Answer to Question #244927 in Civil and Environmental Engineering for Alan Enrico V Tuib

Question

The world’s largest carpet maker has just completed a feasibility study of what to do with the 16,000
tons of overruns, rejects, and remnants it produces every year. The company’s CEO launched the
feasibility study by asking, why pay someone to dig coal out of the ground and then pay someone else
to put our waste into a landfill? Why not just burn our own waste? The company is proposing to build a
$10-million power plant to burn its waste as fuel, thereby saving $2.8 million a year in coal purchases.
Company engineers have determined that the waste burning plant will be environmentally sound, and
after its four-year study period the plant can be sold to a local electric utility for $5 million.
a. What is the IRR of this proposed power plant?
b. If the firm’s MARR is 15% per year, should this project be undertaken?

Answer 1

Initial investment = 10,000,000

Annual Savings = 2,500,000

Study Period = 4 years

Salvage Value = 6,000,000

Calculating the IRR using the Trial and Error Method.

Let the MARR is 15%

Calculate the PW of the investment at MARR of 15%

$PW = -10,000,000 + 2,500,000 (P/A, 15 \%, 4) + 6,000,000 (P/F,15 \%, 4)\\ PW = -10,000,000 + 2,500,000 (2.8550) + 6,000,000 (0.5718) = 568,300$

The PW is positive. So, increase the rate of interest to get negative PW.

Increase the MARR to 16% and calculate the PW.

$PW = -10,000,000 + 2,500,000 (P/A, 16 \%, 4) + 6,000,000 (P/F,16 \%, 4)\\ PW = -10,000,000 + 2,500,000 (2.7982) + 6,000,000 (0.5523) = 309,300$

The PW is still positive. So, increase the rate of interest to get negative PW.

Increase the MARR to 18% and calculate the PW.

$PW = -10,000,000 + 2,500,000 (P/A, 18 \%, 4) + 6,000,000 (P/F,18 \%, 4)\\ PW = -10,000,000 + 2,500,000 (2.6901) + 6,000,000 (0.5158) = -179,950$

Now, use interpolation and calculate the IRR.

$IRR = 16 \% + [309,300 – 0 ÷ 309,300 – (-179,950)] * 2 \%\\ IRR = 17.26 \%$

The IRR is 17.26 (not using the % sing as the question is mentioning)