Ch13 20

Chapter 13Capital Budgeting: Estimating Cash Flows and Analyzing Risk

• Calculate Cash Flows for the new project.• Calculate the cost of capital.• Apply capital budgeting techniques: NPV, IRR, etc..• Project has positive NPV.• Done? • No• Analyze Risk:

• Sensitivity Analysis• Scenario Analysis• Simulation Analysis• Decision Trees

Capital Budgeting: Estimating Cash Flows and Analyzing Risk• To get the cash flows:

Year 0,… middle years,… last yearBuilding -costEquipment -costOperating cash flows:

Units soldSales price

Revenue(=units*price)-Variable cost-Fixed costs-Depreciation=EBIT-Taxes (=EBIT*tax)=NOPAT+depreciation = Operating CF1 Operating CF(last)

NOWC full amount higher/lower/equal to last 0CF from NOWC -full amount last – current + last year’s NOWC

Salvage value + salvage value CF

Net CF building + equip.+ operating CF + Last year’ s CF CF from NOWC + salvage value (do this for all years)

Capital Budgeting: Estimating Cash Flows and Analyzing Risk• Things to be mindful about :

• Sunk Costs– These costs were incurred in the past and your decision to accept or reject the project

cannot change them.– Ignore

• Opportunity Costs– Costs of letting go of the opportunity to do other things with the assets you need to put to

use for this project.– Include

• Externalities– The trickle down effects on other parts of your business, for example, helping sales of

related products, increasing brand loyalty or cannibalizing an existing product line.– Include

• Keep track of timing of cash flows. – Be as precise as possible,

• Use real and current tax rates and depreciation rates.• Take account of installation costs to calculate the depreciable basis for an asset.• Take account of salvage value.

Capital Budgeting: Estimating Cash Flows and Analyzing Risk• A new project is being considered by RIC with an economic life of 4 years.

• RIC’s marketing VP believes that the new sales from the project will be 20,000 units per year priced at 3,000 each. The price will increase by 2% each year but the number of units sold will not grow.

• The engineering department reports that the project will require new space and new machinery. The building can be bought for $12 million and the machinery for $8 million. Building falls in MACRS 39-year class and machinery in 5-year class.

• The building can be sold for $7.5 million and machinery for $2 million at the end of project’s life.

• The production department estimates that the variable cost per year will be $2,100 per unit for the first year and the fixed cost (excluding depreciation) will be $8 million per year.

• Variable cost will increase by 2% and fixed cost by 1% per year.

• They also estimate that the project will require 10% of next year’s total sales as net working capital each year.

• RIC’s marginal tax rate is 40% and its WACC is 12%

Capital Budgeting: Estimating Cash Flows and Analyzing Risk

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767778798081828384858687888990919293949596979899

100101102103104105

A B C D E F G H I

0 1 2 3 4 Investment Outlays: Long-Term AssetsBuildingEquipment

Operating Cash Flows over the Project's LifeUnits soldSales priceSales revenueVariable cost per unitTotal Variable costsFixed operating costsDepreciation (building)Depreciation (equipment)Oper. income before taxes (EBIT)Taxes on operating income (40%)Net Operating Profit After Taxes (NOPAT)Add back depreciation Operating cash flow

Cash Flows Due to Net Operating Working CapitalNet Operating Working Capital (based on sales)Cash flow due to investment in NOWC

Salvage Cash Flows: Long-Term AssetsNet salvage cash flow: BuildingNet salvage cash flow: EquipmentTotal salvage cash flows

Net Cash Flow (Time line of cash flows)

Years

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767778798081828384858687888990919293949596979899

100101102103104

A B C D E F G H I

0 1 2 3 4 Investment Outlays: Long-Term AssetsBuilding ($12,000)Equipment (8,000)

