Chapter 8 Notes: Net Present Value and Other Investment Criteria

Chapter 8: Net Present Value and Other Investment Criteria

Key Notations

• AAR: Average accounting return
• IRR: Internal rate of return
• NPV: Net present value
• PI: Profitability index
• R: Discount rate

Learning Objectives

• Understand why NPV is the best criterion for evaluating investments (LO1).
• Understand the payback rule and its shortcomings (LO2).
• Understand the discounted payback rule and its shortcomings (LO3).
• Understand accounting rates of return and their problems (LO4).
• Understand the IRR criterion and its strengths and weaknesses (LO5).
• Understand the modified IRR (LO6).
• Understand the profitability index and its relation to NPV (LO7).

Introduction

• Capital budgeting decisions, like France Telecom's fibre optic network roll-out, require careful risk and reward assessment.
• Increasing equity value is the goal of financial management.
• The chapter discusses techniques for evaluating investments and explains why the NPV approach is the most reliable.

Capital Budgeting Decision

• Capital budgeting involves deciding what non-current assets to buy.
• It includes broader issues like launching new products or entering new markets.
• These decisions determine a firm's operations and products for years due to the long-lived nature of non-current asset investments.
• Capital budgeting, or strategic asset allocation, is crucial for a firm's business definition.
• Airlines operate airplanes, defining their business, regardless of financing.

Investment Options

• Firms have numerous potential investments; identifying valuable options is key to successful financial management.
• The chapter introduces techniques for analyzing potential business ventures.
• The goal is to present and compare different procedures, highlighting their advantages and disadvantages.
• Net present value (NPV) is the most important concept.

8.1 Net Present Value

• Financial management aims to create value for shareholders.
• Potential investments must be evaluated for their impact on share value.

The Basic Idea

• Investments are worthwhile if they create value for owners. Value is created when an investment is worth more in the marketplace than its acquisition cost.
• Example: Buying a run-down house for $£25,000$, renovating it for $£25,000$, and selling it for $£60,000$ creates $£10,000$ in value.
• This $£10,000$ is the value added by management.
• Capital budgeting determines if a proposed investment will be worth more than its cost once in place.

Net Present Value (NPV)

• NPV is the difference between an investment's market value and its cost.
• NPV measures the value created today by undertaking an investment.
• The capital budgeting process searches for investments with positive NPVs.

Estimating Net Present Value

• Estimating NPV involves assessing what comparable, renovated properties are selling for in the market.

• Estimates of the cost of buying a particular property and bringing it to market are ascertained.

• If the difference between estimated market value and estimated total cost is positive, the investment is worthwhile.

• Risk exists because estimates may not be correct.

• Investment decisions are simplified when there is a market for similar assets. It becomes more difficult when market prices for comparable investments are unobservable.

• Estimating investment value using indirect market information becomes necessary.

• This is the situation usually encountered by financial managers.

Discounted Cash Flow (DCF) Valuation

• Estimate future cash flows the new business is expected to produce.
• Apply discounted cash flow procedure to estimate the present value of those cash flows.
• Estimate NPV as the difference between the present value of future cash flows and the cost of the investment.
• This procedure is called discounted cash flow (DCF) valuation.

Example

• Cash revenues from new fertilizer business: $£20,000$ per year.

• Cash costs: $£14,000$ per year.

• Business duration: eight years.

• Salvage value: $£2,000$.

• Project cost: $£30,000$.

• Discount rate: 15%.

• Net cash inflow: $£20,000 - £14,000 = £6,000$ per year.

• Present value calculation:

  • $Present value = £6,000 \times [1 - (1/1.15^8)]/0.15 + (2,000/1.15^8)$
  • $= (£6,000 \times 4.4873) + (2,000/3.0590)$
  • $= £26,924 + 654$
  • $= £27,578$

• NPV calculation: $NPV = -£30,000 + £27,578 = -£2,422$

• This indicates a bad investment; equity value decreases by $£2,422$.

