Real options Real Options and Risk Analysis in Capital Budgeting Traditional NPV analysis should not be viewed as static. This can lead to decision-making problems in a dynamic environment when not all decisions have to be made today. In reality, management has the ability to: abandon or mothball operations when conditions are unfavorable delay projects until uncertainty is resolved make investments (such as R&D expenditures) which may create / preserve profitable investment options in the future switch technology or inputs Thus, there are several managerial options embedded in capital budgeting decisions. These options, called real options are not captured effectively in the traditional DCF framework, which implicitly, assumes that investment opportunities are now or never. weights all states of nature even those where significant losses could be avoided when determining a project s value-added. => Decision trees allow us to map out alternatives and identify the best, or in other words, value-maximizing actions. EXAMPLE -- ABANDONMENT OPTION ANALYZED VIA DECISION TREE A firm is considering a -year project with an initial outlay of $8,000. The costs of operating in years 1 and are known with certainty to be $0,000. However, the revenues are uncertain. There is a 50% chance that year 1 revenues will be $8,000 and a 50% chance that year 1 revenues will be $0,000. Second year revenues are also uncertain, but depend to some extent on the state realized in year 1. If the good state is realized in year 1 (i.e., revenue of $8,000), there will be a 50% chance of an upturn to $40,000 in year, and a 50% chance of a downturn to $4,000 in year. Similarly, if the bad state (i.e., revenue of $0,000) is realized in year 1, there will be a 50% chance of an upturn to $4,000 in year, and a 50% chance of a downturn to $8,000 in year. 1
YEAR 1 YEAR 0.5 Π=$0,000 0.5 Π=$8,000 0.5 Π=$4,000 0.5 Π=$0 0.5 Π=$4,000 0.5 Π=-$1,000 Use DCF to find the expected NPV of this project assuming a 10% cost of capital. Expected cash flow in year 1 Expected cash flow in year NPV Investment (1 discount rate) (1 discount rate).5*8,000.5*0.5* 0,000.5* 4,000.5* 4,000.5*-1,000-8,000 (1.1) (1.1) $8,000 $4,000 1.1 $4,000 1.1 $1,057.85 Traditional DCF analysis using expected values suggests that this is not a good investment.
However, there is a problem with the preceding analysis! The problem lies with the assumption that the firm is obligated to operate in the second year. In reality, the firm has the right to conduct operations, but is not obligated to do so. Does it make sense to continue to operate in the second year if the first year's revenues were poor? No. Instead, a prudent manager would exercise the abandonment option and would realize a cash flow of zero rather than the possibility of a loss of $1,000 (and an expected loss of 0.5 x $4,000 + 0.5 x -$1,000 = -$4,000). So, the revised year cash flows would be:.5 * 0,000 +.5 * 4,000 +.5 * 0 = $6,000 The project s correct NPV, considering the abandonment option is: $4,000 $6,000 NPV $8,000 $595.04 1.1 1.1 ===============##=============== 3
Scenario Analysis, Sensitivity Analysis, and Simulations The goal in performing a scenario analysis, a sensitivity analysis, or a simulation is to see how much risk (uncertainty) is associated with a project and to determine what the most crucial inputs are. This is best illustrated by way of an example. Capital Budgeting Example Scenario Analysis, Sensitivity Analysis Midwest Control Products is considering a capital budgeting proposal for the manufacture of after-market performance exhaust systems. The initial investment in machinery would total $300,000. This amount will be depreciated on a straight-line basis over the project s 3-year life. The relevant cost of capital has been estimated to be 14% and the applicable tax rate is 40%. The project will require an immediate NWC investment of $40,000 and this would be recovered at the end of the project s life. The machinery will have no salvage value after 3 years. The following represent the yearly cash flow projections. Pessimistic Most likely Optimistic Sales (in units) 1,000 1,00 1,400 Price per unit $350 $400 $450 Variable costs (per unit) $150 $140 $130 Direct labor (per unit) $80 $75 $70 Fixed Production costs $45,000 $40,000 $35,000 Probability of outcome 1/3 1/3 1/3 *For simplicity, assume that the state which is realized at t=1 will be in effect for the project s duration. Questions: 1. Conduct a scenario analysis for the 3 cases specified. What is the NPV and IRR in each case (pessimistic, most likely, optimistic)? What is the expected NPV? What is the standard deviation of the NPV? What is the coefficient of variation? Should the project be accepted?. Conduct a sensitivity analysis on sales (# units), price per unit, variable costs, and fixed production costs. Comment on your findings. 4
