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Capital Rationing Decision Involving Four Proposals

Kopecky Industries Inc. 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 Flows
Proposal Sierra:	$910,000				1	$ 80,000				$ 250,000
					2	80,000				250,000
					3	80,000				250,000
					4	30,000				200,000
					5	(70,000)				100,000
						$200,000				$ 1,050,000
Proposal Tango:	$1,220,000				1	$320,000				$ 560,000
					2	320,000				540,000
					3	160,000				400,000
					4	60,000				300,000
					5	(40,000)				220,000
						$820,000				$2,020,000
Proposal Uniform:	$500,000				1	$ 90,000				$ 200,000
					2	90,000				200,000
					3	90,000				200,000
					4	90,000				200,000
					5	70,000				180,000
						$430,000				$ 980,000
Proposal Victor:	$480,000				1	$44,000				$ 120,000
					2	44,000				120,000
					3	44,000				120,000
					4	4,000				80,000
					5	4,000				80,000
						$140,000				$ 520,000

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

Instructions:

1. Compute the cash payback period for each of the four proposals. Assume that net cash flows are uniform throughout the year.

	Cash Payback Period
Proposal Sierra	answer: 3 years 10 months
Proposal Tango	Answer: 2 years 4 months
Proposal Uniform	Answer: 2 years 6 months
Proposal Victor	Answer: 4 years 6 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. Round to two decimal places.

	Average Rate of Return
Proposal Sierra	% -----
Proposal Tango	% -----
Proposal Uniform	% ------
Proposal Victor	% ------

HINT : DIVIDE THE ESTIMATED AVERAGE ANNUAL INCOME BY THE AVERAGE INSVESTMENT.

3. Using the results from parts (1) and (2) determine which proposals should be accepted for further analysis and which should be rejected.

	Accept / Reject
Proposal Sierra	Reject
Proposal Tango	Accept
Proposal Uniform	Accept
Proposal Victor	Reject

4. For the proposals accepted for further analysis in part (3), compute the net present value. Use a rate of 12% and the present value of $1 table above. If required, use the minus sign to indicate a negative net present value.

Select the proposal accepted for further analysis.	Select (ans)Proposal Tango	Select (ans) Proposal Uniform
Present value of net cash flow total	$ 1530800	$ 709660
Amount to be invested	1220000	500000
Net present value	$ 310800	$ 209660

5. Compute the present value index for each of the proposals in part (4). Round to two decimal places.

Select the proposal to compute present value index.	(ans)Proposal Tango	(ans) Proposal Uniform
Present value index (rounded)	-----------------------	--------------------------

HINT: DIVIDE THE TOTAL PRESENT VALUE OF NET CASH FLOW BY THE AMOUNT TO BE INVESTED. WHICH PROPOSAL HAS THE HIGHER PRESENT VALUE INDEX?

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Internal Rate of Return Introduced

The internal rate of return (IRR) method uses present value concepts to compute the rate of return from a capital investment proposal based on its expected net cash flows. This method, sometimes called the time-adjusted rate of return method, starts with the proposal's net cash flows and works backward to estimate the proposal's expected rate of return.

Internal Rate of Return Calculation (Even Cashflows)

IRR Factor =	Investment
	Annual cash flows

If a project has a 6-year life, requires an initial investment of $174,200, and is expected to yield annual cash flows of $40,000, what is the internal rate of return?

IRR Factor =	$------	= select: 4.355, 4.111, 4.486
	$-------

The calculated value corresponds to which percentage in the table for the present value of ordinary annuities? (Present Value of an Annuity of $1 at Compound Interest.) Select: 10%, 12%, 9%

APPLY THE CONCEPTS: Net present value

Project A This project requires an initial investment of $139,590. The project will have a life of 4 years. Annual revenues associated with the project will be $90,000 and expenses associated with the project will be $45,000 for an annual net cash flow of $-------.

Note: Enter cash flows as positive numbers.

	Cash Flows
Year 0	-$139,590
Year 1	----------
Year 2	---------
Year 3	--------
Year 4	---------

Project B This project requires an initial investment of $129,600. The project will have a life of 4 years. Annual revenues associated with the project will be $100,000, and expenses associated with the project will be $60,000, for an annual net cash flow of $ -----.

	Cash Flows
Year 0	-$129,600
Year 1	------------
Year 2	---------
Year 3	--------
Year 4	--------

The cost of capital for the company is 6%.

Present Value Tables Present Value of $1 (a single sum) at Compound Interest. Present Value of an Annuity of $1 at Compound Interest.

Use the minus sign to indicate a negative NPV. If an amount is zero, enter"0".

Project A NPV Analysis
Year	Cash Flow		Discount Factor					Present Value
0	$139,590		1.000					$139,590
14	45,000		select: 3.465, 0.792, 3.24					----------
NPV								$ -------

Project B NPV Analysis
Year	Cash Flow		Discount Factor					Present Value
0	$129,600		1.000					$129,600
14	40,000		select 3.465, 0.792, 3.24					-----------
NPV								$-----

Based upon net present value, which project has the more favorable profit prospects? select Project A , Project B , Either project

APPLY THE CONCEPTS: Internal rate of return

Calculate the internal rate of return for Project A and Project B (defined previously). Enter the IRR with the percent sign (i.e. 4%).

Project A: IRR Analysis

With an initial investment of $139,590 and annual cash flows of $------, the internal rate of return for Project A is ------.

Project B: IRR Analysis

With an intial investment of $129,600 and annual cash flows of $------, the internal rate of return for Project B is -------.