• Impact per share: $£2,422/1,000 = £2.42$ loss per share.

Net Present Value Rule

• If NPV is negative, the effect on share value will be unfavorable.
• If NPV is positive, the effect would be favorable.
• An investment should be accepted if the NPV is positive, and rejected if it is negative.
• If NPV is exactly zero, indifference exists between taking and not taking the investment.

Important Considerations

• Estimating cash flows and the discount rate is more challenging than the discounting process itself.
• The calculated NPV is an estimate and can vary.
• Reliable estimates are crucial.

Example 8.1: Using the NPV Rule

• Decision: Launch a new consumer product.

• Cash flows over five years: $£2,000$ (years 1-2), $£4,000$ (years 3-4), $£5,000$ (year 5).

• Cost to begin production: $£10,000$.

• Discount rate: 10%.

• Calculate the total value of the product:

• $Present value = (£2,000/1.1) + (2,000/1.1^2) + (4,000/1.1^3) + (4,000/1.1^4) + (5,000/1.1^5)$

  • $= £1,818 + 1,653 + 3,005 + 2,732 + 3,105$
  • $= £12,313$

• $NPV = £12,313 - £10,000 = £2,313$.

• Based on the NPV rule, the project should be undertaken.

Spreadsheet Strategies: Calculating NPVs with a Spreadsheet

• Spreadsheets are commonly used to calculate NPVs.

• The NPV function in spreadsheets may be a PV function, leading to incorrect results if used improperly.

• Correct formula usage: =NPV(B4,C2:G2)+B2

• Blindly using calculators or computers without understanding their functions can lead to errors.

Concept Questions

• 8.1a: What is the net present value rule?
• Answer: Accept investments with positive NPV, reject those with negative NPV.
• 8.1b: What does an NPV of €1,000 mean?
• Answer: The investment is expected to increase the value of the firm by €1,000.

8.2 The Payback Rule

The payback period is the length of time it takes to recover the initial investment.

Defining the Rule

• The payback period rule: An investment is acceptable if its calculated payback period is less than some pre-specified number of years.

Calculation Example

• Initial investment: $£50,000$.
• Cash flows: $£30,000$ (year 1), $£20,000$ (year 2), $£10,000$ (year 3), $£5,000$ (year 4).
• Payback period: two years.

Fractional Years Example

• Initial investment: $£60,000$.
• Cash flows: $£20,000$ (year 1), $£90,000$ (year 2).
• Payback period: $1 + (40,000/90,000) = 1\frac{4}{9}$ years.

Example 8.2: Calculating Payback

• Project cost: $€500$.
• Cash flows: $€100$ (year 1), $€200$ (year 2), $€500$ (year 3).
• Payback period: $2 + (200/500) = 2.4$ years.

Table 8.1: Expected Cash Flows for Projects A-E

• Project A: Payback is 2.6 years.
• Project B: Never pays back.
• Project C: Payback is exactly four years.
• Project D: Has two payback periods (two years and four years).
• Project E: Pays back in six months.

Analysing the Rule

• The Payback Period Rule ignores the time value of money and risk differences.
• There is no objective basis for choosing a particular cut-off number.
• It ignores cash flows beyond the cut-off period.

Table 8.2: Investment Projected Cash Flows

• Consider Long (payback 2.5 years) and Short (payback 1.75 years) projects. Short is acceptable, Long is not, with a two-year cut-off.
• NPV(Short) is negative (-€11.81), while NPV(Long) is positive (€35.50).

Shortcomings of the Payback Period Rule

• By ignoring time value, projects that are worth less than they cost may be taken.
• By ignoring cash flows beyond the cut-off, profitable long-term investments may be rejected.
• It biases towards shorter-term investments.

