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Calculating PW, IRR and Incremental IRR

The management of your company is considering adding a SO2 scrubber unit to your present plant to remove SO2 from stack gases, and you have conceived four designs to accomplish this task. Management does not believe that cleaning the gas just to reduce air pollution is worthwhile unless the government forces this. However, management would make the investment if more than a l0% annual rate of return on the investment can be earned (before taxes) by SO2 savings. Assume that your company can always invest the money and earn a l0% return (MARR = 10). The recommended system, if any, will have to "pay its own way." The life of each alternative is 10 years.

Following are the results of your research of the four designs. Which, if any, would you recommend to your management, and why?

Tot Install Annual OP Val of SO2 MKT Value At End
Cost Cost Recover Yearly of 10 Years
1 $100,000 $21,000 $41,000 $0
2 160,000 33,000 60,000 20,000
3 200,000 41,000 69,000 40,000
4 260,000 53,000 98,500 10,000

Need to calculate the PW at the MARR, IRR, and Incremental Analysis.

Solution Preview

Please refer attached file for better clarity of tables and formulas.

Solution:

Calculating Present Worth
Plant 1
Installation Cost=100000
Annual Op. Costs=21000
Value of SO2=41000
Net annual benefit=20000
Tenure=10
Market value =0
(at the end of 10th year)
PV Factor =6.1446
(ordinary annuity for period=10 and r=10%
PW =-initial cost+PV of net annual benefits for 10 years+PV of market value at the end of 10 years
PW=-100000+20000*6.1446+0/(1.1)^10
PW=22891.34211

Plant 2
Installation Cost=160000
Annual Op. Costs=33000
Value of SO2=60000
Net annual benefit=27000
Tenure=10
Market value =20000
(at the end of 10th year)
PV Factor =6.1446
(ordinary annuity for period=10 and r=10%
PW =-initial cost+PV of net annual benefits for 10 years+PV of market value at the end of 10 years
PW=-160000+27000*6.1446+20000/(1.1)^10
PW=13614.17764

Plant 3
Installation Cost=200000
Annual Op. Costs=41000
Value of SO2=69000
Net annual benefit=28000
Tenure=10
Market value =40000
(at the end of 10th year)
PV Factor =6.1446
(ordinary annuity for period=10 and r=10%
PW =-initial cost+PV of ...

Solution Summary

Solution describes the steps for calculating Present Worth of four different SO2 scrubber units. It calculates the IRR for all the four proposed units. Finally incremental IRRs are calculated to choose the best option available.

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