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Capital budegting project and risk analysis
- 1. Capital Budgeting Project Analysis and Risk 1. Expansion 2. Replacement 3. Mandatory 4. Safety and regulatory 5. Competitive Bid price 6. Risk Analysis: Sensitivity Analysis, Scenario Analysis, and Simulation Analysis
- 2. Outline of CashFlow Analysis • Project Cash Flows: • Incremental Cash Flows • Pro Forma Financial Statements and Project Cash Flows • Alternative Definitions of Operating Cash Flow • Some Special Cases of Cash Flow Analysis
- 3. Relevant Cash Flows •The cash flows that should be included in a capital budgeting analysis are those that will only occur if the project is accepted • These cash flows are called incremental cash flows • The stand-alone principle allows us to analyze each project in isolation from the firm simply by focusing on incremental cash flows
- 4. Common Types ofCash Flows • Sunk costs – costs that have accrued in the past • Opportunity costs – costs of lost options • Side effects – Positive side effects – benefits to other projects – Negative side effects – costs to other projects • Changes in net working capital • Financing costs • Taxes
- 5. Pro Forma Statementsand Cash Flow • Capital budgeting relies heavily on pro forma accounting statements, particularly income statements • Computing cash flows – refresher – Operating Cash Flow (OCF) = EBIT + depreciation – taxes – OCF = Net income + depreciation when there is no interest expense – Cash Flow From Assets (CFFA) = OCF – net capital spending (NCS) – changes in NWC
- 6. Example of ProForma Financial Statements • Sales= 50,000 units Price=$4 • Unit cost=$2.5 R=20% • Fixed cost=$20,000 per year • Initial cost=$90,000 • NWC=$20,000 per year • Tax rate=34% • Straight Line Depreciation: 3 years Life
- 7. Pro Forma IncomeStatement Sales (50,000 units at $4.00/unit) $200,000 Variable Costs ($2.50/unit) 125,000 Gross profit $ 75,000 Fixed costs 12,000 Depreciation ($90,000 / 3) 30,000 EBIT $ 33,000 Taxes (34%) 11,220 Net Income $ 21,780
- 8. Projected Capital Requirements Year 0 1 2 3 NWC $20,000 $20,000 $20,000 $20,000 Net Fixed 90,000 60,000 30,000 0 Assets Total $110,000 $80,000 $50,000 $20,000 Investment
- 9. Projected Total CashFlows Year 0 1 2 3 OCF $51,780 $51,780 $51,780 Change in -$20,000 20,000 NWC Capital -$90,000 Spending CF -$110,00 $51,780 $51,780 $71,780
- 10. Making The Decision •Now that we have the cash flows, we can apply the techniques of capital budgeting. • Enter the cash flows into the calculator and compute NPV and IRR – CF0 = -110,000; C01 = 51,780; F01 = 2; C02 = 71,780 – NPV; I = 20; CPT NPV = 10,648 – CPT IRR = 25.8% • Should we accept or reject the project?
- 11. Depreciation • The depreciationexpense used for capital budgeting should be the depreciation schedule required by the IRS for tax purposes • Depreciation itself is a non-cash expense, consequently, it is only relevant because it affects taxes • Depreciation tax shield = D (TC) – D = depreciation expense – TC = marginal tax rate
- 12. Computing Depreciation • Straight-linedepreciation – D = (Initial cost – salvage) / number of years – Very few assets are depreciated straight-line for tax purposes • MACRS – Need to know which asset class is appropriate for tax purposes – Multiply percentage given in table by the initial cost – Depreciate to zero – Mid-year convention
- 13. DEPRECIATION TABLES Class of Investment Ownership Year 3-Year 5-Year 7-Year 10-Year 1 33% 20% 14% 10% 2 45% 32% 25% 18% 3 15% 19% 17% 14% 4 7% 12% 13% 12% 5 11% 9% 9% 6 6% 9% 7% 7 9% 7% 8 4% 7% 9 7% 10 6% 11 3% 100% 100% 100% 100%
- 14. After-tax Salvage • Ifthe salvage value is different from the book value of the asset, then there is a tax effect • Book value = initial cost – accumulated depreciation • After-tax salvage = salvage – Tax rate (salvage – book value)
- 15. Example: Depreciation andAfter-tax Salvage • You purchase equipment for $100,000 and it costs $10,000 to have it delivered and installed. Based on past information, you believe that you can sell the equipment for $17,000 when you are done with it in 6 years. The company’s marginal tax rate is 40%. What is the depreciation expense each year and the after-tax salvage in year 6 for each of the following situations?
