# 08_Oheads - Lecture Notes 8 Risk Analysis Real Options and...

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1 Lecture Notes 8 Risk Analysis, Real Options and Capital Budgeting Sensitivity analysis • Sensitivity uses a range of values for annual revenues, costs, etc. to examine how changes in underlying assumptions affect NPV. • Using a spreadsheet, a table of NPV values can be calculated where each variable is allowed to take on a range of values. • A wide range of NPV values for reasonable parameter values, with many large negative and many large positive values, should make you skeptical. • The NPV table can also indicate which assumptions have the biggest effect on NPV and where added effort in obtaining more accurate forecasts would be most useful. Sensitivity analysis example • Consider a project with expected cash flows as follows (\$M): i. Initial investment is \$1500, depreciated on a straight-line basis

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2 over 5 years, so depreciation = 300. Salvage value = 0. ii. Revenues in years 1–5 of \$6,000 derived from a market size of 10000 units, market share of 30% and price of \$2, variable costs of \$3,000 (\$1 per unit) and annual fixed costs of \$1,791. iii. Corporate tax rate of 34%, appropriate discount rate of 15%. • Annual taxable income = 6000–4791–300 = 909, so taxes = 309. • Annual cash flow is -1500, 900, 900, 900, 900, 900 yielding: (1) • Table 1 shows how sensitive the NPV is to separate 1% varia- tions in each of the forecasts underlying this analysis: Table 1: Sensitivity analysis a a.Calculations underlying this table were done in an Excel spreadsheet which is available on the web site. Variable NPV- change % NPV + change % Market Size \$1,450.37 -4.38% \$1,583.11 4.38% Market Share \$1,450.37 -4.38% \$1,583.11 4.38% Price \$1,383.99 -8.75% \$1,649.48 8.75% Variable Cost \$1,583.11 4.38% \$1,450.37 -4.38% Fixed Cost \$1,556.36 2.61% \$1,477.11 -2.61% Investment \$1,528.32 0.76% \$1,505.16 -0.76% Discount Rate \$1,527.48 0.71% \$1,506.06 -0.70% NPV 1500 900 1.15 t ----------- t 1 = 5 + 1516.94 = =
3 Break-even analysis • Break-even analysis is sensitivity to sales volume. It calculates the level of sales needed to make NPV = 0. • Distinguish fixed and variable costs, since variations in output will affect costs differently when more of them are variable. Let: i. EAC = equivalent annual cost of initial investment; ii. F = annual fixed cost; iii. V = variable cost per unit of output; iv. P = price of a unit of output; v. D = annual depreciation allowances (depreciation tax shield

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