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

1	Payback period=Year after which cumulative cashflow become positive+(cumulative cashflow of the year after which cumulative cashflow become positive/cashflow for next year)
	Proposal A:
	Year	Net cash flow	Cumulative cash flow
	0	-680000	-680000
	1	200000	-480000
	2	200000	-280000
	3	200000	-80000
	4	160000	80000
	5	160000	240000
	Payback period=3+(80000/160000)=3+0.5=3.5 years=3 years and 6 months
	Proposal B:
	Year	Net cash flow	Cumulative cash flow
	0	-320000	-320000
	1	90000	-230000
	2	90000	-140000
	3	70000	-70000
	4	70000	0
	5	20000	20000
	Payback period=4+(0/160000)=4+0=4 years
	Proposal C:
	Year	Net cash flow	Cumulative cash flow
	0	-108000	-108000
	1	55000	-53000
	2	53000	0
	3	50000	50000
	4	47000	97000
	5	45000	142000
	Payback period=2+(0/160000)=2+0=2 years
	Proposal D:
	Year	Net cash flow	Cumulative cash flow
	0	-400000	-400000
	1	180000	-220000
	2	180000	-40000
	3	160000	120000
	4	100000	220000
	5	80000	300000
	Payback period=2+(40000/160000)=2+0.25=2.25 years=2 years and 3 months
2	Average rate of return=Average operating income/Average Investment
	Average operating income=Total Operating income/number of years
	Average Investment=(Beginning value of investment+Ending value of investment)/2
						Proposal A	Proposal B	Proposal C	Proposal D
	Total Operating income				a	240000	20000	142000	300000
	Number of years				b	5	5	5	5
	Average operating income				c=a/b	48000	4000	28400	60000
	Beginning value of investment				d	680000	320000	108000	400000
	Ending value of investment				e	0	0	0	0
	Average Investment				f=(d+e)/2	340000	160000	54000	200000
	Average rate of return				g=c/f	14.1%	2.5%	52.6%	30.0%