Pessimistic case Input value Sales Quantity 1,000 100% 1,000 Sales Price $350 100% $350 Variable costs / unit $150 100% $150 direct labor / unit $80 100% $80 fixed production costs $45,000 100% $45,000 Year 0 1 3 Sales $350,000.00 $350,000.00 $350,000.00 variable costs -$150,000.00 -$150,000.00 -$150,000.00 direct labor -$80,000.00 -$80,000.00 -$80,000.00 fixed production costs -$45,000.00 -$45,000.00 -$45,000.00 depreciation -$100,000.00 -$100,000.00 -$100,000.00 EBIT -$5,000.00 -$5,000.00 -$5,000.00 taxes $10,000.00 $10,000.00 $10,000.00 NI -$15,000.00 -$15,000.00 -$15,000.00 Add back depreciation $100,000.00 $100,000.00 $100,000.00 OCF $85,000.00 $85,000.00 $85,000.00 capital investment -$300,000.00 NWC -$40,000.00 $40,000.00 Net cash flow -$340,000.00 $85,000.00 $85,000.00 $15,000.00 NPV @14% ($115,66.4) IRR -6.37%
Most likely (middle case) Most likely % of most likely Input value Sales Quantity 1,00 100% 1,00 Sales Price $400 100% $400 Variable costs / unit $140 100% $140 direct labor / unit $75 100% $75 fixed production costs $40,000 100% $40,000 Year 0 1 3 Sales $480,000.00 $480,000.00 $480,000.00 variable costs -$168,000.00 -$168,000.00 -$168,000.00 direct labor -$90,000.00 -$90,000.00 -$90,000.00 fixed production costs -$40,000.00 -$40,000.00 -$40,000.00 depreciation -$100,000.00 -$100,000.00 -$100,000.00 EBIT $8,000.00 $8,000.00 $8,000.00 taxes -$3,800.00 -$3,800.00 -$3,800.00 NI $49,00.00 $49,00.00 $49,00.00 Add back depreciation $100,000.00 $100,000.00 $100,000.00 OCF $149,00.00 $149,00.00 $149,00.00 capital investment -$300,000.00 NWC -$40,000.00 $40,000.00 Net cash flow -$340,000.00 $149,00.00 $149,00.00 $189,00.00 NPV @14% $33,386.36 IRR 19.54%
Optimistic Case Input value Sales Quantity 1,400 100% 1,400 Sales Price $450 100% $450 Variable costs / unit $130 100% $130 direct labor / unit $70 100% $70 fixed production costs $35,000 100% $35,000 Year 0 1 3 Sales $630,000.00 $630,000.00 $630,000.00 variable costs -$18,000.00 -$18,000.00 -$18,000.00 direct labor -$98,000.00 -$98,000.00 -$98,000.00 fixed production costs -$35,000.00 -$35,000.00 -$35,000.00 depreciation -$100,000.00 -$100,000.00 -$100,000.00 EBIT $15,000.00 $15,000.00 $15,000.00 taxes -$86,000.00 -$86,000.00 -$86,000.00 NI $19,000.00 $19,000.00 $19,000.00 Add back depreciation $100,000.00 $100,000.00 $100,000.00 OCF $9,000.00 $9,000.00 $9,000.00 capital investment -$300,000.00 NWC -$40,000.00 $40,000.00 Net cash flow -$340,000.00 $9,000.00 $9,000.00 $69,000.00 NPV @14% $18,65.59 IRR 48.55%
1 (1 x ) Projected NPV probability pessimistic -$115,66.4 0.333333 -$38,554.14 most likely $33,386.36 0.333333 $11,18.79 optimistic $18,65.59 0.333333 $7,884.0 $45,458.85 Expected NPV Variance of NPV $18,700,66,996.65 Std. Dev. Of NPV $136,750.4 Coefficient of variation 3.01 <= Std. Dev / Expected NPV
Sensitivity Analysis Change in NPV for a given % error in input estimation Estimation Error Sales (units) Price Variable costs (unit) Direct labor (unit) Fixed Production Costs -30% -$59,386.06 -$167,0.65 $103,59.51 $70,996.80 $50,10.11-0% -$8,461.9 -$100,339.65 $80,190.46 $58,459.98 $44,530.19-10% $,46. -$33,476.64 $56,788.41 $45,93.17 $38,958.8 0 $33,386.36 $33,386.36 $33,386.36 $33,386.36 $33,386.36 10% $64,310.50 $100,49.36 $9,984.31 $0,849.55 $7,814.44 0% $95,34.64 $167,11.36 -$13,417.74 $8,31.73 $,4.53 30% $16,158.77 $33,975.37 -$36,819.79 -$4,4.08 $16,670.61 Change in NPV given $30,94.14 $66,863.00 -$3,40.05 -$1,536.8 -$5,571.9 a 10% change in the input from the base case scenario 1% error in the sales projection leads to a $3,09.41 change in NPV 1% error in the price projection leads to a $6,686.30 change in NPV 1% error in the variable cost projection leads to a $,340.1 change in NPV 1% error in the direct labor projection leads to a $1,53.68 change in NPV 1% error in the fixed production cost projection leads to a $557.19 change in NPV