Question

Home Security Systems is analyzing the purchase of manufacturing equipment that will cost \(50,000. The annual cash inflows for the next three years will be:

Year	Cash flow
1	\)25,000
2	23,000
3	18,000

a. Determine the internal rate of return.

b. With a cost of capital of 18 percent, should the machine be purchased?

Short answer

1. Internal rate of return is 16.23%.
2. The business entity must not purchase the machine.

Step-by-step solution

Definition Capital Budgeting

Capital budgeting is the method which include the discounting and non-discounting technique to determine whether to accept the any investment and project or not.

Internal rate of return

Calculation of PVIFA:

$\begin{array}{c}{\mathrm{PV}}_{\mathrm{IFA}}=\frac{\mathrm{Initial}\mathrm{investment}}{\mathrm{Average}\mathrm{cash}\mathrm{flow}}\\ =\frac{\mathrm{\$}50,000}{\mathrm{\$}22,000}\\ =2.273\end{array}$

For n=3, we will find 2.273 falls, around 15% or 16%.

Calculation of present value under each percent of estimated IRR:

15%:

Year	Cash flow	PVIF @ 15%	Present value
1	$25,000	0.869	$21,275
2	23,000	0.756	$17,388
3	18,000	0.665	$11,970
			$50,633

16%:

Year	Cash flow	PVIF @ 16%	Present value
1	$25,000	0.862	$21,550
2	23,000	0.743	$17,089
3	18,000	0.641	$11,538
			$50,177

Since NPV is still higher than the initial investment, we will try a higher rate:

Year	Cash flow	PVIF @ 17%	Present value
1	$25,000	0.855	$21,375
2	23,000	0.730	$16,790
3	18,000	0.624	$11,232
			$49,397

The net present value is below the initial investment; the IRR will be between 16% and 17%. Now, We will interpolate:

Particular	Amount $
Present value of 16%	$50,177
Less: Present value of 17%	(49,397)
	$780

Particular	Amount $
Present value of 16%	$50,177
Less: initial investment	(50,000)
	$177

Calculation of IRR:

$\begin{array}{c}\mathrm{IRR}=16\mathrm{\%}+\frac{\mathrm{\$}177}{\mathrm{\$}780}\\ =16\mathrm{\%}+0.23\mathrm{\%}\\ =16.23\mathrm{\%}\end{array}$

Investment Decision

The business entity must not purchase the machine because the internal rate of return is less than the cost of capital.