CHAPTER SEVEN Net present value and other investment

Chapter objectives LO 7. 1 Understand the reasons why the net present value criterion

Chapter objectives LO 7. 4 Understand accounting rates of return and some of the

Chapter organisation • • Net present value The payback rule The discounted payback rule

Net present value (NPV) • Net present value (NPV) is the difference between an

NPV • Recall that the important elements in making financial decisions are: – the

NPV Steps in calculating NPV: 1. Estimate the expected future cash flows. 2. Estimate

NPV illustrated 0 Initial outlay ($1100) 1 Revenues Expenses $1000 500 $500 Cash flow

NPV illustrated • Suppose the cash revenues from our fertiliser business will be $200

NPV illustrated • We have two types of cash inflows. – Operating cash inflows

NPV illustrated NPV = PV of cash inflows – initial outlay = $ 275,

Implications of NPV • An investment should be accepted if the NPV is positive,

Decision criteria test—NPV • Does the NPV rule account for the time value of

Payback period • Payback period is the amount of time required for an investment

Payback period illustrated Initial investment = –$1000 Year 1 2 3 Cash flow $200

Decision criteria test— payback • Does the payback rule account for the time value

Evaluation of payback period • Advantages: – Easy to understand. – Adjusts for uncertainty

Discounted payback period • Discounting payback period is the length of time required for

Example—Discounted payback Initial investment = –$1 000 R = 10% PV of Year Cash

Example—Discounted payback Year 1 2 3 4 Accumulated discounted cash flow $182 513 1039

Ordinary and discounted payback Initial investment = –$300 R = 12. 5% Cash flow

Decision criteria test— discounted payback • Does the discounted payback rule account for the

Evaluation of discounted payback • Advantages – Includes time value of money. – Easy

Accounting rate of return (ARR) • An investment’s average net income divided by its

Example—ARR 1 Sales Expenses Gross profit Depreciation Taxable income Taxes (30%) Net profit $440

Example—ARR continued Copyright © 2017 Mc. Graw-Hill Education (Australia) Pty Ltd PPTs to accompany

Example—ARR Copyright © 2017 Mc. Graw-Hill Education (Australia) Pty Ltd PPTs to accompany Fundamentals

Evaluation of ARR • Advantages – Easy to calculate and understand. – Accounting information

Decision criteria test—ARR • Does the ARR rule account for the time value of

Internal rate of return (IRR) • IRR is the discount rate that equates the

Example 1—IRR Initial investment = –$200 Year Cash flow 1 2 3 $ 50

Example 1—IRR Trial and error Discount rates NPV 0% $100 5% 68 10% 41

Advantages of IRR • Popular in practice. • Does not require a discount rate.

Problems with IRR • Multiple rates of return – Occurs if more than one

Multiple rates of return Assume you are considering a project for which the cash

Multiple rates of return • To find the IRR on this project NPV is

IRR and non-conventional cash flows • When the cash flows change sign more than

IRR, NPV and mutually-exclusive projects Net present value 160 140 120 100 80 60

Decision criteria test—IRR • Does the IRR rule account for the time value of

Present value index (PVI) • The present value index is the present value of

Net present value index (NPVI) • The net present value index is the net

Example—PVI Assume you have the following information on Project X: Initial investment = –$1100

Example—PVI Copyright © 2017 Mc. Graw-Hill Education (Australia) Pty Ltd PPTs to accompany Fundamentals

Evaluation of PVI and NPVI • Advantages – Closely related to NPV, generally leading

Capital budgeting in practice • We should consider several investment criteria when making decisions.

