Break-Even Analysis What is the value of the parameter at which NPV becomes 0? Allows to see how sensitive your decision is to errors in estimating this parameter Example: HomeNet IRR
Break even levels for some HomeNet parameters Parameter Break-even level Value used in NPV calculations Units sold 79,759 per year 100,000 per year Wholesale price $232 per unit $260 per unit Cost of goods $138 per unit $110 per unit Cost of capital 24.1%12%
Sensitivity Analysis Similar to the break-even analysis but here we explicitly check how NPV is sensitive to assumptions about parameters. Often worst case and best case are considered
Green bars show the change in NPV under the best-case assumption for each parameter; red bars show the change under the worst-case assumption. Also shown are the break-even levels for each parameter. Under the initial assumptions, HomeNets NPV is $5.0 million.
Break even + sensitivity analysis allow to explore effect of errors in the estimates of parameters on NPV To the estimation of which parameters we should devote most effort To the estimation of which parameters we should devote most effort Which aspects of the project are most critical when managing the project Which aspects of the project are most critical when managing the project Scenario analysis Extension of sensitivity analysis: Different parameters can in fact be interrelated. E.g. price and sales are both likely to fall in case of a negative demand shock. Then it makes little sense to consider them separately Hence, managers analyze different scenarios of parameters values that depend on some underlying factor (like demand shock)
Investments with unequal lives There are times when application of the NPV rule can lead to a wrong decision. Consider a factory which must have an air cleaner. There are two choices: The Cadillac cleaner costs $4,000 today, has annual operating costs of $100 and lasts for 10 years. The Cadillac cleaner costs $4,000 today, has annual operating costs of $100 and lasts for 10 years. The cheaper cleaner costs $1,000 today, has annual operating costs of $500 and lasts for 5 years. The cheaper cleaner costs $1,000 today, has annual operating costs of $500 and lasts for 5 years. Which one should we choose?
At first glance, the cheap cleaner has lower NPV (R = 10%): 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: -$4,000 – $1,000 – , The cheaper cleaner time line of cash flows over ten years:
How to take into account the difference in lives? Matching cycles: Matching cycles: Lives: x and y years Find the least common multiple of x and y: LCM = z. Compare the sequences of each project over z years (NPV) Replacement chain: repeat the projects forever, find the PV of that perpetuity. Replacement chain: repeat the projects forever, find the PV of that perpetuity. Equivalent annual value (equivalent annual cost) Equivalent annual value (equivalent annual cost)
Equivalent annual value (equivalent annual cost) method NPV = ANPV × A R T, where A R T is the annuity of $1 for T years discounted at R. Then Choose the one with the highest ANPV
If the projects differ only by costs its called EAC method: EAC = NPV of Cost / A R T Choose the one with the lowest EAC Matching cycles, replacement chain and EAV give the same answer Note: R must be the same for both projects Note: R must be the same for both projects These methods are correct only if we indeed believe that we are going to use machines exactly for some common multiple of machines lives or at least for time much longer than machines lives (than the methods are approx. correct). Otherwise we should just consider cash flows from each machine in each year until liquidation and their salvage values and explicitly compute and compare NPVs.
Replacement Problem Consider a dentists office; he needs an autoclave to sterilize his instruments. He has an old one that is in use, but the maintenance costs are rising and so is considering replacing this indispensable piece of equipment. New Autoclave Cost = $3,000 today, Cost = $3,000 today, Maintenance cost = $20 per year Maintenance cost = $20 per year Resale value after 6 years = $1,200 Resale value after 6 years = $1,200 NPV of new autoclave (at r = 10%): NPV of new autoclave (at r = 10%): EAC of new autoclave = -$553.29
Existing Autoclave Year Maintenance Resale Total Annual Cost Total Cost for year 1 = (900 × 1.10 – 850) = $ Total Cost for year 2 = (850 × 1.10 – 775) = $ Total Cost for year 3 = (775 × 1.10 – 700) = $ Total Cost for year 4 = (700 × 1.10 – 600) = $620 Total Cost for year 5 = (600 × 1.10 – 500) = $ 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 didnt get from selling it in year 0 less the $850 we have if we still own it at year 1.
New Autoclave EAC of new autoclave = -$ Existing Autoclave Year Maintenance Resale Total Annual Cost We should keep the old autoclave until its cheaper to buy a new one. Replace the autoclave after year 3: at that point the new one will cost $ for the next years autoclaving and the old one will cost $620 for one more year. Note: we ignored taxes and depreciation in this example