Compute the Discount Factors You Would Need to Conduct a Benefit-Cost

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The Answer is The discount factors are computed using the following relationship between the discount factor and the discount rate where t represents time:

f = \frac { 1 } { ( 1 + r ) ^ { t } }

\begin{array} { | c | l | } \hline ext { Year } & ext { f value } \\hline ext { Year 0 } & 1 \\hline ext { Year 1 } & 0.95 \\hline ext { Year 2 } & 0.91 \\hline ext { Year 3 } & 0.86 \\hline ext { Year 4 } & 0.82 \\hline ext { Year 5 } & 0.78 \\hline\end{array}

Using the discount factors and the probabilities of each population growth scenario,we calculate the expected net present value (ENPV)of each of the three options as follows:
ENPV_E = .75[-100 + .95(0)+ .91(30)+ .86(50)+ .82(60)+ .78(60)] + .25[-150 + .95(-15)+ .91(40)+ .86(45)+ .82(50)+ .78(50)] = 80
NPV_T = .75[-50 + .95(25)+ .91(35)+ .86(35)+ .82(35)+ .78(35)] + .25[-100 + .95(-10)+ .91(30)+ .86(30)+ .82(30)+ .78(30)] = 88.75
NPV_S = .75[-15 + .95(5)+ .91(10)+ .86(10)+ .82(10)+ .78(10)] + .25[-30 + .95(10)+ .91(15)+ .86(15)+ .82(15)+ .78(15)] = 32.5
The municipality should choose the Tertiary option since it generates the highest expected net present value of the three choices.

Compute the Discount Factors You Would Need to Conduct a Benefit-Cost

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