Redeeming Qualities of the Rule

• Used for minor decisions where detailed analysis is unwarranted.
• Investments with rapid payback and benefits beyond the cut-off likely have a positive NPV.
• Simple to use and understand.
• Biased towards liquidity i.e. favours investments that free up cash for other uses quickly.
• Adjusts for the extra riskiness of later cash flows i.e. ignores later cash flows.

Summary of the Rule

• The payback period is a 'break-even' measure in an accounting (not economic) sense.
• The biggest drawback is that it doesn't consider the impact on equity value.
• Companies use it as a screen for minor decisions.
• Table 8.3 Pros and Cons of the Payback Period Rule

Concept Questions

• 8.2a: What is the payback period? The payback period rule?
• Answer: Time to recover initial investment; accept projects with payback less than a specified period.
• 8.2b: Why is the payback period an accounting break-even measure?
• Answer: Ignores time value and focuses on recovering initial accounting cost.

8.3 The Discounted Payback

• Discounted payback period accounts for the time value of money.
• The discounted payback period is the length of time until the sum of the discounted cash flows is equal to the initial investment.

Rule

• Based on the discounted payback rule, an investment is acceptable if its discounted payback is less than some pre-specified number of years.

Calculation Example

• Required return: 12.5%.
• Investment cost: €300.
• Cash flows: €100 per year for five years.
• The regular payback is three years.
• The discounted payback is four years.

Interpretation

• The discounted payback includes the time value of money, breaking even in an economic or financial sense.

• We get our money back, along with the interest we could have earned elsewhere.

• If a project pays back on a discounted basis, it must have a positive NPV.

• If we use a discounted payback rule, we won't accidentally take any projects with a negative estimated NPV.

Drawbacks

• Not any simpler to use than NPV.

• Requires discounting cash flows, adding them up, and comparing them with the cost, just as with NPV.

• Cut-off still has to be arbitrarily set, and cash flows beyond that point are ignored

• A project with a positive NPV may be found unacceptable because the cut-off is too short.

• Just because one project has a shorter discounted payback than another does not mean it has a larger NPV.

• It's a compromise between regular payback and NPV lacking the simplicity of the first and the conceptual rigour of the second.

• Nonetheless, if we need to assess the time it will take to recover the investment required by a project, then the discounted payback is better than the ordinary payback, because it considers time value.

• The discounted payback recognizes that we could have invested the money elsewhere and earned a return on it. The ordinary payback does not take this into account

• Table 8.5 Advantages and Disadvantages of the Discounted Payback Period Rule

Example 8.3: Calculating Discounted Payback

• Investment cost: $£400$.
• Cash flows: $£100$ per year forever i.e. perpetuity
• Discount rate: 20%.
• NPV: $£100/0.2 - £400 = £100$. The ordinary payback is four years.
• For discounted payback, we need discount rate where $£400/100 = 4$ at 20 per cent, the number of periods ≈ nine years.

Concept Questions

• 8.3a: What is the discounted payback period? Why is it a financial/economic break-even measure?
• Answer: Time to recover investment with discounted cash flows; includes time value of money.
• 8.3b: What advantages does the discounted payback have over ordinary payback?
• Answer: Considers time value of money.

8.4 The Average Accounting Return

• Another (flawed) approach to making capital budgeting decisions involves the average accounting return (AAR).

Definition

• The AAR is always defined as some measure of average accounting profit divided by some measure of average accounting value.
  • $\frac{Average \, net \, income}{Average \, book \, value}$

Example

• Investment in improvements: $£500,000$.
• Store life: five years; depreciated 100% straight-line over five years.
• Depreciation: $£500,000/5 = £100,000$ per year.
• Tax rate: 25 %.

Average Book Value

• $(\frac{£500,000 + 0}{2}) = £250,000$. (One-half of the initial investment.)

Calculation

• Average net income: $[£100,000 + 150,000 + 50,000 + 0 + (-50,000)]/5 = £50,000$
• $AAR = \frac{£50,000}{£250,000} = 20 \%$.
• Acceptable if target AAR is less than 20%.
• Based on the average accounting return rule, a project is acceptable if its average accounting return exceeds a target average accounting return.

