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 operating income, and net cash flow for each proposal are as follows:

	Investment	Year		Operating Income		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 analysis indicates 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

working
	Project A
Year	Cash flow C	Cumulative cash flow	Discount factor 15% D	Discounted Cash flow D	PV of cash inflow
0	-680000	-680000	1	-680000
1	200000	-480000	0.87	174000	174000
2	200000	-280000	0.756	151200	151200
3	200000	-80000	0.658	131600	131600
4	160000	80000	0.572	91520	91520
5	160000	240000	0.497	79520	79520
			NPV	-52160	627840
Payback Period = A +	A+B/c
A is the last period with a negative cumulative cash flow
B is the absolute value of cumulative cash flow at the end of the period A
C is the total cash flow during the period after A
Payback =	3+(80000/160000)	3.5
Average rate of Return
Avg Income/Avg investment*100
Avg income 240000/5	48000
Average investment	340000
(680000+0)/2
Average rate of Return	14.12	%
48000/340000*100
Present value Index
PV of cash inflow/Initail investment
627840/680000	0.92
	Project B
Year	Cash flow C	Cumulative cash flow	Discount factor 15% D	Discounted Cash flow D	PV of cash inflow
0	-320000	-320000	1	-320000
1	90000	-230000	0.87	78300	78300
2	90000	-140000	0.756	68040	68040
3	70000	-70000	0.658	46060	46060
4	70000	0	0.572	40040	40040
5	20000	20000	0.497	9940	9940
			NPV	-77620	242380
Payback Period = A +	A+B/c
A is the last period with a negative cumulative cash flow
B is the absolute value of cumulative cash flow at the end of the period A
C is the total cash flow during the period after A
Payback =	3+(70000/70000)	3
Average rate of Return
Avg Income/Avg investment*100
Avg income 20000/5	4000
Average investment	160000
(320000+0)/2
Average rate of Return	2.5	%
4000/160000*100
Present value Index
PV of cash inflow/Initail investment
242380/320000	0.76
	Project C
Year	Cash flow C	Cumulative cash flow	Discount factor 15% D	Discounted Cash flow D	PV of cash inflow
0	-108000	-108000	1	-108000
1	55000	-53000	0.87	47850	47850
2	53000	0	0.756	40068	40068
3	50000	50000	0.658	32900	32900
4	47000	97000	0.572	26884	26884
5	45000	142000	0.497	22365	22365
			NPV	62067	170067
Payback Period = A +	A+B/c
A is the last period with a negative cumulative cash flow
B is the absolute value of cumulative cash flow at the end of the period A
C is the total cash flow during the period after A
Payback =	2+(53000/530000)	2
Average rate of Return
Avg Income/Avg investment*100
Avg income 142000/5	28400
Average investment	54000
(108000+0)/2
Average rate of Return	52.59	%
28400/54000*100
Present value Index
PV of cash inflow/Initail investment
170067/108000	1.57
	Project D
Year	Cash flow C	Cumulative cash flow	Discount factor 15% D	Discounted Cash flow D	PV of cash inflow
0	-400000	-400000	1	-400000
1	180000	-220000	0.87	156600	156600
2	180000	-40000	0.756	136080	136080
3	160000	120000	0.658	105280	105280
4	100000	220000	0.572	57200	57200
5	80000	300000	0.497	39760	39760
			NPV	94920	494920
Payback Period = A +	A+B/c
A is the last period with a negative cumulative cash flow
B is the absolute value of cumulative cash flow at the end of the period A
C is the total cash flow during the period after A
Payback =	2+(40000/160000)	2.25
Average rate of Return
Avg Income/Avg investment*100
Avg income 300000/5	60000
Average investment	200000
Average rate of Return	30.00	%
60000/200000*100
Present value Index
PV of cash inflow/Initail investment
494920/400000	1.24
ans 1
	Payback period
Project A	3.5
Project B	3
Project C\	2
Project D	2.25
ans b	ARR
Project A	14.12
Project B	2.5
Project C\	52.59
Project D	30.00
ans 3	Payback period	ARR
Project A	3.5	14.12	Reject
Project B	3	2.50	Reject
Project C\	2	52.59	Accept
Project D	2.25	30.00	Accept
ans 4
NPV	Project C	Project D
PV of Net cash inflows	170067	494920
Less: initial Investment	108000	400000
NPV	62067	94920
ans 5	Project C	Project D
	1.57	1.24
ans 6
Rank 1	Project D
Rank 2	Project C
ans 7
Rank 1	Project C
Rank 2	Project D

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