You are a city Planner who is considering buying an automated trash truck with a
ID: 2720002 • Letter: Y
Question
You are a city Planner who is considering buying an automated trash truck with a robotic arm to pick up the cans. The initial investment will be $4,500,000 immediately. The checks will allow you to immediately released 30 workers that would've been paid $900,000 at the end of this year and every year after that for the eight years you will have the truck. The cities discount rate is 7%. Ignore all the taxes and working capital.
A) using the NPV decision rule, calculate NPV and state whether u accept or reject.
B) using payback rule. Do u accept or reject if u require full payback by end of year 3?
C) what is the irr? Set up the basic equation
Explanation / Answer
(‘1) NPV = Present Value of Cash Inflow – Cash Outflow
In the given question saving due to release of worker will be considered as inflow.
Life of Truck = 8 years
Discount rate = 7 %
Present value of annuity factor for 8 year at 7 % = 5.971
Hence present value of cash inflow = PVF x Inflow per annum
NPV = (900,000 x 5.971 )- 4500,000
NPV = $873,900
Considering positive NPV the project should be accepted.
(‘2) Payback Period
Year
Inflow
Cumulative Inflow
PVF
Discounted Cash Inflow
Cumulative discounted cash inflow
1
900,000
900,000
0.935
841,500
841,500
2
900,000
1800,000
0.873
785,700
1627,200
3
900,000
2700,000
0.816
734,400
2361,600
4
900,000
3600,000
0.763
686,700
3048,300
5
900,000
4500,000
0.713
641,700
3690,000
6
900,000
5400,000
0.666
599,400
4289,400
7
900,000
6300,000
0.623
560,700
4850,100
8
900,000
7200,000
0.582
523,800
5373,900
Simple Payback Period = Investment/ Annual Cash Inflow
Simple payback = 4500,000/900,000
Payback period = 5 years
As desired payback is 3 year while payback of project is 5 years hence project should be rejected.
(‘3) IRR-
IRR is the rate of return at which NPV of project becomes zero.
IRR is calculated by using trial and error method.
PVF for 12 % = 4.968
PVF for 11 % = 5.146
NPV (11 %) = 131,400
NPV (12 %) = -28,800
As NPV moves from positive to negative, when rate moves from 11 % to 12 %
Hence IRR will be somewhere between 11 and 12 %.
When Movement of rate by 1 % , NPV decrease by 160,200
Hence to decrease NPV by 131,400 only increase in rate = 131,400 x 1 /160,200
Increase in rate = 0.82
Hence IRR = Start rate + Increase in rate
IRR = 11.82 %
Year
Inflow
Cumulative Inflow
PVF
Discounted Cash Inflow
Cumulative discounted cash inflow
1
900,000
900,000
0.935
841,500
841,500
2
900,000
1800,000
0.873
785,700
1627,200
3
900,000
2700,000
0.816
734,400
2361,600
4
900,000
3600,000
0.763
686,700
3048,300
5
900,000
4500,000
0.713
641,700
3690,000
6
900,000
5400,000
0.666
599,400
4289,400
7
900,000
6300,000
0.623
560,700
4850,100
8
900,000
7200,000
0.582
523,800
5373,900
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