Strategy and Analysis in Using NPV. How Positive NPV Arises

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Strategy and Analysis in Using NPV

(Text reference: Chapter 8) Topics

how positive NPV arises decision trees

sensitivity analysis scenario analysis break-even analysis investment options

AFM 271 - Strategy and Analysis in Using NPV Slide 1

How Positive NPV Arises

should we believe our NPV calculations? Why would a project have a positive NPV?

introduction of a new product development of a core technology creation of a barrier to entry

introduction of a variation on an existing product product differentiation

organizational innovation

key point: in order to have positive NPV, a project should incorporate something like the characteristics listed above

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Decision Trees

useful when you must make a set of sequential decisions

example: Wild Kitty Drilling Co. owns some land in Alberta, but is unsure if there is oil underneath it. An exploratory well can be drilled today, at a cost of $20 million. Assume that there is an 80% chance that the well will come up dry. Even if it does, there is still some chance that there is oil present. Whether or not the well is dry, production capacity can be installed in one year for $100 million. The discount rate for both phases of the project is 10%. Once production capacity is installed, the same amount of after tax cash flow will be generated each year forever (starting in year 2), as described in the following table:

success failure

probability payoff probability payoff

0.25 $50 million 0.1 $30 million

0.50 $30 million 0.3 $15 million

0.25 $10 million 0.6 $0

Cont’d

Should Wild Kitty invest in the exploratory well?

t = 0 drill ($20m) success (20%) failure (80%) invest ($100m) do not invest t = 1 NPVt=0 invest ($100m) do not invest t = 1

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Sensitivity Analysis

considers how project NPV changes with varying outcomes for a single variable; allows identification of key variables

e.g. a firm is considering developing a small electric car. Preliminary cash flow forecasts (in $ millions) are:

Year 0 Years 1-10

Initial cost 150

Revenue 375

Variable costs 300

Fixed costs 30

Depreciation for tax purposes (straight line) 15

Pretax profit 30

Tax (Tc=50%) 15

Net profit 15

Operating cash flow 30

Net cash flow -$150 $30

Cont’d

based on a 10% discount rate, we have

NPV = −150 + 30 × A10_.₁₀ =$34.33 million underlying these projections are the following:

unit sales equals market share (1%) times size of market (10 million), or 100,000

revenues are unit sales (100,000) times price per unit ($3,750)

unit costs are $3,000

fixed costs are $30 million

sensitivity analysis involves estimating a range for each of these factors and seeing what happens to NPV

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Cont’d

Range NPV ($ millions)

Variable Pessimistic Expected Optimistic Pessimistic Expected Optimistic Market size 9 million 10 million 11 million 11.29 34.33 57.38 Market share 0.004 0.01 0.016 -103.92 34.33 172.59 Unit price $3,500 $3,750 $3,800 -42.47 34.33 49.70 Unit variable cost $3,600 $3,000 $2,750 -150 34.33 111.14 Fixed costs $40 million $30 million $20 million 3.61 34.33 65.06

what are the implications?

project is not sure to have positive NPV

very sensitive to market share and unit variable cost ⇒ may be worthwhile to seek further information

about these variables (e.g. more research, pilot testing of production process, industry consultant, etc.)

no real need for further information about market size

Scenario Analysis

a limitation of sensitivity analysis is that the underlying

variables are likely to be related, e.g. if market size is higher than expected, then strong demand would indicate that unit price is also likely to be higher than expected; inflation may mean high unit prices, but also high unit costs, etc.

scenario analysis changes more than one variable at a time, so as to consider some alternative plausible combinations

continuing with the electric car example: suppose a sharp increase in oil prices would lead to inflation and a recession, a smaller market size (8 million), a higher market share (1.3%), but an increase of 15% in prices and costs above expected values. What effect would this have? (As an exercise, verify

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Break-Even Analysis

another way of examining sensitivity to assumptions basic question: how low can sales go before the project loses money?

electric car example, in terms of accounting profit:

Unit sales 0 50,000 100,000 150,000 Revenues $0 $187.5 $375 $562.5 Variable costs $0 $150 $300 $450 Fixed costs $30 $30 $30 $30 Depreciation $15 $15 $15 $15 Pretax profit -$45 -$7.5 $30 $67.5 Tax -$22.5 -$3.75 $15 $33.75 Net profit -$22.5 -$3.75 $15 $33.75

Cont’d

Unit sales $ millions 0 100 200 300 400 500 600 50,000 100,000 150,000 Total revenues

Fixed costs + dep.

Variable costs Total costs

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Cont’d

calculation of the accounting break-even point:

net profit = [(price− var. costs) × Q − fixed costs − dep.](1 − Tc) =0

⇒(1 − T_c) (price − var. costs) × Q = [fixed costs + dep.](1 − T_c) ⇒Q = [fixed costs + dep.](1 − Tc)

(price − var. costs)(1 − Tc)

in this example:

Q = $45,000,000(.5) ($3,750 − $3,000)(.5) =60,000 units

Cont’d

we can also calculate the present value break-even point (note that this takes into account the entire project, whereas the accounting break-even point considers only one year) the PV break-even point is:

Q = after tax costs independent of Q

contribution margin

= EAC + fixed costs(1 − Tc) −dep.Tc (price− variable costs)(1 − Tc)

continuing with our example, the EAC for the investment is EAC = $150,000,000

A10

.10 =

$24,411,809

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Cont’d

note that the formula on slide 12 only works if all variables (sales price, variable costs, fixed costs, etc.) are constant throughout the life of the project; in general we have to use a spreadsheet to solve numerically for the PV break-even point also note that the accounting break-even point (60,000) is lower than the PV break-even point (85,098)

using accounting profit subtracts depreciation ⇒ selling 60,000 electric cars per year will cover the depreciation expense of $15 million plus other costs

this ignores the opportunity cost of making the investment, i.e. when we discount at 10%, we are saying that we could have earned a 10% return on the $150 million ⇒ the true cost per year is the EAC of $24.4 million plus other costs

Cont’d

straight line depreciation is simple, but not very realistic. We can incorporate CCA by calculating present value of CCA tax shield, converting it to an equivalent annuity, and replacing the dep.Tc term with the annuity

e.g. suppose the required investment of $150 million will be in class 8 (20%) (with many other assets) and it will be sold after 10 years for a salvage value of $10 million:

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Investment Options

it is important to recognize that firms often have options to delay, expand, contract, or abandon projects as more information arrives and business conditions change properly incorporating this is very difficult, and requires an understanding of financial option pricing theory (so we will only consider some simple examples here)

consider the Wild Kitty example again. If the exploratory well is dry, then the firm is not committed to install the production capacity for $100 million. The firm has an implicit option to abandon the project.

alternatively, suppose that the firm purchased the land from the Alberta government and at that time agreed to install the production capacity if any drilling was done, including an exploratory well

Cont’d

in this case, the firm no longer has the option to abandon. How does the analysis change?

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Cont’d

text problem 8.13:

base case scenario: initial investment is $55,000, expected sales are 500 units per year at $20 net cash flow each for 10 years, relevant discount rate is 25%.

if the first year is a success, expected sales will increase to 750 units per year; if it is a failure, sales will fall to 250 units per year.

the firm also has an option to expand in that it can double the project’s scale after one year if desired. (a) What is the base case NPV?

Cont’d

(b) At the end of the first year, the project can be dismantled and sold for $40,000. At what level of expected sales should the project be abandoned?

(c) If success and failure are equally likely, what is the NPV of the project?

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Cont’d

(d) Assuming that success and failure are equally likely, what is the value of the option to abandon?