Example of accounting for salvage Example of accounting for salvage value (see last lecture)value (see last lecture)

Analyzing the HomeNet projectAnalyzing the HomeNet project

Break-Even Analysis Break-Even Analysis

Sensitivity AnalysisSensitivity Analysis

Scenario AnalysisScenario Analysis

Break-Even Analysis Break-Even Analysis

What is the value of the parameter at What is the value of the parameter at which NPV becomes 0?which NPV becomes 0?

Allows to see how sensitive your decision Allows to see how sensitive your decision is to errors in estimating this parameteris to errors in estimating this parameter

Example: HomeNet IRR Example: HomeNet IRR

Break even levels for some Break even levels for some HomeNet parametersHomeNet parameters

ParameterParameter Break-even levelBreak-even level Value used in Value used in NPV calculationsNPV calculations

Units soldUnits sold 79,759 per year79,759 per year 100,000 per year100,000 per year

Wholesale priceWholesale price $232 per unit$232 per unit $260 per unit$260 per unit

Cost of goodsCost of goods $138 per unit$138 per unit $110 per unit$110 per unit

Cost of capitalCost of capital 24.1%24.1% 12%12%

Sensitivity AnalysisSensitivity Analysis

Similar to the break-even analysis but here we explicitly Similar to the break-even analysis but here we explicitly check how NPV is sensitive to assumptions about check how NPV is sensitive to assumptions about parameters. Often worst case and best case are parameters. Often worst case and best case are consideredconsidered

Green bars show the change in NPV under the best-case assumption Green bars show the change in NPV under the best-case assumption for each parameter; red bars show the change under the worst-case for each parameter; red bars show the change under the worst-case assumption. Also shown are the break-even levels for each parameter. assumption. Also shown are the break-even levels for each parameter. Under the initial assumptions, HomeNet’s NPV is $5.0 million.Under the initial assumptions, HomeNet’s NPV is $5.0 million.

Break even + sensitivity analysis allow to Break even + sensitivity analysis allow to explore effect of errors in the estimates of explore effect of errors in the estimates of parameters on NPVparameters on NPV To the estimation of which parameters we should To the estimation of which parameters we should

devote most effortdevote most effort Which aspects of the project are most critical when Which aspects of the project are most critical when

managing the projectmanaging the project

Scenario analysisScenario analysisExtension of sensitivity analysis:Extension of sensitivity analysis:

Different parameters can in fact be interrelated. E.g. price Different parameters can in fact be interrelated. E.g. price and sales are both likely to fall in case of a negative and sales are both likely to fall in case of a negative demand shock. Then it makes little sense to consider them demand shock. Then it makes little sense to consider them separatelyseparately

Hence, managers analyze different scenarios of Hence, managers analyze different scenarios of parameters’ values that depend on some underlying factor parameters’ values that depend on some underlying factor (like demand shock)(like demand shock)

Investments with unequal livesInvestments with unequal lives

There are times when application of the NPV There are times when application of the NPV rule can lead to a wrong decision. Consider a rule can lead to a wrong decision. Consider a factory which must have an air cleaner.factory which must have an air cleaner.

There are two choices:There are two choices: The “Cadillac cleaner” costs $4,000 today, has annual The “Cadillac cleaner” costs $4,000 today, has annual

operating costs of $100 and lasts for 10 years.operating costs of $100 and lasts for 10 years. The “cheaper cleaner” costs $1,000 today, has annual The “cheaper cleaner” costs $1,000 today, has annual

operating costs of $500 and lasts for 5 years.operating costs of $500 and lasts for 5 years.

Which one should we choose?Which one should we choose?

At first glance, the cheap cleaner has lower NPV (At first glance, the cheap cleaner has lower NPV (RR = 10%): = 10%):

46.614,4)10.1(

100$000,4$

10

1Cadillac

tt

NPV

39.895,2)10.1(

500$000,1$

5

1cheap

tt

NPV

This overlooks the fact that the Cadillac cleaner lasts twice as long.When we incorporate that, the Cadillac cleaner is actually cheaper.