Operating Cash Flows over the Project's LifeUnits sold 20,000 20,000 20,000 20,000Sales price $3.00 $3.06 $3.12 $3.18Sales revenue $60,000 $61,200 $62,424 $63,672Variable costs 42,000 42,840 43,697 44,571Fixed operating costs 8,000 8,080 8,161 8,242Depreciation (building) 156 312 312 312Depreciation (equipment) 1,600 2,560 1,520 960Oper. income before taxes (EBIT) 8,244 7,408 8,734 9,587Taxes on operating income (40%) 3,298 2,963 3,494 3,835Net Operating Profit After Taxes (NOPAT) 4,946 4,445 5,241 5,752Add back depreciation 1,756 2,872 1,832 1,272 Operating cash flow $6,702 $7,317 $7,073 $7,024

Cash Flows Due to Net Operating Working CapitalNet Operating Working Capital (based on sales) $6,000 $6,120 $6,242 $6,367 $0Cash flow due to investment in NOWC ($6,000) ($120) ($122) ($125) $6,367

Salvage Cash Flows: Long-Term AssetsNet salvage cash flow: Building $8,863Net salvage cash flow: Equipment 1,744Total salvage cash flows $10,607

Net Cash Flow (Time line of cash flows) ($26,000) $6,582 $7,194 $6,948 $23,999

Years

Capital Budgeting: Estimating Cash Flows and Analyzing Risk• Once your cash flows are in place and you have calculated things like NPV and IRR,

you need to get some idea of the risk of the project.

• Where does risk come from?– Riskiness of project implies things will not be the same in reality as you

expected.– In other words, your cash flows might change from your projections.

• What can make cash flows change?– Things can change for three broad reasons:– The project specific (and only those) factors (i.e. your decision variables)

change.• Stand-alone Risk

– Company-wide factors change• Corporate Risk

– Economy-wide conditions change and everyone is affected.• Market Risk (Systemic Risk)

• Now rank these risks in the order of importance:• Market Risk• Corporate Risk• Stand alone Risk


• How can we figure out how much stand alone risk is in a project?

– We need to see what happens when the values of project variables change.

– Are we in trouble if the actual value of a variable is slightly different from out base line scenario?

• We can try to answer this question in three main ways:


• Sensitivity Analysis

• The most straight forward thing to do would be to change our variables within a broad (reasonable) range and see what happens.

• We can do this by using Excel Table command and find out NPVs for different values of a particular variable.

• Which variables posses the most risk?

• The ones for which a small change in the value brings about a relatively large change in the final NPV.

• The easiest way to figure it out is to make a graph of NPV values for each range of values we gave to our variables in sensitivity analysis.

-30 -20 -10 Base 10 20 30 Value (%)

88

NPV(000s)

Unit Sales

Salvage

r


• The variable posing the highest risk would have the steepest slope.

• Once you have found your areas of concern, you need to sit down and re-evaluate how confident you are in your projections of those variables.

• Suppose you are very confident. • For example, your NPV changes sharply if your variable cost changes

but you can enter a long term purchase agreement with your (very reliable) supplier. So a change in that variable has maximum impact but the likelihood of that happening is very low.

• In this case, the risk of your project does not increase (at least because of that one variable) and you may decide to go ahead with it.

• Otherwise? What do you do otherwise?

• You can subjectively increase your cost of capital (WACC) and run your analysis one more time.

• If it still comes out to be a winner, go for it.


• Previous discussion highlighted one point (or two if you are already racing through all the what ifs in your mind).

1. The values of variables can change but what is the chance (probability) of that happening.

2. In real life, not just one variable changes at a time, a combination of them might change simultaneously.


We can handle that through what is called:

Scenario Analysis• Take a set of variables and change their values at the same time according to a possible

scenarios that you think might happen.

• You can think of a lot of scenarios and in real life people do test for a multitude of scenarios.

• For the sake of simplicity in explaining, let’s just go with three scenarios:

• Base Case– The way things were when you originally did the analysis

• Best Case– The most rosy picture of things

• Worst Case– All hell breaks loose.– Well not really, but the worst it can reasonably go.

• Find NPV for each scenario• Assign a probability to each scenario• Find the expected value, standard deviation and the coefficient of variation from those

NPVs.• Compare it with the CV’s of firm’s regular projects.• If CV of NPVs is too high, what do you do?• Adjust the WACC and re-evaluate the project.


