Question

You are considering building waste treatment plan. The project lasts 40 years and occurs construction costs of $100 (all numbers are in millions of $). Annual operation cost is $8, and annual operation benefit is $15. Assume constant interest rest of 4.5%

a) Using annuity formula compute annuity factor, PV of benefits, PV of costs, NPV of the project.

b) (Sensitivity analysis) What is the minimum annual benefit needed to keep the project desirable? (NPV>0)

Answer 1

(a) r = 4.5% = 0.045, N = 40

Annuity factor: P/A(r%, N) = [1 - (1 + r)^-N] / = [1 - (1.045)^-40] / 0.045 = (1 - 0.1719) / 0.045 = 0.8281 / 0.045

= 18.4016

PV of benefits ($ Million) = 15 x P/A(4.5%, N) = 15 x 18.4016 = 276.02

PV of costs ($ Million) = 100 + [8 x P/A(4.5%, N)] = 100 + (8 x 18.4016) = 100 + 147.21 = 247.21

NPV ($ Million) = PV of benefits - PV of costs = 276.02 - 247.21 = 28.81

(b) If minimum annual benefit be $B Million, then

PV of benefits ($ Million) = PV of costs ($ Million)

B x 18.4016 = $247.21 Million

B = $247.21 Million / 18.4016 = $13.4342 Million