Question

Capital Rationing Decision Involving Four Proposals

Kopecky Industries Inc. is considering allocating a limited amount of capital investment funds among four proposals. The amount of proposed investment, estimated income from operations, and net cash flow for each proposal are as follows:

	Investment				Year	Income from Operations				Net Cash Flows
Proposal Sierra:	$850,000				1	$ 80,000				$ 250,000
					2	80,000				250,000
					3	80,000				250,000
					4	30,000				200,000
					5	(70,000)				100,000
						$200,000				$ 1,050,000
Proposal Tango:	$1,200,000				1	$320,000				$ 560,000
					2	320,000				540,000
					3	160,000				400,000
					4	60,000				300,000
					5	(40,000)				220,000
						$820,000				$2,020,000
Proposal Uniform:	$550,000				1	$ 90,000				$ 200,000
					2	90,000				200,000
					3	90,000				200,000
					4	90,000				200,000
					5	70,000				180,000
						$430,000				$ 980,000
Proposal Victor:	$380,000				1	$44,000				$ 120,000
					2	44,000				120,000
					3	44,000				120,000
					4	4,000				80,000
					5	4,000				80,000
						$140,000				$ 520,000

The company's capital rationing policy requires a maximum cash payback period of three years. In addition, a minimum average rate of return of 12% is required on all projects. If the preceding standards are met, the net present value method and present value indexes are used to rank the remaining proposals.

Present Value of $1 at Compound Interest
Year	6%	10%	12%	15%	20%
1	0.943	0.909	0.893	0.870	0.833
2	0.890	0.826	0.797	0.756	0.694
3	0.840	0.751	0.712	0.658	0.579
4	0.792	0.683	0.636	0.572	0.482
5	0.747	0.621	0.567	0.497	0.402
6	0.705	0.564	0.507	0.432	0.335
7	0.665	0.513	0.452	0.376	0.279
8	0.627	0.467	0.404	0.327	0.233
9	0.592	0.424	0.361	0.284	0.194
10	0.558	0.386	0.322	0.247	0.162

Required:

1. Compute the cash payback period for each of the four proposals. Assume that net cash flows are uniform throughout the year.

	Cash Payback Period
Proposal Sierra	3 years 6 months
Proposal Tango	2 years 3 months
Proposal Uniform	2 years 9 months
Proposal Victor	3 years 8 months

2. Giving effect to straight-line depreciation on the investments and assuming no estimated residual value, compute the average rate of return for each of the four proposals. Round to one decimal place.

	Average Rate of Return
Proposal Sierra	%
Proposal Tango	%
Proposal Uniform	%
Proposal Victor	%

3. Using the results from parts (1) and (2) determine which proposals should be accepted for further analysis and which should be rejected.

	Accept / Reject
Proposal Sierra	Reject
Proposal Tango	Accept for further analysis
Proposal Uniform	Accept for further analysis
Proposal Victor	Reject

4. For the proposals accepted for further analysis in part (3), compute the net present value. Use a rate of 12% and the present value of $1 table above. If required, use the minus sign to indicate a negative net present value.

Select the proposal accepted for further analysis.	Proposal Sierra	Proposal Uniform
Present value of net cash flow total	$	$
Amount to be invested
Net present value	$	$

5. Compute the present value index for each of the proposals in part (4). Round to two decimal places.

Select the proposal to compute present value index.	Proposal Sierra	Proposal Uniform
Present value index (rounded)

Answer 1

2
Average Rate of Return
Proposal Sierra	4.7%
Proposal Tango	13.7%
Proposal Uniform	15.6%
Proposal Victor	7.4%

Year	Proposal Sierra		Proposal Tango		Proposal Uniform		Proposal Victor
	Operations	Flows	Operations	Flows	Operations	Flows	Operations	Flows
1	80,000	250,000	320,000	560,000	90,000	200,000	44,000	120,000
2	80,000	250,000	320,000	540,000	90,000	200,000	44,000	120,000
3	80,000	250,000	160,000	400,000	90,000	200,000	44,000	120,000
4	30,000	200,000	60,000	300,000	90,000	200,000	4,000	80,000
5	(70,000)	100,000	(40,000)	220,000	70,000	180,000	4,000	80,000
Total	200,000	1,050,000	820,000	2,020,000	430,000	980,000	140,000	520,000
Average Profit per Year	40,000		164,000		86,000		28,000
Investment	850,000		1,200,000		550,000		380,000
Average Rate of Return	4.7%		13.7%		15.6%		7.4%

Average rate of Return = Average Profit/Investment

4 Proposal Tango Proposal Uniform Present value of net cash flow total                                                                                               1,530,800                     709,660 Amount to be invested                                                                                               1,200,000                     550,000 Net present value                                                                                                  330,800                     159,660

Proposal Tango Proposal Uniform Year PV Factor Flows Present Value Flows Present Value 1 0.893       560,000        500,080.00    200,000              178,600 2 0.797       540,000        430,380.00    200,000              159,400 3 0.712       400,000        284,800.00    200,000              142,400 4 0.636       300,000        190,800.00    200,000              127,200 5 0.567       220,000        124,740.00    180,000              102,060           1,530,800              709,660

5
	Proposal Tango	Proposal Uniform
Present Value Index	1.28	1.29

Present Value Index

Present value of net cash flow total/Amount invested

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