Question

A project has an initial investment at time zero of 30. It generates cash ows in perpetuity of 3 a year.
1- What is the payback period of this project?
2- What is the NPV if the discount rate is equal to theAccounting Rate of Return?

Answer 1

1)

Payback period of the project = Payback year + [ Initial investment - cumulative cash flow in payback year ] $\div$ Cash flow in next year

Payback period of the project = 10 + [ $ 30 - $ 30 ] $\div$ 3

Payback period of the project = 10 years

Year	Cash flows	Cumulative cash flows
1	$3	$3
2	$3	$6
3	$3	$9
4	$3	$12
5	$3	$15
6	$3	$18
7	$3	$21
8	$3	$24
9	$3	$27
10	$3	$30
11	$3	$33

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2)

Accounting rate of return = Average annual cash flows  $\div$ Initial investment

Accounting rate of return = $ 3 $\div$ $ 30

Accounting rate of return = 10%

NPV of the project = - Initial investment + Present value of the perpetual cash flows

NPV of the project = - $ 30 + $ 3 $\div$ 0.10

NPV of the project = $ 0