Quick quiz • Consider an investment that costs $100 000 and has a cash

Comprehensive problem • An investment project has the following cash flows: CF 0 =

Summary and conclusions • Six criteria used to evaluate proposed investments are: – –

Summary and conclusions • Financial managers act in the best interests of shareholders by

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Chapter objectives LO 7. 1 Understand the reasons why the net present value criterion is the best way to evaluate proposed investments. LO 7. 2 Understand the payback rule and some of its shortcomings. LO 7. 3 Understand the discounted payback rule and some of its shortcomings. continued Copyright © 2017 Mc. Graw-Hill Education (Australia) Pty Ltd PPTs to accompany Fundamentals of Corporate Finance 7 e by Ross et al. 2 -2

Chapter objectives LO 7. 4 Understand accounting rates of return and some of the problems with them. LO 7. 5 Understand the internal rate of return criterion and its strengths and weaknesses. LO 7. 6 Understand the profitability index and its relation to net present value. Copyright © 2017 Mc. Graw-Hill Education (Australia) Pty Ltd PPTs to accompany Fundamentals of Corporate Finance 7 e by Ross et al. 2 -3

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 Copyright © 2017 Mc. Graw-Hill Education (Australia) Pty Ltd PPTs to accompany Fundamentals of Corporate Finance 7 e by Ross et al. 2 -4

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. Copyright © 2017 Mc. Graw-Hill Education (Australia) Pty Ltd PPTs to accompany Fundamentals of Corporate Finance 7 e by Ross et al. 2 -5

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 Copyright © 2017 Mc. Graw-Hill Education (Australia) Pty Ltd PPTs to accompany Fundamentals of Corporate Finance 7 e by Ross et al. 2 -6

NPV Steps in calculating NPV: 1. Estimate the expected future cash flows. 2. Estimate the required return for projects of this risk level. 3. Find the present value of the cash flows and subtract the initial investment. Copyright © 2017 Mc. Graw-Hill Education (Australia) Pty Ltd PPTs to accompany Fundamentals of Corporate Finance 7 e by Ross et al. 2 -7

NPV illustrated 0 Initial outlay ($1100) 1 Revenues Expenses $1000 500 $500 Cash flow – $1100. 00 $500 x +454. 55 2 Revenues Expenses $2000 1000 Cash flow $1000 1 1. 10 $1000 x +826. 45 1 1. 102 +$181. 00 NPV continued Copyright © 2017 Mc. Graw-Hill Education (Australia) Pty Ltd PPTs to accompany Fundamentals of Corporate Finance 7 e by Ross et al. 2 -8

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 Copyright © 2017 Mc. Graw-Hill Education (Australia) Pty Ltd PPTs to accompany Fundamentals of Corporate Finance 7 e by Ross et al. 2 -9

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 lumpsum. § To find the PV of this we have to use the PV of a single amount formula. continued Copyright © 2017 Mc. Graw-Hill Education (Australia) Pty Ltd PPTs to accompany Fundamentals of Corporate Finance 7 e by Ross et al. 2 -10

NPV illustrated NPV = PV of cash inflows – initial outlay = $ 275, 777 – $300, 000 = – $24, 223 Is this a good investment? Copyright © 2017 Mc. Graw-Hill Education (Australia) Pty Ltd PPTs to accompany Fundamentals of Corporate Finance 7 e by Ross et al. 2 -11

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. Copyright © 2017 Mc. Graw-Hill Education (Australia) Pty Ltd PPTs to accompany Fundamentals of Corporate Finance 7 e by Ross et al. 2 -12

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? Copyright © 2017 Mc. Graw-Hill Education (Australia) Pty Ltd PPTs to accompany Fundamentals of Corporate Finance 7 e by Ross et al. 2 -13

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. Copyright © 2017 Mc. Graw-Hill Education (Australia) Pty Ltd PPTs to accompany Fundamentals of Corporate Finance 7 e by Ross et al. 2 -14

Payback period illustrated Initial investment = –$1000 Year 1 2 3 Cash flow $200 400 600 Accumulated cash flow $200 600 1200 Payback period = 2 + 400/600 = 2 ⅔ years Copyright © 2017 Mc. Graw-Hill Education (Australia) Pty Ltd PPTs to accompany Fundamentals of Corporate Finance 7 e by Ross et al. 2 -15

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? Copyright © 2017 Mc. Graw-Hill Education (Australia) Pty Ltd PPTs to accompany Fundamentals of Corporate Finance 7 e by Ross et al. 2 -16