- 16. Example: Straight-line Depreciation •Suppose the appropriate depreciation schedule is straight-line – D = (110,000 – 17,000) / 6 = 15,500 every year for 6 years – BV in year 6 = 110,000 – 6(15,500) = 17,000 – After-tax salvage = 17,000 - .4(17,000 – 17,000) = 17,000
- 17. Example: Three-year MACRS Year MACRS D BV in year 6 = percent 110,000 – 36,663 – 48,884 – 16,302 – 1 .3333 .3333(110,000) = 36,663 8,151 = 0 2 .4444 .4444(110,000) = After-tax salvage 48,884 = 17,000 - . 4(17,000 – 0) = 3 .1482 .1482(110,000) = $10,200 16,302 4 .0741 .0741(110,000) = 8,151
- 18. Example: 7-Year MACRS Year MACRS D BV in year 6 = Percent 110,000 – 15,719 – 1 .1429 .1429(110,000) = 15,719 26,939 – 19,239 – 13,739 – 9,823 – 2 .2449 .2449(110,000) = 26,939 9,823 = 14,718 3 .1749 .1749(110,000) = 19,239 After-tax salvage = 17,000 - . 4 .1249 .1249(110,000) = 13,739 4(17,000 – 14,718) = 5 .0893 .0893(110,000) = 9,823 16,087.20 6 .0893 .0893(110,000) = 9,823
- 19. Example: Replacement Problem • New Machine • Original Machine – Initial cost = 150,000 – Initial cost = 100,000 – 5-year life – Annual depreciation = – Salvage in 5 years = 0 9000 – Cost savings = 50,000 – Purchased 5 years per year ago – 3-year MACRS – Book Value = 55,000 depreciation – Salvage today = 65,000 • Required return = – Salvage in 5 years = 10% 10,000 • Tax rate = 40%
- 20. Replacement Problem –Computing Cash Flows • Remember that we are interested in incremental cash flows • If we buy the new machine, then we will sell the old machine • What are the cash flow consequences of selling the old machine today instead of in 5 years?
- 21. Replacement Problem –Pro Forma Income Statements Year 1 2 3 4 5 Cost 50,000 50,000 50,000 50,000 50,000 Savings Depr. New 49,500 67,500 22,500 10,500 0 Old 9,000 9,000 9,000 9,000 9,000 Increm. 40,500 58,500 13,500 1,500 (9,000) EBIT 9,500 (8,500) 36,500 48,500 59,000 Taxes 3,800 (3,400) 14,600 19,400 23,600 NI 5,700 (5,100) 21,900 29,100 35,400
- 22. Replacement Problem –Incremental Net Capital Spending • Year 0 – Cost of new machine = 150,000 (outflow) – After-tax salvage on old machine = 65,000 - . 4(65,000 – 55,000) = 61,000 (inflow) – Incremental net capital spending = 150,000 – 61,000 = 89,000 (outflow) • Year 5 – After-tax salvage on old machine = 10,000 - . 4(10,000 – 10,000) = 10,000 (outflow because we no longer receive this)
- 23. Replacement Problem –Cash Flow From Assets Year 0 1 2 3 4 5 OCF 46,200 53,400 35,400 30,600 26,400 NCS -89,000 -10,000 ∆ In 0 0 NWC CF -89,000 46,200 53,400 35,400 30,600 16,400
- 24. Replacement Problem –Analyzing the Cash Flows • Now that we have the cash flows, we can compute the NPV and IRR – Enter the cash flows – Compute NPV = 54,812.10 – Compute IRR = 36.28% • Should the company replace the equipment?
