Question

(Ignore income taxes in this problem.) An investment project has the following characteristics:

Cost of equipment	$22,820
Annual cash inflows	$ 5,000
Internal rate of return	12%

The life of the equipment is closest to:

a. It is impossible to determine from the data given

b. 7 years

c. 12 years

d. 4.56 years

Answer 1

At irr,present value of inflows=present value of outflows.

Hence present value of annual cash flows=22820

Present value of annuity=Annuity[1-(1+interest rate)^-time period]/rate

22820=5000[1-(1.12)^-time period]/0.12

22820=41666.6667[1-(1.12)^-time period]

(22820/41666.6667)=[1-(1.12)^-time period]

[1-(1.12)^-time period]=0.54768

(1.12)^-time period=1-0.54768

(1/1.12)^time period=0.45232

Taking log on both sides;

time period*log (1/1.12)=log 0.45232

time period=log 0.45232/log (1/1.12)

=7 years(Approx).