Question

You are a Financial Analyst with ABC Ltd and the chief financial officer (CFO) requests you to evaluate two new capital budgeting proposals. Specifically, you are asked to provide a recommendation and also respond to a number of questions aimed at assessing your level of competence in capital budgeting process.

Instructions are as follows:

Provide an evaluation of two proposed projects, both with identical initial outlays of $400,000. Both of these projects involve additions to a client’s highly successful product line. The required rate of return on both projects is set at 11%. The expected after-tax cash flows from each project are as presented in the table below.

	PROJECT X	PROJECT Y
Initial outlay	-$400,000	-$400,000
Inflow year 1	$80,000	$160,000
Inflow year 2	$140,000	$160,000
Inflow year 3	$130,000	$160,000
Inflow year 4	$160,000	$160,000
Inflow year 5		$160,000
Inflow year 6		$160,000

Distinguish between “required rate of return” and “internal rate of return”. Illustrate your answer with examples.

What is the payback period on each project? If ABC Ltd imposes a 2.5-year maximum acceptable payback period, which of these projects should be accepted?

What are the main limitations of the pay back method of valuation. Despite these limitations, chief financial officers (CFOs) use it. Explain why.

Determine the NPV for each of these projects? Should the projects be accepted? Explain.

Determine the IRR for each of these projects? Should the projects be accepted? Explain.

Under what circumstances will the NPV and IRR offer different recommendations, and which recommendation is preferred? Carefully explain

How would you accommodate unequal lives of the project while determining the NPVs of the project? Demonstrate using calculations.

Explain why unequal lives of projects make NPVs of the projects incomparable.

Determine the profitability index for each of these projects? Should the projects be accepted? Explain.

Clarity of Presentation.

Answer 1

Required rate of return is also known as the hurdle rate and is the minimum rate that a project should earn in order to make it viable. On the other hand IRR (internal rate of return) is that rate that makes the NPV (net present value) as nil. The rule is that if IRR>required rate of return then the project is viable. For example take the case of a project which has a required rate of return of 10% and whose IRR is 9%. As IRR is less than the hurdle rate the project is not financially feasible.

Payback:

Project X				Project Y
Year	Cash flow	Cumulative cash flow		Year	Cash flow	Cumulative cash flow
0	- 400,000.00	-                         400,000.00		0	- 400,000.00	-                         400,000.00
1	80,000.00	-                         320,000.00		1	160,000.00	-                         240,000.00
2	140,000.00	-                         180,000.00		2	160,000.00	-                           80,000.00
3	130,000.00	-                           50,000.00		3	160,000.00	80,000.00
4	160,000.00	110,000.00		4	160,000.00
5				5	160,000.00
6				6	160,000.00

Thus payback of X = 3+(50000/160000) = 3.31 years

Payback of Y = 2+(80000/160000) = 2.5 years. Thus project Y will be selected.

The main limitation of payback is that fails to consider the time value of money. Secondly cash flows beyond the payback period are not considered at all. Despite these limitations CFO use this method because the method is simple both in concept as well as in application.

NPV:

Project X				Project Y
Year	Cash flow	1+r	PVIF	PV of X = cash flow of X * PVIF	Cash flow	PV of Y = cash flow of Y * PVIF
0	- 400,000.00	1.11	1.0000	-      400,000.00	- 400,000.00	-                         400,000.00
1	80,000.00		0.9009	72,072.07	160,000.00	144,144.14
2	140,000.00		0.8116	113,627.14	160,000.00	129,859.59
3	130,000.00		0.7312	95,054.88	160,000.00	116,990.62
4	160,000.00		0.6587	105,396.96	160,000.00	105,396.96
5			0.5935		160,000.00	94,952.21
6			0.5346		160,000.00	85,542.53
			NPV	-         13,848.95		276,886.06

NPV of X = -$13,848.95 and NPV of Y = $276,888.06

Y will be selected as it has a positive NPV.

IRR of X:

Year	Cash flow	1+r	PVIF	PV of X = cash flow of X * PVIF
0	- 400,000.00	1.0951	1.0000	-      400,000.00
1	80,000.00		0.9131	73,050.46
2	140,000.00		0.8338	116,733.08
3	130,000.00		0.7614	98,978.81
4	160,000.00		0.6952	111,237.65
5			0.6348
6			0.5797
			NPV	0.00

IRR of X = 9.51%

Y's IRR:

Year	1+r	PVIF	Cash flow	PV of Y = cash flow of Y * PVIF
0	1.32662	1.0000	- 400,000.00	-                         400,000.00
1		0.7538	160,000.00	120,607.33
2		0.5682	160,000.00	90,913.30
3		0.4283	160,000.00	68,530.06
4		0.3229	160,000.00	51,657.67
5		0.2434	160,000.00	38,939.34
6		0.1835	160,000.00	29,352.31
		NPV		0.00

IRR of Y = 32.66%

Y will be selected as it has a higher IRR.

The circumstances in which NPV and IRR can give different results is when there is different cash flow patterns in the two projects. One of the projects might be having conventional cash flows while the other project might be having unconventional cash flows. In such scenarios NPV and IRR will give conflicting results and the recommendation that will be preferred will be NPV method because NPV gives a single NPV value irrespective of the pattern of cash flow while the IRR method can lead to multiple rates of return.

For projects with unequal lives the NPV method is modified to compute the annual net present value. This is also known as the equivalent annual annuity. Annual net present value = net present value/annuity discount factor for the project life. For instance NPV of X = -13,848.95 and that of Y = 276,886.06. Now annuity discount factor for X = PVIFA(11%,4) = 3.102 and for Y = PVIFA(11%,6) = 4.231. Thus annual net present value of X = -13848.95/3.102 = -$4,464.52 and of Y = 276886.06/4.231 = 65442.23

Unequal lives make NPVs incomparable because the duration of cash flow is different for the two projects and hence one project gets cash inflow for a longer duration when compared to another project which has a lower life. This makes NPV not comparable.

Profitability index = present value of future cash flows/investment

X = 386,151.05/400,000 = 0.97

Y = 676,886.06/400,000 = 1.69

As profitability index of Y > 1 Y will be selected.