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Unformatted text preview: 1 Homework 9 Evaluation with Risk P1 We are to invest $20,000 on a money making project for 10 years. The project has an annual income, but no salvage. The annual income from the investment is not known with certainty. An experienced manager predicts that the annual income has a normal distribution with mean value of $4000 and a standard deviation of $1000. The minimum acceptable rate of return is 15%. a. What is the breakeven value for the net income? Breakeven = 3985 b. Write formulas involving the equivalency factors and the mean and variance of the annual income that compute the mean NPW and variance of the NPW . Evaluate the formulas. Mean(NPW) = -20000 + Mean(Income)(P/A, 0.15, 10) Value for the Mean of the NPW. Mean(NPW) = -20000 +4000(5.0187)= 74.8 or 75.07 more accurately Formula for the Variance of the NPW. Var(NPW) = Var(Income)(P/A, 0.15, 10) 2 =[ (1000)(5.0187)] 2 Var(NPW) = (1000 2 )*(5.0187 2 )= 25187349 Std(NPW) = Sqrt(Var)= 5019 c. From the results of b, find the probability that the investment has a return greater than the MARR . 0.506 P2 We are to invest $20,000 on a money making project for 10 years. The project has an annual income, but no salvage. The annual income from the investment is not known with certainty. The minimum acceptable rate of return is 15%. a. An experienced manager predicts that the least annual income that one will expect is $3,000, the most one could expect is $7,000, but the most likely value is $4,000. Say that these estimates represent the lower bound, upper bound and most likely values for a triangular distribution. Use the Economics add-in to find the mean and standard deviation of the NPW . Value for the Mean of the NPW = 3421 Value for the Standard Deviation of the NPW = 4265 b. Say the manager is confident that the annual income will be at the 60th percentile of its distribution. What is the NPW with this point estimate of the annual income? Value for the Estimate of the NPW = 4136 c. Simulate 1000 observations of this situation with the Economics add-in . From the simulation determine the probability that the investment will return the MARR . 2 P(NPW > 0) =RV_prob(P_2_,0) = 0.7610 The model for this problem is presented below in two parts. The model uses Quartile point estimates. Project Definition Periods Rates (%) Name P_2 Life (yrs) 10MARR(/yr) 15.% Repetitions 1 Study Period 10 Cash Flow Data - Amounts Negative for Expenditures and Positive for Revenues Index escriptio Dist. Min. ost Likel Max. Mean Var. Perc. Quantile 1 Invest Tri (20000) (20000) (20000) (20000) 60.% (20000) 2 Return Tri 3000 4000 7000 4667 722222 60.% 4809 Worth($) Mean Variance Std. Dev. Point Est....
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- Spring '10