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	3 years 6 months
Proposal B	4 years
Proposal C	2 years
Proposal D	2 years 3 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. 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	3 years, 6 months	%		Reject
B	4 years	%		Reject
C	2 years	%		Accept
D	2 years, 3 months	%		Accept

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.	Proposal C	Proposal D
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.	Proposal C	Proposal D
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	Proposal D
Rank 2nd	Proposal C

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

Rank 1st	Proposal C
Rank 2nd	Proposal D

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

Answer 1

Compute the cash payback period for each of the four proposals.

CUMULATIVE CASH FLOW	A	B	C	D
1	200000	90000	55000	180000
2	400000	180000	108000	360000
3	600000	250000	158000	520000
4	760000	320000	205000	620000
5	920000	340000	250000	700000

PAYBACK PERIOD = years before full investment recovery+ unrecovered/cash flow of neXt year

A =3+(680000-600000)/24000

=3+80000/160000

=3+0.5

=3.5 = 3 years 6months

B = 4 YEARS

C=2YEARS

D=2+(400000-360000)/160000

=2+0.25

=2 YEAR 3 MONTHS

	Cash Payback Period
Proposal A	3 years 6 months
Proposal B	4 years
Proposal C	2 years
Proposal D	2 years 3 months

2. average rate if return = average profit / average investment

average investment = initial investment+salvage /2

	A	B	C	D
AVERAGE INCOME [ TOTAL INCOME/ YEARS]	48000[240000/5]	4000[20000/5]	28400[142000/5]	60000[300000/5]
AVERAGE INVESTMENT [INITIAL INVESTMENT+SALVAGE/2]	340000$[680000+0/2]	160000$[320000+0/2]	54000[108000+0/2]	200000[400000+0/2]
average rate of return	14.1%[48000/340000]*100	2.5%[4000/160000]*100	52.6%[28400/54000]*100	30%[60000/200000]*100

Proposal	Cash Payback Period	Average Rate of Return		Accept or Reject
A	3 years, 6 months	%14.1		Reject
B	4 years	%2.5		Reject
C	2 years	%52.6		Accept
D	2 years, 3 months	%30		Accept

4.

PRESENT VALUE

YEARS	PV FACTOR AT 15%	c CASH FLOW	PRESENT VALUE	D CASH FLOW	PRESENT VALUE
1	0.870	55000	47850[0.870*55000]	180000	156600[180000*0.870]
2	0.756	53000	40068	180000	136080
3	0.658	50000	32900	160000	105280
4	0.572	47000	26884	100000	57200
5	0.497	45000	22365	80000	39760
		TOTAL	170067		494920

Select the proposal accepted for further analysis.	Proposal C	Proposal D
Present value of net cash flow total	$ 170067	$494920
Less amount to be invested	$108000	$400000
Net present value	$ 62067[170067-108000]	$94920

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.	Proposal C	Proposal D
Present value index (rounded)	1.57[PRESENT VALUE OF CASH FLOW/INITIAL CASH OUTFLOW][170067/108000]	1.24[494920/400000]

6.