The Cadillac cleaner time line of cash flows:The Cadillac cleaner time line of cash flows:

-$4,000 –100 -100 -100 -100 -100 -100 -100 -100 -100 -100

0 1 2 3 4 5 6 7 8 9 10

-$1,000 –500 -500 -500 -500 -1,500 -500 -500 -500 -500 -500

0 1 2 3 4 5 6 7 8 9 10

The “cheaper cleaner” time line of cash flows over ten years:

20.693,4$)10.1(

500$

)10.1(

000,1$

)10.1(

500$000,1$

10

65

5

1cheap

tt

tt

NPV

46.614,4)10.1(

100$000,4$

10

1Cadillac

tt

NPV

How to take into account the difference in How to take into account the difference in lives?lives? Matching cycles:Matching cycles:

Lives: x and y yearsLives: x and y yearsFind the least common multiple of x and y: LCM = Find the least common multiple of x and y: LCM = z. Compare the sequences of each project over z z. Compare the sequences of each project over z years (NPV)years (NPV)

Replacement chain: repeat the projects Replacement chain: repeat the projects forever, find the forever, find the PVPV of that perpetuity. of that perpetuity.

Equivalent annual value (equivalent annual Equivalent annual value (equivalent annual cost)cost)

Equivalent annual value (equivalent Equivalent annual value (equivalent annual cost) methodannual cost) method

NPV = ANPV NPV = ANPV × A× ARRT T ,,

wherewhere A ARRT T is the annuity of $1 foris the annuity of $1 for T T years years

discounted atdiscounted at R. R. ThenThen

Choose the one with the highest ANPVChoose the one with the highest ANPV

T

T

tt

t

T

tt

T

tt

t

RR

RCF

I

R

RCF

IANPV

)1(1

11

)1(

)1(1

)1( 1

1

1

If the projects differ only by costs it’s called EAC method:If the projects differ only by costs it’s called EAC method: EACEAC = = NPV of Cost / ANPV of Cost / ARR

T T Choose the one with the lowestChoose the one with the lowest EAC EAC

Matching cycles, replacement chain and EAV give the Matching cycles, replacement chain and EAV give the samesame answer answer

Note:Note: RR must be the same for both projects must be the same for both projects

These methods are correct only if we indeed believe that These methods are correct only if we indeed believe that we are going to use machines exactly for some common we are going to use machines exactly for some common multiple of machines’ lives or at least for time much multiple of machines’ lives or at least for time much longer than machines’ lives (than the methods are longer than machines’ lives (than the methods are approx. correct).approx. correct).Otherwise we should just consider cash flows from each Otherwise we should just consider cash flows from each machine in each year until liquidation and their salvage machine in each year until liquidation and their salvage values and explicitly compute and compare NPVs.values and explicitly compute and compare NPVs.

Replacement Problem Replacement Problem Consider a dentist’s office; he needs an autoclave to Consider a dentist’s office; he needs an autoclave to sterilize his instruments. He has an old one that is in sterilize his instruments. He has an old one that is in use, but the maintenance costs are rising and so is use, but the maintenance costs are rising and so is considering replacing this indispensable piece of considering replacing this indispensable piece of equipment.equipment.New AutoclaveNew Autoclave

Cost = $3,000 today, Cost = $3,000 today, Maintenance cost = $20 per yearMaintenance cost = $20 per year Resale value after 6 years = $1,200Resale value after 6 years = $1,200 NPVNPV of new autoclave (at of new autoclave (at rr = 10%): = 10%):

6

6

1 )10.1(

200,1$

)10.1(

20$000,3$74.409,2$

tt

6

1 )10.1(

29.553$74.409,2$

tt

EAC of new autoclave = -$553.29

Existing AutoclaveExisting Autoclave

YearYear 00 11 22 33 44 55

Maintenance Maintenance 00 200200 275275 325325 450450 500500

ResaleResale 900900 850850 775775 700700 600600 500500

Total Annual CostTotal Annual Cost

Total Cost for year 1 = (900 × 1.10 – 850) + 200 = $340

340 435

Total Cost for year 2 = (850 × 1.10 – 775) + 275 = $435

478

Total Cost for year 3 = (775 × 1.10 – 700) + 325 = $478

620

Total Cost for year 4 = (700 × 1.10 – 600) + 450 = $620Total Cost for year 5 = (600 × 1.10 – 500) + 500 = $660

660

Note that the total cost of keeping an autoclave for the first year includes the $200 maintenance cost as well as the opportunity cost of the foregone future value of the $900 we didn’t get from selling it in year 0 less the $850 we have if we still own it at year 1.

340 435 478 620 660

New Autoclave EAC of new autoclave = -$553.29

Existing AutoclaveYear 0 1 2 3 4

5Maintenance 0 200 275 325 450 500Resale 900 850 775 700 600

500Total Annual Cost•We should keep the old autoclave until it’s cheaper to buy a new one.

•Replace the autoclave after year 3: at that point the new one will cost $553.29 for the next year’s autoclaving and the old one will cost $620 for one more year.

•Note: we ignored taxes and depreciation in this example