- 25. Example: Cost Cutting •Your company is considering new computer system that will initially cost $1 million. It will save $300,000 a year in inventory and receivables management costs. The system is expected to last for five years and will be depreciated using 3-year MACRS. The system is expected to have a salvage value of $50,000 at the end of year 5. There is no impact on net working capital. The marginal tax rate is 40%. The required return is 8%. • Click on the Excel icon to work through the example
- 26. Example: Setting theBid Price • Consider the example in the book: – Need to produce 5 modified trucks per year for 4 years – We can buy the truck platforms for $10,000 each – Facilities will be leased for $24,000 per year – Labor and material costs are $4,000 per truck – Need $60,000 investment in new equipment, depreciated straight-line to a zero salvage – Actually expect to sell it for $5000 at the end of 4 years – Need $40,000 in net working capital – Tax rate is 39% – Required return is 20%
- 27. Example: Equivalent AnnualCost Analysis • Machine A • Machine B – Initial Cost = $5,000,000 – Initial Cost = $6,000,000 – Pre-tax operating cost = – Pre-tax operating cost = $500,000 $450,000 – Straight-line depreciation – Straight-line depreciation over 5 year life over 8 year life – Expected salvage = – Expected salvage = $400,000 $700,000 The machine chosen will be replaced indefinitely and neither machine will have a differential impact on revenue. No change in NWC is required. The required return is 9% and the tax rate is 40%.
- 28. Capital Budgeting andRisk Analysis What’s the Big Idea? Earlier Topics on capital budgeting focused on the appropriate size and timing of cash flows. This section discusses the effect of risk on investment decision when the cash flows are risky.
- 29. What does “risk”mean in capital budgeting? • Uncertainty about a project’s future cash flows or profitability. • Measured by σNPV, σIRR, beta. • Will taking on the project increase the firm’s and stockholders’ risk?
- 30. Is risk analysisbased on historical data or subjective judgment? • Can sometimes use historical data, but generally cannot. • So risk analysis in capital budgeting is usually based on subjective judgments.
- 31. What three typesof risk are relevant in capital budgeting? • Stand-alone risk • Corporate risk • Market (or beta) risk
- 32. Stand-Alone Risk • Theproject’s risk if it were the firm’s only asset and there were no shareholders. • Ignores both firm and shareholder diversification. • Measured by the σ or CV of NPV, IRR, or MIRR.
- 33. Probability Density Flatter distribution, larger σ , larger stand-alone risk. 0 E(NPV) NPV
- 34. Corporate Risk • Reflectsthe project’s effect on corporate earnings stability. • Considers firm’s other assets (diversification within firm). • Depends on project’s σ, and its correlation, ρ, with returns on firm’s other assets. • Measured by the project’s corporate beta.
- 35. Project X isnegatively correlated to firm’s other assets, so has big diversification benefits. If r = 1.0, no diversification Profitability benefits. If r < 1.0, some diversification benefits. Project X Total Firm Rest of Firm 0 Years
- 36. Market Risk • Reflectsthe project’s effect on a well- diversified stock portfolio. • Takes account of stockholders’ other assets. • Depends on project’s σ and correlation with the stock market. • Measured by the project’s market beta.
- 37. How is eachtype of risk used? • Market risk is theoretically best in most situations. • However, creditors, customers, suppliers, and employees are more affected by corporate risk. • Therefore, corporate risk is also relevant.
- 38. Stand-Alone Risk • Stand-alonerisk is easiest to measure, more intuitive. • Core projects are highly correlated with other assets, so stand-alone risk generally reflects corporate risk. • If the project is highly correlated with the economy, stand-alone risk also reflects market risk.
- 39. Sensitivity Analysis • Examinesseveral possible situations, usually worst case, most likely case, and best case. • Provides a range of possible outcomes. • Shows how changes in a variable such as unit sales affect NPV or IRR. • Each variable is fixed except one. Change this one variable to see the effect on NPV or IRR. • Answers “what if” questions, e.g. “What if sales decline by 30%?”
- 40. What are theweaknesses of sensitivity analysis? • Does not reflect diversification. • Says nothing about the likelihood of change in a variable, i.e. a steep sales line is not a problem if sales won’t fall. • Ignores relationships among variables.
- 41. Why is sensitivityanalysis useful? • Gives some idea of stand-alone risk. • Identifies dangerous variables. • Gives some breakeven information.
- 42. scenario analysis • Onlyconsiders a few possible out-comes. • Assumes that inputs are perfectly correlated--all “bad” values occur together and all “good” values occur together. • Focuses on stand-alone risk, although subjective adjustments can be made.
- 43. Simulation Analysis • Acomputerized version of scenario analysis which uses continuous probability distributions. • Computer selects values for each variable based on given probability distributions.
- 44. Process for Simulation •NPV and IRR are calculated. • Process is repeated many times (1,000 or more). • End result: Probability distribution of NPV and IRR based on sample of simulated values. • Generally shown graphically.