Scenario AnalysisFor the exercise we did in the lab, if we change our variable values for

different scenarios, we get the following NPVs:

Calculate the Expected NPV, standard deviation of NPV and the coefficient of variation.

161162163164165166

A B C D E F G HSales Unit Variable Growth

Probability Price Sales Costs Rate NPV

25% $3.90 26,000 $1.47 30% $146,18050% $3.00 20,000 $2.10 0% $5,80925% $2.10 14,000 $2.73 -30% ($37,257)

Scenario

Worst Case Base CaseBest Case


• You would get the following values:

• Now compare the CV to company’s “normal” CV. If this value it higher than that, the project is riskier than what the firm normally does.

• What would you do then?

168169170

D E F G HExpected NPV = sum, prob times NPV $30,135Standard Deviation = Sq Root of column I sum $69,267Coefficient of Variation = Std Dev / Expected NPV 2.30


• The company’s normal WACC is 12%.• Suppose the firm adds 3% to WACC for projects that are as riskier as the

current one.• So, we recalculate the NPV using 15% WACC and we get the NPV of

$3454.• Will you accept this project?• Why?


• Well, why stop at 3 scenarios or 30 scenarios? Why not have a 1000 or 10,000 scenarios.

• We can do that by using, what is called Monte-Carlo Simulation or just Simulation Analysis

• How can you think of so many values for so many variables?• You should not. If you think of the numbers yourself, you are violating the rules of

simulation analysis.• Those values should be random. You need to generate random values for each

of your variables.• But those random values should follow the overall behavior of the variables you

are simulating.• That is, they should be from the same probability as what you think your original

variable comes from.• If you think that your sales cost behaves like a normal random variable with a

mean (expected value) of $3.00 and 68% of the time will stay within $3 + or - $0.35 then you would generate a normal random variable with mean 3 and standard deviation 0.35.

• Excel can do that for you. • And since, Excel does all the work, you can generate a very large number (in

fact, the larger the better) say, 10,000 values of your potential sales cost figure.• You do this for all the important variables (the one that can change) in your

analysis.• Find NPVs for all the 10,000 sets of numbers you have generated.• Find out the mean, standard deviation and the number of times your NPV goes

negative relative to total NPV figures

Capital Budgeting: Estimating Cash Flows and Analyzing Risk• Depending on how confident you want to be in statistical sense, if you see your NPV

crossing the negative line say more than 10% of the time, you will categorize your project as risky. Or you can base your decision on the expected value and standard deviation of the resulting NPVs.

• The easiest way to see the results of simulation analysis is to make a histogram of your NPV values. Like this:

• Probability in this chart is the percentage of times, NPV was in that particular range relative to total number of NPV’s calculated (sample size).

-$60,000 $45,000 $150,000 $255,000 $360,000

NPV ($)

Probability


• Final “what if” for this section.• What if you had the choice to change tracks

mid-way? What if you had the choice to make a different decision based on the outcome in the future periods.

• In this case, you can make a decision tree and find out the possible NPVs and calculate statistics like expected NPV, standard deviation and coefficient of variation.

• Let’s take the example in the book.


• Stage 1: At t=0, the firm has the opportunity to spend $500,000 on a feasibility study.

• Stage 2: At t=1 the firm will learn whether the project appears feasible (there is an 80% chance that the project will be feasible). If it is feasible, the firm can spend $1,000,000 on a prototype.

• Stage 3: At t=2 the firm will learn whether the prototype is successful (there is a 60% chance the prototype will be successful). If it is successful, the firm can spend $10,000,000 to launch the project.

• Stage 4: At t=3 the firm will learn how well the market accepts the project. There is a 30% chance the project will have cash flows of $18,000,000 per year for 3 years, a 40% chance the project will have cash flows of $8,000,000 per year for three years, and a 30% chance the project will have cash flows of -$2,000,000 per year for three years. If the project is not successful, the firm can abandon the project after t=3.

