Wendell’s Donut Shoppe is investigating the purchase of a new $48,300 donut-making machine. The new machine would permit the company to reduce the amount of part-time help needed, at a cost savings of $6,800 per year.

Wendell’s Donut Shoppe is investigating the purchase of a new $48,300 donut-making machine. The new machine would permit the company to reduce the amount of part-time help needed, at a cost savings of $6,800 per year. In addition, the new machine would allow the company to produce one new style of donut, resulting in the sale of 1,700 dozen more donuts each year. The company realizes a contribution margin of $2.00 per dozen donuts sold. The new machine would have a six-year useful life.

Required:

1. What would be the total annual cash inflows associated with the new machine for capital budgeting purposes?

2. What discount factor should be used to compute the new machine’s internal rate of return? (Round your answers to 3 decimal places.)

3. What is the new machine’s internal rate of return? (Round your final answer to nearest whole percentage.)

4. In addition to the data given previously, assume that the machine will have a $15,685 salvage value at the end of six years. Under these conditions, what is the internal rate of return? (Hint: You may find it helpful to use the net present value approach; find the discount rate that will cause the net present value to be closest to zero.) (Round your final answer to nearest whole percentage.)

Explanation

1.

Annual savings in part-time help	$	6,800
Added contribution margin from expanded sales (1,700 dozen × $2.00 per dozen)		3,400
Annual cash inflows	$	10,200

2.

Factor of the internal rate of return	=	investment required
		Annual cash inflow
	=	$48,300	= 4.735
		$10,200

3.

Looking in Exhibit 13B-2, and scanning along the six-period line, we can see that the factor computed above, 4.735, is closest to 4.767, the factor for the 7% rate of return. Therefore, to the nearest whole percent, the internal rate of return is 7%.

4.

The cash flows will not be even over the six-year life of the machine because of the extra $15,685 inflow in the sixth year. Therefore, the above approach cannot be used to compute the internal rate of return in this situation. Using trial-and-error or some other method, the internal rate of is 13%:

	Now			Years 1-6		Year 6
Purchase of machine	$	(48,300	)
Reduced part-time help				$	6,800
Added contribution margin					3,400
Salvage value of machine						$	15,685
Total cash flows (a)		(48,300	)	$	10,200	$	15,685
Discount factor (13%) (b)		1.000			3.998		0.480
Present value (a) × (b)	$	(48,300	)	$	40,780	$	7,529
Net present value	$	0

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The Elberta Fruit Farm of Ontario always has hired transient workers to pick its annual cherry crop. Janessa Wright, the farm manager, just received information on a cherry picking machine that is being purchased by many fruit farms.

The Elberta Fruit Farm of Ontario always has hired transient workers to pick its annual cherry crop. Janessa Wright, the farm manager, just received information on a cherry picking machine that is being purchased by many fruit farms. The machine is a motorized device that shakes the cherry tree, causing the cherries to fall onto plastic tarps that funnel the cherries into bins. Ms. Wright has gathered the following information to decide whether a cherry picker would be a profitable investment for the Elberta Fruit Farm:

1. Currently, the farm is paying an average of $160,000 per year to transient workers to pick the cherries.
2. The cherry picker would cost $152,000. It would be depreciated using the straight-line method and it would have no salvage value at the end of its 10-year useful life.
3. Annual out-of-pocket costs associated with the cherry picker would be: cost of an operator and an assistant, $92,000; insurance, $4,000; fuel, $11,000; and a maintenance contract, $14,000.

Required:

1. Determine the annual savings in cash operating costs that would be realized if the cherry picker were purchased.

2a. Compute the simple rate of return expected from the cherry picker.

2b. Would the cherry picker be purchased if Elberta Fruit Farm’s required rate of return is 21%?

3a. Compute the payback period on the cherry picker.

3b. The Elberta Fruit Farm will not purchase equipment unless it has a payback period of four years or less. Would the cherry picker be purchased?

