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)

Answer 1

1 Coputation of pay back period for each of the four proposal
proosal A
	Year	month	Net cash flow	cumulative net cash flow
	1	12	$          2,00,000.00	$                          2,00,000.00
	2	12	$          2,00,000.00	$                          4,00,000.00
	3	12	$          2,00,000.00	$                          6,00,000.00
	4	6	$              80,000.00	$                          6,80,000.00
	Payback Period		3 year 6 month
proosal B	Year	month	Net cash flow	cumulative net cash flow
	1	12	$              90,000.00	$                             90,000.00
	2	12	$              90,000.00	$                          1,80,000.00
	3	12	$              70,000.00	$                          2,50,000.00
	4	12	$              70,000.00	$                          3,20,000.00
	Payback Period		4 year
proposal C	Year	month	Net cash flow	cumulative net cash flow
	1	12	$              55,000.00	$                             55,000.00
	2	12	$              53,000.00	$                          1,08,000.00
	Payback Period		2 year
proposal D	Year	month	Net cash flow	cumulative net cash flow
	1	12	$          1,80,000.00	$                          1,80,000.00
	2	12	$          1,80,000.00	$                          3,60,000.00
	3	3	$              40,000.00	$                          4,00,000.00
	Payback Period		2 years 3 month
2	Average rate of return
	proposal A
	total income		$          2,40,000.00
	life in years		5
	average annual income		$              48,000.00
	(total income/years )
	initial investment		$          6,80,000.00
	Average rate of return		7.1%
	( average income/investment)
	proposal B
	total income		$              20,000.00
	life in years		5
	average annual income		$                4,000.00
	(total income/years )
	initial investment		$          3,20,000.00
	Average rate of return		1%
	( average income/investment)
	proposal C
	total income		$          1,42,000.00
	life in years		5
	average annual income		$              28,400.00
	(total income/years )
	initial investment		$          1,08,000.00
	Average rate of return		26.3%
	( average income/investment)
	Proposal D
	total income		$          3,00,000.00
	life in years		5
	average annual income		$              60,000.00
	(total income/years )
	initial investment		$          4,00,000.00
	Average rate of return		15.0%
	( average income/investment)
3	proposal	cash backback period	avg rate of return	accept/ reject for analysis
	A	3 Year 6 month	7.1%	reject
	B	4 years	1.3%	reject
	C	2 years	26.3%	accept
	D	2 years 3 month	15%	accept
4	Net present value
	proposal C
	Year	pvf 15%	Net cash flow	present value
	1	0.87	55000	47850
	2	0.756	53000	40068
	3	0.658	50000	32900
	4	0.572	47000	26884
	5	0.497	45000	22365
	total			170067
	initial investment			-108000
	Net present value			62067
	present value index (170067/108000)			1.57
	Net present value
	proposal D
	Year	pvf 15%	Net cash flow	present value
	1	0.87	$          1,80,000.00	$                          1,56,600.00
	2	0.756	$          1,80,000.00	$                          1,36,080.00
	3	0.658	$          1,60,000.00	$                          1,05,280.00
	4	0.572	$          1,00,000.00	$                             57,200.00
	5	0.497	$              80,000.00	$                             39,760.00
	total			$                          4,94,920.00
	initial investment			$                        -4,00,000.00
	Net present value			$                             94,920.00
	present value index (494920/400000)			$                                        1.24
	Here net present value = present value of cash inflow - cash outflow
	present value index = present value of cash inflow/ cash outflow