Drawbacks

• Not a rate of return in any economic sense; it's a ratio of accounting numbers.
• Ignores time value.
• Lacks an objective cut-off period.
• Based on net income and book value, not cash flow and market value. Hence doesn't tell us what the effect on share price will be of taking an investment

Redeeming Features

• Can almost always be computed because accounting information is almost always available.
• Table 8.7 Advantages and Disadvantages of the Average Accounting Return

Concept Questions

• 8.4a: What is an average accounting rate of return (AAR)?
• Answer: Average net income divided by average book value.
• 8.4b: What are the weaknesses of the AAR rule?
• Answer: Not a true rate of return, ignores time value, uses arbitrary benchmark, based on accounting values.

8.5 The Internal Rate of Return

The internal rate of return (IRR) is closely related to NPV.

IRR Meaning

• IRR summarizes the merits of a project as a single rate of return.

• It’s an 'internal' rate based only on the project's cash flows.

• Consider a project costing $€100$ today and paying $€110$ in one year. The return is 10%.

The IRR Rule

• Based on the IRR rule, an investment is acceptable if the IRR exceeds the required return. It should be rejected otherwise.

Calculation

• The IRR is the discount rate that makes the NPV equal to zero.
• $NPV = -€100 + [110/(1 + R)]$. Setting NPV to zero and solving for R gives 10%.
• The IRR on an investment is the required return that results in a zero NPV when it is used as the discount rate.

More Complex Investments

• For investments with more than one period, finding IRR is more complicated.

• Cash flows: -€100, €60 per year for two years.

• $NPV = 0 = -€100 + [60/(1 + IRR)] + [60/(1 + IRR)^2]$. Solve for IRR by trial and error, calculator, or spreadsheet.

• IRR is approximately 13.1%. If the required return is less than 13.1%, take the investment.

Net Present Value Profile

• Graphs the NPVs at different discount rates.
• The IRR is the point where the curve cuts through the x-axis (NPV = 0).
• In our example with an IRR is approximately 13.1%, at discount rates less than at NPV is positive and we shall accept the investment.
• The two rules give equivalent results in this case.

Example 8.4: Calculating the IRR

• Total up-front cost: $€435.44$.
• Cash flows: $€100$ (year 1), $€200$ (year 2), $€300$ (year 3).

Calculating NPV at different discount rates identifies 15 % as the IRR. If we require an 18 per cent return, then we should not take the investment.

Conditions for Identical Decisions

• The IRR and NPV rules lead to identical decisions if two conditions are met.
• The project's cash flows must be conventional (negative initial investment, all the rest positive).
• The project must be independent (accepting/rejecting it doesn't affect other decisions).

Spreadsheet Strategies: Calculating IRRs with a Spreadsheet

• Use the IRR function in spreadsheets to easily calculate the IRR.
• The formula in cell B4 gives an IRR of 27.27 per cent.

Problems with the IRR

• Non-conventional cash flows and comparing multiple investments can cause issues.

Non-Conventional Cash Flows

• Strip-mining project: -€60 investment; €155 in year 1; -€100 in year 2.

Multiple Rates of Return exist if cash flow flips from negative to positive, back to negative.

Example 8.5: What's the IRR?

• Invest €51 today; get €100 in one year, pay out €50 in two years. What is the IRR on this investment?

• There is no IRR. The NPV is negative at every discount rate, so we shouldn't take this investment under any circumstances. What's the return on this investment? Your guess is as good as ours.

Example 8.6:

• You get more than one IRR. If you wanted to make sure that you had found all the possible IRRs, how could you do it? The answer comes from the great mathematician, philosopher and financial analyst Descartes (of 'I think, therefore I am' fame).

• Descartes' Rule of Sign says that the maximum number of IRRS that there can be is equal to the number of times that the cash flows change sign from positive to negative and/or negative to positive.