4a. Compute the internal rate of return promised by the cherry picker.

4b. Based on this computation, does it appear that the simple rate of return is an accurate guide in investment decisions?

Explanation

1.

Present cost of transient workers			$	160,000
Less out-of-pocket costs to operate the cherry picker:
Cost of an operator and assistant	$	92,000
Insurance		4,000
Fuel		11,000
Maintenance contract		14,000		121,000
Annual savings in cash operating costs			$	39,000

2.

a.

The first step is to determine the annual incremental net operating income:

  

Annual savings in cash operating costs	$	39,000
Less annual depreciation [$152,000 ÷ 10 years]		15,200
Annual incremental net operating income	$	23,800

Simple rate of return	=	Annual incremental net operating income
		Initial investment
	=	$23,800	= 15.66% (rounded)
		$152,000

b.

No, the cherry picker would not be purchased. The expected return is less than the 21% return required by the farm.

3

a.

The formula for the payback period is:

Payback period	=	Investment required
		Annual net cash inflow
	=	$152,000	= 3.90 years
		$39,000*

*In this case, the cash inflow is measured by the annual savings in cash operating costs.

b.

Yes, the cherry picker would be purchased. The payback period is less than 4 years. Note that this answer conflicts with the answer in Part 2a.

4.

a.

The formula for the internal rate of return is:

Factor of the internal rate of return	=	Investment required
		Annual net cash inflow
	=	$152,000	= 3.897
		$39,000

Looking in Exhibit 13B-2 and scanning along the 10-period line, we can see that the factor computed above, 3.897, is closest to 3.923, the factor for the 22% rate of return. Therefore, to the nearest whole percent, the internal rate of return is 22%.

b.

No, the simple rate of return is not an accurate guide in investment decisions. It ignores the time value of money.

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Henrie’s Drapery Service is investigating the purchase of a new machine for cleaning and blocking drapes. The machine would cost $171,650, including freight and installation. Henrie’s estimated the new machine would increase the company’s cash inflows, net of expenses, by $50,000 per year. The machine would have a five-year useful life and no salvage value.

Henrie’s Drapery Service is investigating the purchase of a new machine for cleaning and blocking drapes. The machine would cost $171,650, including freight and installation. Henrie’s estimated the new machine would increase the company’s cash inflows, net of expenses, by $50,000 per year. The machine would have a five-year useful life and no salvage value.

Required:

1. What is the machine’s internal rate of return? (Round your answer to whole decimal place i.e. 0.123 should be considered as 12%.)

2. Using a discount rate of 14%, what is the machine’s net present value? Interpret your results.

3. Suppose the new machine would increase the company’s annual cash inflows, net of expenses, by only $44,130 per year. Under these conditions, what is the internal rate of return? (Round your answer to whole decimal place i.e. 0.123 should be considered as 12%.)

Explanation

1.

Factor of the internal rate of return	=	Investment required
		Annual net cash inflow
	=	$171,650	= 3.433
		$50,000

Looking in Exhibit 13B-2 and scanning along the 5-period line, a factor of 3.433 represents an internal rate of return of 14%.

 

2.

The machine’s net present value is computed as follows:

	Now			Years 1-5
Purchase of machine	$	(171,650	)
Annual cash inflows				$	50,000
Total cash flows (a)	$	(171,650	)	$	50,000
Discount factor (b)		1.000			3.433
Present value (a) × (b)	$	(171,650	)	$	171,650
Net present value	$	0

The reason for the zero net present value is that 14% (the discount rate we have used) represents the machine’s internal rate of return. The internal rate of return is the discount rate that results in a zero net present value.

 

3.

Factor of the internal rate of return	=	Investment required
		Annual net cash inflow
	=	$171,650	= 3.890 (rounded)
		$44,130

Looking in Exhibit 13B-2 and scanning along the 5-period line, a factor of 3.890 corresponds to the factor for 9%. Thus, the internal rate of return is 9%.

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