Problem 1 · Time value of money
A plant's energy cost is $15,000 at the end of year 1 and is expected to escalate 5% per year for a total of 10 years. At an interest rate of 8% per year, the present worth of the energy costs is most nearly:
- A.$100,651
- B.$122,753
- C.$127,953
- D.$188,668
Show the answer and solution
Answer: B: $122,753
For a geometric gradient with g ≠ i, P = A1[1 − ((1 + g)/(1 + i))^n]/(i − g) = 15,000[1 − (1.05/1.08)^10]/0.03 = 15,000(8.1835) = $122,753. Discounting at i − g is only an approximation and overstates the value here.
Time value of money · Reference Handbook: Engineering Economics