Mutually Exclusive Investments

• If two investments, X and Y, are mutually exclusive, then taking one of them means that we cannot take the other.
• We are ultimately interested in creating value for the shareholders, so the option with the higher NPV is preferred, regardless of the relative returns.
  *

Example 8.7: Calculating the Crossover Rate

• The crossover rate is the discount rate at which the NPVs of two projects are equal.
• Find the IRR for (B - A); you'll see it's the same number. Also, for practice, you might want to find the exact crossover in Fig. 8.8. (Hint: It's 11.0704 per cent.)

Investing or Financing?

Consider the following two independent investments:

• The company initially pays out cash with investment A and initially receives cash for investment B. The IRR is really a rate that you are paying, not receiving.
• These projects has financing-type cash flows, whereas investment A has investing-type cash flows. You should take a project with financing-type cash flows only if it is an inexpensive source of financing, meaning that its IRR is lower than your required return.

Redeeming Qualities of the IRR

• Popular in practice because people prefer talking about rates of return.
• Provides a simple way of communicating information about a proposal.
• Can estimate the IRR without knowing the discount rate.
• Table 8.9 Advantages and Disadvantages of the Internal Rate of Return

The Modified Internal Rate of Return (MIRR)

• MIRRs modify cash flows to address standard IRR problems.

• Three methods:

  • Method 1: The Discounting Approach
  • Method 2: The Reinvestment Approach
  • Method 3: The Combination Approach

• MIRRs are controversial because there are three different ways of calculating them.

• There is no clear reason to say that one of our three methods is better than any other.

• Calculating an MIRR requires discounting, compounding, or both so why not calculate the NPV and be done with it?

• Because an MIRR depends on an externally supplied discount (or compounding) rate, the answer you get is not truly an 'internal' rate of return.

• We shall take a stand on one issue that frequently comes up in this context. The value of a project does not depend on what the firm does with the cash flows generated by that project.

• As a result, there is generally no need to consider reinvestment of interim cash flows.

Concept Questions

• 8.5a: When will IRR and NPV lead to the same decisions? When might they conflict?
• Answer: Identical if conventional cash flows and projects are independent; conflict with non-conventional flows or mutually exclusive projects.
• 8.5b: Is it advantageous that we do not need to know required return to use IRR rule?
• Answer: No. Required return is needed for comparison.

8.6 The Profitability Index

The profitability index (PI) (or benefit-cost ratio) is the present value of the future cash flows divided by the initial investment.

• Measures value created per cash unit invested.
• If a project costs $€200$ and the present value of its future cash flows is $€220$, the profitability index value would be $€220/200 = 1.1$.

Table 8.10 Advantages and Disadvantages of the Profitability Index

Concept Questions

• 8.6a: What does the profitability index measure?
• Answer: Value created per cash unit invested.
• 8.6b: How would you state the profitability index rule?
• Answer: A profitability index > 1 indicates a positive NPV investment, and a profitability index < 1 indicates a negative NPV investment.

8.7 The Practice of Capital Budgeting

• Firms use multiple criteria for evaluating a proposal due to uncertainty about the future.

Example 8.8: Bringing It All Together: Evaluating a Project Using Several Capital Budgeting Appraisal Techniques

• Sandy Grey Ltd is considering revising its mobile phone line.

• The revision will cost $£220,000$.

• Cash flows from increased sales will be $£80,000$ in the first year, increasing by 5% per year.

• The new line will be obsolete five years from now.

• The company requires a 10 per cent return for such an investment.

• We shall look at NPV, IRR and the profitability index. However, it is easy to consider the payback period or discounted payback period.

• The NPV of the investment is $£112,047$

• The IRR of the investment using trial and error, the IRR is, $IRR = 27.69\%$

• The profitability index of the investment is, $PI = 1.509$

• With all methods the project looks viable, and should be undertaken.