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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