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. Copyright © 2017 Mc. Graw-Hill Education (Australia) Pty Ltd PPTs to accompany Fundamentals of Corporate Finance 7 e by Ross et al. 2 -17

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. Copyright © 2017 Mc. Graw-Hill Education (Australia) Pty Ltd PPTs to accompany Fundamentals of Corporate Finance 7 e by Ross et al. 2 -18

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 Copyright © 2017 Mc. Graw-Hill Education (Australia) Pty Ltd PPTs to accompany Fundamentals of Corporate Finance 7 e by Ross et al. 2 -19

Example—Discounted payback Year 1 2 3 4 Accumulated discounted cash flow $182 513 1039 1244 Discounted payback period is just under three years. Copyright © 2017 Mc. Graw-Hill Education (Australia) Pty Ltd PPTs to accompany Fundamentals of Corporate Finance 7 e by Ross et al. 2 -20

Ordinary and discounted payback Initial investment = –$300 R = 12. 5% Cash flow Year 1 2 3 4 5 Non-discounted $100 100 100 Accumulated cash flow Discounted $89 79 70 62 55 Non-discounted $100 200 300 400 500 Discounted $ 89 168 238 300 355 • What is the ordinary payback period? • What is the discounted payback period? Copyright © 2017 Mc. Graw-Hill Education (Australia) Pty Ltd PPTs to accompany Fundamentals of Corporate Finance 7 e by Ross et al. 2 -21

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? Copyright © 2017 Mc. Graw-Hill Education (Australia) Pty Ltd PPTs to accompany Fundamentals of Corporate Finance 7 e by Ross et al. 2 -22

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 longterm and new products. Copyright © 2017 Mc. Graw-Hill Education (Australia) Pty Ltd PPTs to accompany Fundamentals of Corporate Finance 7 e by Ross et al. 2 -23

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. Copyright © 2017 Mc. Graw-Hill Education (Australia) Pty Ltd PPTs to accompany Fundamentals of Corporate Finance 7 e by Ross et al. 2 -24

Example—ARR 1 Sales Expenses Gross profit Depreciation Taxable income Taxes (30%) Net profit $440 220 80 140 42 $ 98 Year 2 3 $240 120 80 40 12 $28 $160 80 80 80 0 0 $0 Assume initial investment = $240 continued Copyright © 2017 Mc. Graw-Hill Education (Australia) Pty Ltd PPTs to accompany Fundamentals of Corporate Finance 7 e by Ross et al. 2 -25

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. Copyright © 2017 Mc. Graw-Hill Education (Australia) Pty Ltd PPTs to accompany Fundamentals of Corporate Finance 7 e by Ross et al. 2 -28

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? Copyright © 2017 Mc. Graw-Hill Education (Australia) Pty Ltd PPTs to accompany Fundamentals of Corporate Finance 7 e by Ross et al. 2 -29

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. Copyright © 2017 Mc. Graw-Hill Education (Australia) Pty Ltd PPTs to accompany Fundamentals of Corporate Finance 7 e by Ross et al. 2 -30

Example 1—IRR Initial investment = –$200 Year Cash flow 1 2 3 $ 50 100 150 • Find the IRR such that NPV = 0 0 = – 200 + 50 (1+IRR) 1 50 200 = (1+IRR) 1 + 100 (1+IRR)2 100 + (1+IRR)2 + 150 (1+IRR)3 150 + (1+IRR)3 continued Copyright © 2017 Mc. Graw-Hill Education (Australia) Pty Ltd PPTs to accompany Fundamentals of Corporate Finance 7 e by Ross et al. 2 -31

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% Copyright © 2017 Mc. Graw-Hill Education (Australia) Pty Ltd PPTs to accompany Fundamentals of Corporate Finance 7 e by Ross et al. 2 -32

Example 2—NPV profile Net present value 120 Year 0 1 2 3 4 100 80 60 Cash flow –$275 100 100 40 20 0 – 20 Discount rate – 40 2% 6% 10% 14% 18% 22% IRR Copyright © 2017 Mc. Graw-Hill Education (Australia) Pty Ltd PPTs to accompany Fundamentals of Corporate Finance 7 e by Ross et al. 2 -33

