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.

Note: Select the proposals in alphabetic order.

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

Answer 1

	Ans 1
	Cash payback period
Year	Income from operations I	Depreciation D	Net cash flow I +D	Cumulative cash flow
0			($680,000)	($680,000)
1	$64,000	136000	$200,000	($480,000)
2	$64,000	136000	$200,000	($280,000)
3	$64,000	136000	$200,000	($80,000)
4	$24,000	136000	$160,000	$80,000
5	$24,000	136000	$160,000	$240,000
Annual cash inflow
Income from operations+Depreciation
Depreciation
680000/5	136000
Payback period= last period with negative cumulative cash flow+absolute value d cumulative cash at the period end/total cash flow in the period after last period negative cash flow
Payback	3+(80000/160000)	3.5
Proposal B
	Cash payback perod
Year	Income from operations I	Depreciation D	Net cash flow I +D	Cumulative cash flow
0			($320,000)	($320,000)
1	$26,000	64000	$90,000	($230,000)
2	$26,000	64000	$90,000	($140,000)
3	$6,000	64000	$70,000	($70,000)
4	$6,000	64000	$70,000	$0
5	($44,000)	64000	$20,000	$20,000
Annual cash inflow
Income from operations+Depreciation
Depreciation
320000/5	64000
Payback	4	Years
Proposal C
	Cash payback perod
Year	Income from operations I	Depreciation D	Net cash flow I +D	Cumulative cash flow
0			($108,000)	($108,000)
1	$33,400	21600	$55,000	($53,000)
2	$55,000	21600	$76,600	$23,600
3	$53,000	21600	$74,600	$98,200
4	$47,000	21600	$68,600	$166,800
5	$45,000	21600	$66,600	$233,400
Annual cash inflow
Income from operations+Depreciation
Depreciation
108000/5	21600
Payback	1.69	Years
1+(53000/76600)
Proposal D
	Cash payback perod
Year	Income from operations I	Depreciation D	Net cash flow I +D	Cumulative cash flow
0			($400,000)	($400,000)
1	$100,000	80000	$180,000	($220,000)
2	$100,000	80000	$180,000	($40,000)
3	$80,000	80000	$160,000	$120,000
4	$20,000	80000	$100,000	$220,000
5	$0	80000	$80,000	$300,000
Annual cash inflow
Income from operations+Depreciation
Depreciation
400000/5	80000
Payback	2.25	Years
2+(40000/160000)
answer	Cash Payback Period		if one decimal
	Proposal A:	3.5
	Proposal B:	4
	Proposal C:	1.69	1.7
	Proposal D:	2.25	2.3
ans 2
Average rate of return=average profit/average investment*100
		Proposal A	Proposal B	Proposal C	Proposal D
	Total income from operations	$240,000	$20,000	142000	$300,000
	No. of years	5	5	5	5
	Average profit A	$48,000	$4,000	$28,400	$60,000
	Av erage investment B	340000	160000	90000	200000
	(initial investment+salvage value)/2	(680000+0)/2	(320000+0)/2	(180000+0)/2	(400000+0)/2
	answer
	ARR A/B	14.1	2.5	31.6	30
	Average Rate of Return
	Proposal A:	14.1
	Proposal B:	2.5
	Proposal C:	31.6
	Proposal D:	30
ans 3
Proposal	Cash Payback Period	Average Rate of Return		Accept or Reject
A	3.5	14.1	%	Reject	(as paybck is more)
B	4.0	2.5	%	Reject	(as paybck is more and return less)
C	1.7	31.6	%	Accept
D	2.3	30.0		Accept
ans 4	Present value of net cash flow total
	Proposal C
	Year	Net Cash	Discount factor	Discounted cash flow
		Flow	15%
	1	$33,400	0.87	$29,058
	2	31,400	0.756	$23,738
	3	28,400	0.658	$18,687
	4	25,400	0.572	$14,529
	5	23,400	0.497	$11,630
	Total	$142,000		$97,642
	Present value of net cash flow total
	Proposal D
	Year	Net Cash	Discount factor	Discounted cash flow
		Flow	15%
	1	$180,000	0.87	$156,600
	2	$180,000	0.756	$136,080
	3	$160,000	0.658	$105,280
	4	$100,000	0.572	$57,200
	5	$80,000	0.497	$39,760
	Total	$700,000		$494,920
	Select the proposal accepted for further analysis.	Proposal C	Proposal D
	Present value of net cash flow total	$97,642	$494,920
	Less amount to be invested	-108000	-400000
	Net present value	($10,358)	$94,920
			Accepted
If any doubt please comment.