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. 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	%

2. 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 Tango	Proposal Uniform
Present value of net cash flow total	$	$
Amount to be invested
Net present value	$	$

3. 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 Tango	Proposal Uniform
Present value index (rounded)

Answer 1

Proposal Sierra			Proposal Tango			Proposal Uniform			Proposal Victor
Year	income form operations		Year	income form operations		Year	income form operations		Year	income form operations
1	80000		1	320000		1	90000		1	44000
2	80000		2	320000		2	90000		2	44000
3	80000		3	160000		3	90000		3	44000
4	30000		4	60000		4	90000		4	4000
5	-70000		5	-40000		5	70000		5	4000
Average income from operation = (200000/5)	40000		Average income from operation = (200000/5)	164000		Average income from operation = (200000/5)	86000		Average income from operation = (200000/5)	28000
Initial Investment	850000		Initial Investment	1200000		Initial Investment	550000		Initial Investment	380000
Average rate of return = average income from operation/initial investment	4.71%		Average rate of return = average income from operation/initial investment	13.67%		Average rate of return = average income from operation/initial investment	15.64%		Average rate of return = average income from operation/initial investment	7.37%
Project Sierra and proposal Victor would be dropped as ARR is less than the required rate of 12%
Proposal Tango				Proposal Uniform
Year	net operating cash flow	present value of cash inflow		Year	net operating cash flow	present value of cash inflow
0	-1200000			0	-550000
1	560000	500000		1	200000	178571.4
2	540000	446428.57		2	200000	159438.8
3	400000	284712.1		3	200000	142356
4	300000	190655.42		4	200000	127103.6
5	220000	124833.91		5	180000	102136.8
sum of present value of cash inflow		1546630		sum of present value of cash inflow		709606.7
less cash outflow		1200000		less cash outflow		550000
NPV		346630		NPV		159606.7
PI	sum of present value of cash inflow/cash outflow	1.29		PI	sum of present value of cash inflow/cash outflow	1.29