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. Copyright © 2017 Mc. Graw-Hill Education (Australia) Pty Ltd PPTs to accompany Fundamentals of Corporate Finance 7 e by Ross et al. 2 -34

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. Copyright © 2017 Mc. Graw-Hill Education (Australia) Pty Ltd PPTs to accompany Fundamentals of Corporate Finance 7 e by Ross et al. 2 -35

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 Copyright © 2017 Mc. Graw-Hill Education (Australia) Pty Ltd PPTs to accompany Fundamentals of Corporate Finance 7 e by Ross et al. 2 -36

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 at 30%: NPV = 0. 06 at 40%: NPV = – 0. 31 NPV crosses zero • Two questions: 1. What is going on here? 2. How many IRRs can there be? Copyright © 2017 Mc. Graw-Hill Education (Australia) Pty Ltd PPTs to accompany Fundamentals of Corporate Finance 7 e by Ross et al. 2 -37

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. Copyright © 2017 Mc. Graw-Hill Education (Australia) Pty Ltd PPTs to accompany Fundamentals of Corporate Finance 7 e by Ross et al. 2 -39

IRR, NPV and mutually-exclusive projects Net present value 160 140 120 100 80 60 40 20 0 Year 0 1 2 3 4 Project A: – $350 50 100 150 200 Project B: – $250 125 100 75 50 Crossover Point – 20 – 40 – 60 – 80 – 100 0 2% 6% 10% 14% IRR A 18% IRR Copyright © 2017 Mc. Graw-Hill Education (Australia) Pty Ltd PPTs to accompany Fundamentals of Corporate Finance 7 e by Ross et al. 22% 26% Discount rate B 2 -40

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? Copyright © 2017 Mc. Graw-Hill Education (Australia) Pty Ltd PPTs to accompany Fundamentals of Corporate Finance 7 e by Ross et al. 2 -41

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. Copyright © 2017 Mc. Graw-Hill Education (Australia) Pty Ltd PPTs to accompany Fundamentals of Corporate Finance 7 e by Ross et al. 2 -42

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. Copyright © 2017 Mc. Graw-Hill Education (Australia) Pty Ltd PPTs to accompany Fundamentals of Corporate Finance 7 e by Ross et al. 2 -43

Example—PVI Assume you have the following information on Project X: Initial investment = –$1100 Required return = 10% Annual cash revenues and expenses are as follows: Year 1 2 Revenues $1 000 2 000 Expenses $ 500 1 000 continued Copyright © 2017 Mc. Graw-Hill Education (Australia) Pty Ltd PPTs to accompany Fundamentals of Corporate Finance 7 e by Ross et al. 2 -44

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. Copyright © 2017 Mc. Graw-Hill Education (Australia) Pty Ltd PPTs to accompany Fundamentals of Corporate Finance 7 e by Ross et al. 2 -46

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. Copyright © 2017 Mc. Graw-Hill Education (Australia) Pty Ltd PPTs to accompany Fundamentals of Corporate Finance 7 e by Ross et al. 2 -47

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? Copyright © 2017 Mc. Graw-Hill Education (Australia) Pty Ltd PPTs to accompany Fundamentals of Corporate Finance 7 e by Ross et al. 2 -48

Comprehensive problem • An investment project has the following cash flows: CF 0 = – 1 000; C 01 – C 08 = 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? Copyright © 2017 Mc. Graw-Hill Education (Australia) Pty Ltd PPTs to accompany Fundamentals of Corporate Finance 7 e by Ross et al. 2 -49

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 Copyright © 2017 Mc. Graw-Hill Education (Australia) Pty Ltd PPTs to accompany Fundamentals of Corporate Finance 7 e by Ross et al. 2 -50

Summary and conclusions • Financial managers act in the best interests of shareholders by identifying and undertaking positive NPV investments. • The other investment criteria provide additional information about whether a project truly has a positive NPV. Copyright © 2017 Mc. Graw-Hill Education (Australia) Pty Ltd PPTs to accompany Fundamentals of Corporate Finance 7 e by Ross et al. 2 -51