Cost Reduction Proposal: IRR, NPV, and Payback Period JB Chemical currently disc
ID: 2570242 • Letter: C
Question
Cost Reduction Proposal:
IRR, NPV, and Payback Period
JB Chemical currently discharges liquid waste into Calgary's municipal sewer system. However, the Calgary municipal government has informed JB that a surcharge of $4 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 200,000 liters of liquid waste would be processed in a normal workday. The company operates 300 days per year. The initial investment in the system would be $450,000, and annual operating costs are predicted to be $150,000. The system has a predicted useful life of eight years and a salvage value of $50,000.
(a) Determine the project's net present value at a discount rate of 12 percent. (Round to the nearest whole number.)
$ Answer
(b) Determine the project's approximate internal rate of return. (Round answer to the nearest whole percentage.)
Answer %
(c) Determine the project's payback period.
Answer in years
Explanation / Answer
a)
Year
Cash Flow(C)
PV Factor(F) '@ 12 %
PV(=C x F)
0
$ (450,000)
1/(1+0.12)^0
1
$ (450,000.00)
1
$ 90,000
1/(1+0.12)^1
0.89285714
$ 80,357.14
2
$ 90,000
1/(1+0.12)^2
0.79719388
$ 71,747.45
3
$ 90,000
1/(1+0.12)^3
0.71178025
$ 64,060.22
4
$ 90,000
1/(1+0.12)^4
0.63551808
$ 57,196.63
5
$ 90,000
1/(1+0.12)^5
0.56742686
$ 51,068.42
6
$ 90,000
1/(1+0.12)^6
0.50663112
$ 45,596.80
7
$ 90,000
1/(1+0.12)^7
0.45234922
$ 40,711.43
8
$ 140,000
1/(1+0.12)^8
0.40388323
$ 56,543.65
NPV
$ 17,281.74
Cash flow from year 1st to 7th = ($ 4 x 200 x 300) - $ 150,000 = $ 240,000 - $ 150,000 = $ 90,000
Cash flow from year 8th = $ 90,000 + $ 50,000 = $ 140,000
NPV is $ 17,282
b)
Let’s calculate IRR by trial and error method.
Let’s calculate NPV at 13 %.
Year
Cash Flow('C)
PV Factor(F) '@ 13 %
PV(=C x F)
0
$ (450,000)
1/(1+0.13)^0
1
$ (450,000.00)
1
$ 90,000
1/(1+0.13)^1
0.88495575
$ 79,646.02
2
$ 90,000
1/(1+0.13)^2
0.78314668
$ 70,483.20
3
$ 90,000
1/(1+0.13)^3
0.69305016
$ 62,374.51
4
$ 90,000
1/(1+0.13)^4
0.61331873
$ 55,198.69
5
$ 90,000
1/(1+0.13)^5
0.54275994
$ 48,848.39
6
$ 90,000
1/(1+0.13)^6
0.48031853
$ 43,228.67
7
$ 90,000
1/(1+0.13)^7
0.42506064
$ 38,255.46
8
$ 140,000
1/(1+0.13)^8
0.37615986
$ 52,662.38
NPV
$ 697.32
As NPV is + ve, let’s calculate NPV at 14 %.
Year
Cash Flow('C)
PV Factor(F) '@ 14 %
PV(=C x F)
0
$ (450,000)
1/(1+0.13)^0
1
$ (450,000.00)
1
$ 90,000
1/(1+0.13)^1
0.87719298
$ 78,947.37
2
$ 90,000
1/(1+0.13)^2
0.76946753
$ 69,252.08
3
$ 90,000
1/(1+0.13)^3
0.67497152
$ 60,747.44
4
$ 90,000
1/(1+0.13)^4
0.59208028
$ 53,287.22
5
$ 90,000
1/(1+0.13)^5
0.51936866
$ 46,743.18
6
$ 90,000
1/(1+0.13)^6
0.45558655
$ 41,002.79
7
$ 90,000
1/(1+0.13)^7
0.39963732
$ 35,967.36
8
$ 140,000
1/(1+0.13)^8
0.35055905
$ 49,078.27
NPV
$ (14,974.30)
IRR = R1 + [NPV1 x (R2-R1)%/(NPV1-NPV2)]
= 13 % + $ 697.32 x (14 -13) % /($ 697.32 -(- $ 14,974.30)
= 13 % + $ 697.32 x 1 % / $ 697.32 + $ 14,974.30
= 13 % + $ 6.97/$ 15,671.62
= 13 % + 0.00044496
= 13 % + 0.044496
= 13.044 % or 13 %
IRR is 13 %
c)
Year
Cash Flow('C)
Cumulative cash flow
0
$ (450,000)
$ (450,000)
1
$ 90,000
$ (360,000)
2
$ 90,000
$ (270,000)
3
$ 90,000
$ (180,000)
4
$ 90,000
$ (90,000)
5
$ 90,000
$ 0
6
$ 90,000
$ 90,000
7
$ 90,000
$ 180,000
8
$ 140,000
$ 320,000
Payback period = A + B/C
Where,
A = last period with a negative cumulative cash flow = 4 years
B = absolute value of cumulative cash flow at the end of the period A = $ 90,000
C = total cash flow during the period after A = $ 90,000
Payback period = 4 + $ 90,000/$ 90,000 = 4 + 1 = 5 years.
Year
Cash Flow(C)
PV Factor(F) '@ 12 %
PV(=C x F)
0
$ (450,000)
1/(1+0.12)^0
1
$ (450,000.00)
1
$ 90,000
1/(1+0.12)^1
0.89285714
$ 80,357.14
2
$ 90,000
1/(1+0.12)^2
0.79719388
$ 71,747.45
3
$ 90,000
1/(1+0.12)^3
0.71178025
$ 64,060.22
4
$ 90,000
1/(1+0.12)^4
0.63551808
$ 57,196.63
5
$ 90,000
1/(1+0.12)^5
0.56742686
$ 51,068.42
6
$ 90,000
1/(1+0.12)^6
0.50663112
$ 45,596.80
7
$ 90,000
1/(1+0.12)^7
0.45234922
$ 40,711.43
8
$ 140,000
1/(1+0.12)^8
0.40388323
$ 56,543.65
NPV
$ 17,281.74