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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:

Proposal Investment Year Operating Income Net Cash Flow

Proposal A: $$500,0001$ $ $45,000$ $ $145,000$

Proposal A: $240,000140,000$

Proposal A: $325,000125,000$

Proposal A: $420,000120,000$

Proposal A: $55,000105,000$

Total $$135,000$ $$635,000$

Proposal B: $$400,0001$ $ $40,000$ $ $120,000$

Proposal B: $220,000100,000$

Proposal B: $310,00090,000$

Proposal B: $410,00090,000$

Proposal B: $56,00086,000$

Total $ $86,000$ $$486,000$

Proposal C: $$380,0001$ $ $54,000$ $ $130,000$

Proposal C: $249,000125,000$

Proposal C: $349,000125,000$

Proposal C: $444,000120,000$

Proposal C: $544,000120,000$

Total $$240,000$ $$620,000$

Proposal D: $$675,0001$ $$135,000$ $$270,000$

Proposal D: $2120,000255,000$

Proposal D: $390,000225,000$

Proposal D: $415,000150,000$

Proposal D: $510,000145,000$

Total $$370,000$ $$1,045,000$

The company's capital rationing policy requires a maximum cash payback period of $3$ years. In addition, a minimum average rate of return of $10\%$ 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 $6\%10\%12\%15\%20\%$

$10\mathrm{.}9430\mathrm{.}9090\mathrm{.}8930\mathrm{.}8700\mathrm{.}833$

$20\mathrm{.}8900\mathrm{.}8260\mathrm{.}7970\mathrm{.}7560\mathrm{.}694$

$30\mathrm{.}8400\mathrm{.}7510\mathrm{.}7120\mathrm{.}6580\mathrm{.}579$

$40\mathrm{.}7920\mathrm{.}6830\mathrm{.}6360\mathrm{.}5720\mathrm{.}482$

$50\mathrm{.}7470\mathrm{.}6210\mathrm{.}5670\mathrm{.}4970\mathrm{.}402$

$60\mathrm{.}7050\mathrm{.}5640\mathrm{.}5070\mathrm{.}4320\mathrm{.}335$

$70\mathrm{.}6650\mathrm{.}5130\mathrm{.}4520\mathrm{.}3760\mathrm{.}279$

$80\mathrm{.}6270\mathrm{.}4670\mathrm{.}4040\mathrm{.}3270\mathrm{.}233$

$90\mathrm{.}5920\mathrm{.}4240\mathrm{.}3610\mathrm{.}2840\mathrm{.}194$

$100\mathrm{.}5580\mathrm{.}3860\mathrm{.}3220\mathrm{.}2470\mathrm{.}162$

Required:

$1.$ Compute the cash payback period for each of the four proposals.

Proposal 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.

Proposal Average Rate of Return

Proposal A fill in the blank $5\%$

Proposal B fill in the blank $6\%$

Proposal C fill in the blank $7\%$

Proposal D fill in the blank $8\%$

$3.$ 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

fill in the blank $10\%$

B

fill in the blank $13\%$

C

fill in the blank $16\%$

D

fill in the blank $19\%$

$4.$ 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.

Line Item Description Answer Answer

Select the proposal accepted for further analysis.

Present value of net cash flow total $fill in the blank $23$ $fill in the blank $24$

Less amount to be invested fill in the blank $25$ fill in the blank $26$

Net present value $fill in the blank $27$ $fill in the blank $28$

$5.$ Compute the present value index for each of the proposals in part $(4).$ If required, round your answers to two decimal places.

Line Item Description Answer Answer

Select proposal to compute Present value index.

Present value index $($rounded$)$ fill in the blank $31$ fill in the blank $32$

$6.$ Rank the proposals from most attractive to least attractive, based on the present values of net cash flows computed in part $(4).$

Rank $1$st

Rank $2$nd

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

Rank $1$st

Rank $2$nd

$8.$ The analysis indicates that although Proposal fill in the blank $1$ of $5$

has the larger net present value, it is not as attractive as Proposal fill in the blank $2$ of $5$

in terms of the amount of present value per dollar invested. Proposal fill in the blank $3$ of $5$

requires the larger investment. Thus, management should use investment resources for Proposal fill in the blank $4$ of $5$

before investing in Proposal fill in the blank $5$ of $5$

$,$ absent any other qualitative considerations that may impact the decision.

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Feedback

$1.$ For each project, start with year $1$ and accumulate the net cash flows until the amount to be invested is reached.

$2.$ Divide the estimated average annual income by the average investment.

$3.$ Which proposals meet the payback requirements and the minimum average rate of return?

$4,6.$ For each proposal, multiply the present value factor by the net cash flow $($