Question

A plasma arc furnace is being considered for the incineration of medical wastes at a public hospital. The initial investment is $3,000,000 and annual revenues are expected to be $1,800,000 over the six-year life of the furnace. Annual expenses will be $1,000,000 at the end of year one and will increase by ($10,000 ) each year thereafter. The salvage value of the furnace after six years is $700,000. Assume MARR is 10%.What is the simple payback period of the furnace (in years), the discounted payback period of the furnace (in years), the PW of this furnace? Also,  Is it worth investing in this furnace? Why and What is the Internal Rate of Return (IRR) on this furnace? Try 10% and 20%, and then use the interpolation method to find the IRR. (50marks)

Answer 1

Initial Investment = $3000000
Life = 6 Years
MARR = 10%
Salvage Value = $700000

a) Simple Payback
We will create a cash flow table
Net annual cash flow for year 1
1800000 - (1000000 + (10000 * 0)) = 800000
Year 2,
1800000 - (1000000 + (10000 * 1)) = 790000

Year 6
1800000 - (1000000 + (10000 * 5)) + 700000 = 1450000

Year	Cash Flow	Cumulative
0	-3000000	-3000000
1	800000	-2200000
2	790000	-1410000
3	780000	-630000
4	770000	140000
5	760000	900000
6	1450000	2350000

Payback Period = 3 + (630000 / (630000 + 140000))
= 3 + 0.81 or 3.81 years

b) Discounted Payback.
In this method we will have take into account the discounted cash flow
PV = Cash Flow / (1+Discount Rate)Duration

Year 1 = -3000000
Year 2 = 800000 / 1.10 = 727272.72
Year 3 = 790000 / (1.10)2 = 652892.56

Year	Cash Flow	PV @ 10%	Cumulative
0	-3000000	-3000000	-3000000
1	800000	727272.73	-2272727.27
2	790000	652892.56	-1619834.71
3	780000	586025.54	-1033809.17
4	770000	525920.36	-507888.81
5	760000	471900.21	-35988.60
6	1450000	818487.20	782498.60

Discounted Payback Period = 5 + (35988.60 / (35988.60 + 782498.60))
= 5 + 0.044 or 5.044 Years

c) NPV is the sum of the discounted cash flow
NPV = $782498.60
The project has a positive NPV so the project should be accepted.

d) The IRR is the rate which equates the NPV of the cash flow to zero.
If we use 10% then the NPV is $782498.60

Next we have used 20% discount rate and the NPV is $-170969.44

It means the IRR lies in between 10% and 20%
Now we will use 18% now and NPV is -13449.95

Further trial gives the rate of 17.84% as the IRR.

Year	Cash Flow	PV @ 10%	PV @ 20%	PV @ 18%	PV @ 17.84%
0	-3000000	-3000000	-3000000	-3000000	-3000000
1	800000	727272.73	666666.67	677966.10	678886.63
2	790000	652892.56	548611.11	567365.70	568907.45
3	780000	586025.54	451388.89	474732.08	476668.44
4	770000	525920.36	371334.88	397157.43	399318.83
5	760000	471900.21	305426.95	332203.00	334464.42
6	1450000	818487.20	485602.07	537125.73	541516.38
NPV		782498.60	-170969.44	-13449.95	-237.85