- 45. Summary • Sensitivity, scenario,and simulation analyses do not provide a decision rule. They do not indicate whether a project’s expected return is sufficient to compensate for its risk. • Sensitivity, scenario, and simulation analyses all ignore diversification. Thus they measure only stand-alone risk, which may not be the most relevant risk in capital budgeting.
- 46. Should subjective risk factors be considered? • Yes. A numerical analysis may not capture all of the risk factors inherent in the project. • For example, if the project has the potential for bringing on harmful lawsuits, then it might be riskier than a standard analysis would indicate.
Editor's Notes
- #5 With each of these types of cash flows, you should ask the class the question on the previous slide so that they can start to determine if the cash flows are relevant. Sunk costs – our government provides ample examples of inappropriately including sunk costs in their capital allocation decisions. Opportunity costs – the classic example of an opportunity cost is the use of land or plant that is already owned. It is important to point out that this is not “free.” At the very least we could sell the land; consequently if we choose to use it, we cost ourselves the selling price of the asset. A good example of a positive side effect is when you will establish a new distribution system with this project that can be used for existing or future projects. The benefit provided to those projects needs to be considered. The most common negative side effect is erosion or cannibalism, where the introduction of a new product will reduce the sales of existing, similar products. A good real-world example is McDonald’s introduction of the Arch Deluxe sandwich. Instead of generating all new sales, it primarily reduced sales in the Big Mac and the Quarter Pounder. It is important to consider changes in NWC. We need to remember that operating cash flow derived from the income statement assumes all sales are cash sales and that the COGS was actually paid in cash during that period. By looking at changes in NWC specifically, we can adjust for the difference in cash flow that results from accounting conventions. Most projects will require an increase in NWC initially as we build inventory and receivables. We do not include financing costs. Students often have difficulty understanding why when it appears that we will only raise capital if we take the project. It is important to point out that because of economies of scale, companies generally do not finance individual projects. Instead, they finance the entire portfolio of projects at one time. The other reason has to do with maintaining a target capital structure over time, but not necessarily each year. Taxes will change as the firm’s taxable income changes. Consequently, we have to consider cash flows on an after-tax basis.
- #6 Operating cash flow – students often have to go back to the income statement to see that the two definitions of operating cash flow are equivalent when there is no interest expense.
- #9 Ask the students why net fixed assets is decreasing each year. It is important that they understand that when they go to compute the net capital spending in the next slide.
- #10 OCF = EBIT + depreciation – taxes = 33,000 + 30,000 – 11,220 = 51,780; or OCF = NI + depreciation = 21,780 + 30,000 = 51,780 Note that in the Table in the book, the negative signs have already been carried throughout the table so that the columns can just be added. Ultimately, students seem to do better with this format even though the CFFA equation says to subtract the changes in NWC and net capital spending. Change in NWC = We have a net investment in NWC in year 0 of 20,000; we get the investment back at the end of the project when we sell our inventory, collect on our receivables and pay off our payables. Students often forget that we get the investment back at the end. Capital Spending – remember that Net capital spending = change in net fixed assets + depreciation. So in year one NCS = (60,000 – 90,000) + 30,000 = 0; The same is true for the other years.
- #11 You can also use the formulas to compute NPV and IRR, just remember that the IRR computation is trial and error. Click on the excel icon to go to an embedded spreadsheet that illustrates how the pro formas and cash flows can be set-up and computes the NPV and IRR.
- #13 The MACRS percentages are given in Table 9-7
- #18 Note that with MACRS you do not subtract the expected salvage from the initial cost. Also note that the MACRS % is multiplied by the initial cost every year. For some reason, students want to multiply by the book value.
- #23 The year 5 cash flow is the most difficult for students to grasp. It is important to point out that we are looking for ALL changes in cash flow associated with selling the machine today instead of in 5 years. If we do not sell the machine today, then we will have after-tax salvage of 10,000 in 5 years. Since we do sell the machine today, we LOSE the 10,000 cash flow in 5 years.
- #24 The negative signs in the CFFA equation were once again carried through the table. That way outflows are in the table as negative and inflows are positive.
- #26 There are two worksheets. The first allows you to enter the information and work the example during class. The second provides the solutions. You may go directly to this one if you do not wish to show the students how to set up the spreadsheet during class time.
- #27 Click on the worksheet to see the solution to the problem. The format used was the same as that in the book. If you wanted to set up a separate spreadsheet using Solver, you certainly could.