future cash flows divided by the initial investment. • The NPVI differs from the PVI by a scale of one. • The ranking problems associated with the PVI are also applicable to the NPVI.

  44. Example—PVI Assume you have the following information on Project X: Required return = 10% Initial investment = –$1100 Annual cash revenues and expenses are as follows: Year Revenues Expenses 1 $1 000 $ 500 2 2 000 1 000 continued

  45. Example—PVI

  46. Evaluation of PVI and NPVI • Advantages • Closely related to NPV, generally leading to identical decisions. • Easy to understand. • May be useful when available investment funds are limited. • Disadvantages • May lead to incorrect decisions in comparisons of mutually-exclusive investments.

  47. Capital budgeting in practice • We should consider several investment criteria when making decisions. • NPV and IRR are the most commonly used primary investment criteria. • Payback is a commonly used secondary investment criteria.

  48. Quick quiz • Consider an investment that costs $100 000 and has a cash inflow of $25 000 every year for 5 years. The required return is 9%, and required payback is 4 years. • What is the payback period? • What is the discounted payback period? • What is the NPV? • What is the IRR? • Should we accept the project? • What decision rule should be the primary decision method? • When is the IRR rule unreliable?

  49. Comprehensive problem • An investment project has the following cash flows: CF0 = –1 000 000; C01 – C08 = 200 000 each • If the required rate of return is 12%, what decision should be made using NPV? • How would the IRR decision rule be used for this project, and what decision would be reached? • How are the above two decisions related?

  50. Summary and conclusions • Six criteria used to evaluate proposed investments are: • Net present value (NPV) • Payback period • Discounted payback period • Accounting rate of return (ARR) • Internal rate of return (IRR) • Present value index (PVI). continued

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