Capital Budgeting: Estimating Cash Flows and Analyzing Riskt0 t1 t2 t3 t4 t5

-500


-1,000

-500Stop

0.8

0.2


-10,000-1,000

Stop-500

Stop

0.8

0.2

0.6

0.4


18,000 18,000 18,000-10,000 8,000 8,000 8,000

-2,000 Stop-1,000

Stop-500

Stop

How many ways to travel through this tree to a different end node?As many as the end nodes.How many different scenarios?As many as the end nodes.

0.8

0.2

0.6

0.4

0.30.4

0.3


Joint Probability

18,000 18,000 18,0000.144

-10,000 8,000 8,000 8,0000.192

-2,000 Stop0.144

-1,000

Stop0.320

-500

Stop0.200

Find the probability and the NPV for each scenario and then find the expected NPV,Standard deviation and the CV.

WACC is 11.5%

0.8

0.2

0.6

0.4

0.30.4

0.3

Capital Budgeting: Estimating Cash Flows and Analyzing Risk• Time 0 1 2 3 4 5 NPV P• Cash Flows• Scenario:• 1 -500 -1,000 -10,000 18,000 18,000 18,000 25,635

.144• 2 -500 -1,000 -10,000 8,000 8,000 8,000 6,149

.192• 3 -500 -1,000 -10,000 -2,000 -10,883

.144• 4 -500 -1,000 -1,397

.320• 5 -500 - 500

.200•• `

Capital Budgeting: Estimating Cash Flows and Analyzing Risk• Expected NPV = 2,758• St dev = 10,584• CV = 3.84


• Parker Products manufactures a variety of household products. The company is considering introducing a new detergent. The company's CFO has collected the following information about the proposed product. (Note: You may or may not need to use all of this information, use only the information that is relevant.)

• · The project has an anticipated economic life of 4 years.• · The company will have to purchase a new machine to produce the detergent. The

machine has an up-front cost (t = 0) of $2 million. The machine will be depreciated on a straight-line basis over 4 years (that is, the company's depreciation expense will be $500,000 in each of the first four years (t = 1, 2, 3, and 4). The company anticipates that the machine will last for four years, and that after four years, its salvage value will equal zero.

• · If the company goes ahead with the proposed product, it will have an effect on the company's net operating working capital. At the outset, t = 0, inventory will increase by $140,000 and accounts payable will increase by $40,000. At t = 4, the net operating working capital will be recovered after the project is completed.

• · The detergent is expected to generate sales revenue of $1 million the first year (t = 1), $2 million the second year (t = 2), $2 million the third year (t = 3), and $1 million the final year (t = 4). Each year the operating costs (not including depreciation) are expected to equal 50 percent of sales revenue.

• · The company's interest expense each year will be $100,000.• · The new detergent is expected to reduce the after-tax cash flows of the company's

existing products by $250,000 a year (t = 1, 2, 3, and 4).• · The company's overall WACC is 10 percent. However, the proposed project is riskier than

the average project for Parker; the project's WACC is estimated to be 12 percent.• · The company's tax rate is 40 percent.• What is the net present value of the proposed project?


• (In Thousands of Dollars)• t = 0 t = 1 t = 2 t = 3 t = 4• Initial cost• Change in NWC

•• Sales• Op. Costs• Depr. • Op. Inc. bef. taxes• Taxes (40%) • Oper. Inc. from project• Depr.• Change in other products• • Net cash flow (NCF)


• (In Thousands of Dollars)• t = 0 t = 1 t = 2 t = 3 t = 4• Initial cost -2,000• Change in NWC -100 + 100•• Sales $1,000 $2,000 $2,000 $1,000• Op. Costs 500 1,000 1,000 500• Depr. 500 500 500 500• Op. Inc. bef. taxes $ 0 $ 500 $ 500 $ 0• Taxes (40%) 0 200 200 0• Oper. Inc. from project $ 0 $ 300 $ 300 $ 0• Depr. 500 500 500 500• Change in other products - 250 - 250 - 250 - 250• • Net cash flow (NCF) -2,100 $ 250 $ 550 $ 550 $ 350

• NPV @ 12% = -$824,418.62

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Ch13 20