Cost Reduction Proposal: IRR, NPV, and Payback Period PA Chemical currently disc
ID: 2576639 • Letter: C
Question
Cost Reduction Proposal: IRR, NPV, and Payback Period
PA Chemical currently discharges liquid waste into Pittsburgh’s municipal sewer system. However,
the Pittsburgh municipal government has informed PA that a surcharge of $5 per thousand cubic liters
will soon be imposed for the discharge of this waste. This has prompted management to evaluate the
desirability of treating its own liquid waste.
A proposed system consists of three elements. The first is a retention basin, which would permit
unusual discharges to be held and treated before entering the downstream system. The second is a
continuous self-cleaning rotary filter required where solids are removed. The third is an automated
neutralization process required where materials are added to control the alkalinity-acidity range.
The system is designed to process 600,000 liters a day. However, management anticipates that
only about 250,000 liters of liquid waste would be processed in a normal workday. The company oper-
ates 300 days per year. The initial investment in the system would be $900,000, and annual operating
costs are predicted to be $162,000. The system has a predicted useful life of ten years and a salvage
value of $70,000.
Required
a. Determine the project’s net present value at a discount rate of 16 percent.
b. Determine the project’s approximate internal rate of return. (Refer to Appendix 12B if you use the
table approach.)
c. Determine the project’s payback period.
Explanation / Answer
(1) Net Present Value 250000*5/1000*300 1/(1+.16)^n Year Initial Outflow Operating Cost Saving Net Cash Flow Discount rate PV 0 (9,00,000) (9,00,000) 1 (9,00,000) 1 (1,62,000) 3,75,000 2,13,000 0.862069 1,83,621 2 (1,62,000) 3,75,000 2,13,000 0.743163 1,58,294 3 (1,62,000) 3,75,000 2,13,000 0.640658 1,36,460 4 (1,62,000) 3,75,000 2,13,000 0.552291 1,17,638 5 (1,62,000) 3,75,000 2,13,000 0.476113 1,01,412 6 (1,62,000) 3,75,000 2,13,000 0.410442 87,424 7 (1,62,000) 3,75,000 2,13,000 0.353830 75,366 8 (1,62,000) 3,75,000 2,13,000 0.305025 64,970 9 (1,62,000) 3,75,000 2,13,000 0.262953 56,009 10 70,000 (1,62,000) 3,75,000 2,83,000 0.226684 64,151 Net Present value 1,45,345 Assumed no Taxation as no tax rate is given (2)IRR 20% 21% 250000*5/1000*300 1/(1+.20)^n 1/(1+.21)^n Year Initial Outflow Operating Cost Saving Net Cash Flow Discount rate Discount rate PV=20% PV=21% 0 (9,00,000) (9,00,000) 1 1 (9,00,000) (9,00,000) 1 (1,62,000) 3,75,000 2,13,000 0.833333 0.826446 1,77,500 1,76,033 2 (1,62,000) 3,75,000 2,13,000 0.694444 0.683013 1,47,917 1,45,482 3 (1,62,000) 3,75,000 2,13,000 0.578704 0.564474 1,23,264 1,20,233 4 (1,62,000) 3,75,000 2,13,000 0.482253 0.466507 1,02,720 99,366 5 (1,62,000) 3,75,000 2,13,000 0.401878 0.385543 85,600 82,121 6 (1,62,000) 3,75,000 2,13,000 0.334898 0.318631 71,333 67,868 7 (1,62,000) 3,75,000 2,13,000 0.279082 0.263331 59,444 56,090 8 (1,62,000) 3,75,000 2,13,000 0.232568 0.217629 49,537 46,355 9 (1,62,000) 3,75,000 2,13,000 0.193807 0.179859 41,281 38,310 10 70,000 (1,62,000) 3,75,000 2,83,000 0.161506 0.148644 45,706 42,066 Net Present value 4,302 (26,076) Assumed no Taxation as no tax rate is given IRR=20+4302/(4302+26076)*(21-20) 20.14% (c ) Payback Period Annual cash Inflow 2,13,000 Initial Outflow 9,00,000 Payback period=900000/213000 4.23 Years