Question

Capital Rationing Decision for a Service Company Involving Four Proposals

Renaissance Capital Group 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 Flow
Proposal A:	$680,000	1		$ 64,000		$ 200,000
		2		64,000		200,000
		3		64,000		200,000
		4		24,000		160,000
		5		24,000		160,000
				$240,000		$ 920,000
Proposal B:	$320,000	1		$ 26,000		$ 90,000
		2		26,000		90,000
		3		6,000		70,000
		4		6,000		70,000
		5		(44,000)		20,000
				$ 20,000		$340,000
Proposal C:	$108,000	1		$ 33,400		$ 55,000
		2		31,400		53,000
		3		28,400		50,000
		4		25,400		47,000
		5		23,400		45,000
				$142,000		$ 250,000
Proposal D:	$400,000	1		$100,000		$ 180,000
		2		100,000		180,000
		3		80,000		160,000
		4		20,000		100,000
		5		0		80,000
				$300,000		$700,000

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.

	Cash Payback Period
Proposal A
Proposal B
Proposal C
Proposal D

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. If required, round your answers to one decimal place.

	Average Rate of Return
Proposal A	%
Proposal B	%
Proposal C	%
Proposal D	%

3. Using the following format, summarize the results of your computations in parts (1) and (2) by placing the calculated amounts in the first two columns on the left and indicate which proposals should be accepted for further analysis and which should be rejected. If required, round your answers to one decimal place.

Proposal	Cash Payback Period	Average Rate of Return		Accept or Reject
A		%
B		%
C		%
D		%

4. For the proposals accepted for further analysis in part (3), compute the net present value. Use a rate of 15% and the present value of $1 table above. Round to the nearest dollar.

Select the proposal accepted for further analysis.
Present value of net cash flow total	$	$
Less amount to be invested	$	$
Net present value	$	$

5. Compute the present value index for each of the proposals in part (4). If required, round your answers to two decimal places.

Select proposal to compute Present value index.
Present value index (rounded)

6. Rank the proposals from most attractive to least attractive, based on the present values of net cash flows computed in part (4).

Rank 1st
Rank 2nd

7. Rank the proposals from most attractive to least attractive, based on the present value indexes computed in part (5).

Rank 1st
Rank 2nd

8. The present value indexes indicate that although Proposal   has the larger net present value, it is not as attractive as Proposal   in terms of the amount of present value per dollar invested. Proposal   requires the larger investment. Thus, management should use investment resources for Proposal   before investing in Proposal  , absent any other qualitative considerations that may impact the decision.

Answer 1

Answer to Question No.1
Cash Pay Back Period - Non Discounted
Proposal A
	Year	CFAT	Unrecovered Cash Flow
	0	-680000	-680000
	1	200000	-480000
	2	200000	-280000
Base Year	3	200000	-80000
	4	160000	80000
	5	160000
Formula
Base Year +	(Unrecovered Cash Flow of the base year/Cash Flow of the next Year) *12
Pay back period:
3 Years	6.00	Months
Proposal B
	Year	CFAT	Unrecovered Cash Flow
	0	-320000	-320000
	1	90000	-230000
	2	90000	-140000
Base Year	3	70000	-70000
	4	70000	0
	5	20000
Pay back period:
3 Years	12.00	Months
i.e. 4 Years
Proposal C
	Year	CFAT	Unrecovered Cash Flow
	0	-108000	-108000
Base Year	1	55000	-53000
	2	53000	0
	3	50000	50000
	4	47000	97000
	5	45000
Pay back period:
1 Years	12.00	Months
i.e 2 Years
Proposal D
	Year	CFAT	Unrecovered Cash Flow
	0	-400000	-400000
	1	180000	-220000
Base Year	2	180000	-40000
	3	160000	120000
	4	100000	220000
	5	80000
Pay back period:
2 Years	3.00	Months
Summary
Proposal	Pay Back Period
Proposal A	3 years 6 Months
Proposal B	4 Years
Proposal C	2 Years
Proposal D	2 Years 3 Months
Answer to Question No.2
Average Rate of Return
Proposal A
Year	CFAT	Depreciation(SLM)	Profit after Tax (PAT)
0	-680000
1	200000	-136000	336000
2	200000	-136000	336000
3	200000	-136000	336000
4	160000	-136000	296000
5	160000	-136000	296000
			1600000
		Average Profits	320000
	ARR=	Average PAT/Initial/Average Investment
		Based on Initial Investment
		47%
		47.05882353
		Based on Average Investment
		24%
		23.52941176
		Average Investment = Simple average of Begining Value of Investment and Ending Value of the invetment
Proposal B
Year	CFAT	Depreciation(SLM)	Profit after Tax (PAT)
0	-320000
1	90000	-64000	154000
2	90000	-64000	154000
3	70000	-64000	134000
4	70000	-64000	134000
5	20000	-64000	84000
			660000
			132000
		Based on Initial Investment
		41%
		41.25
		Based on Average Investment
		21%
		20.625
Proposal C
Year	CFAT	Depreciation(SLM)	Profit after Tax (PAT)
0	-108000
1	55000	-64000	119000
2	53000	-64000	117000
3	50000	-64000	114000
4	47000	-64000	111000
5	45000	-64000	109000
			570000
			114000
		Based on Initial Investment
		106%
		105.5555556
		Based on Average Investment
		53%
		52.77777778
Proposal D
Year	CFAT	Depreciation(SLM)	Profit after Tax (PAT)
0	-400000
1	180000	-64000	244000
2	180000	-64000	244000
3	160000	-64000	224000
4	100000	-64000	164000
5	80000	-64000	144000
			1020000
			204000
		Based on Initial Investment
		51%
		51
		Based on Average Investment
		26%
		25.5
Summary
Proposal	ARR (Initial Investment)	ARR (Average Investment)
Proposal A	47	24
Proposal B	41	21
Proposal C	106	53
Proposal D	51	26
Answer to Question No.3
Proposal	Pay Back Period	ARR (Initial Investment)	Accept/Reject
Proposal A	3 years 6 Months	47	Reject
Proposal B	4 Years	41	Reject
Proposal C	2 Years	106	Accept
Proposal D	2 Years 3 Months	51	Accept
Answer to Question No.4
Net present value Analysis (NPV)
Proposal C			15.00%
		PV Factor
Year	CFAT	D.F 15%	DCFAT
0	-108000	1	-108000
1	55000	0.87	47850
2	53000	0.756	40068
3	50000	0.658	32900
4	47000	0.572	26884
5	45000	0.497	22365
		Net Present Value(NPV)	62067
		170067	PV of Inflow
			15.00%
Proposal D		PV Factor
Year	CFAT	D.F 15%	DCFAT
0	-400000	1	-400000
1	180000	0.87	156600
2	180000	0.756	136080
3	160000	0.658	105280
4	100000	0.572	57200
5	80000	0.497	39760
		Net Present Value(NPV)	94920
		494920	PV of Inflow
Answer to Question No.5
Present value Index
Proposal C
PI=	PV of Inflow/PV of Outflow
PI	1.574694444	(170067/108000)
Proposal D
PI	1.2373	(494920/400000)
Answer to Question No.6
Rankin Based on Q4 Above (NPV)
Proposal	Rank
Proposal C	2
Proposal D	1
Answer to Question No.7
Rankin Based on Q5 Above PI
Proposal	Rank
Proposal C	1
Proposal D	2