Question

Wendell’s Donut Shoppe is investigating the purchase of a new $42,700 donut-making machine. The new machine would permit the company to reduce the amount of part-time help needed, at a cost savings of $6,400 per year. In addition, the new machine would allow the company to produce one new style of donut, resulting in the sale of 2,400 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.

Click here to view Exhibit 13B-1 and Exhibit 13B-2, to determine the appropriate discount factor(s) using tables.

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 $12,840 salvage value at the end of six years. Under these conditions, what is the internal rate of return? (Round your final answer to nearest whole percentage.)

Answer 1

1.

Annual savings in part time help	6,400.00
Added contribution margin (2400*2)	4,800.00
Annual cash inflows	11,200.00

2. Discount factor = Investment required/annual cash inflow

= 42700/11200

= 3.813

3. Discount factor = 3.813 and no. of years = 6 years

Thus the IRR corresponding the above two figures will be 15% (from exhibit 13B-2)

4. Here the IRR has been computed using the trial and error method i.e. I have used trail and error to determine that rate that makes NPV as nil.

Year	Initial investment	Cost savings	Added contribution margin	Salvage value	Total cash flow
0	(42,700.00)				(42,700.00)
1		6,400.00	4,800.00		11,200.00
2		6,400.00	4,800.00		11,200.00
3		6,400.00	4,800.00		11,200.00
4		6,400.00	4,800.00		11,200.00
5		6,400.00	4,800.00		11,200.00
6		6,400.00	4,800.00	12,840.00	24,040.00

After the annual cash flows have been determined we will now compute IRR.

Year	Total cash flow	1+r	PVIF	PV of cash flow
0	(42,700.00)	1.1901	1.00	-42,700.00
1	11,200.00		0.84	9,411.03
2	11,200.00		0.71	7,907.82
3	11,200.00		0.59	6,644.71
4	11,200.00		0.50	5,583.35
5	11,200.00		0.42	4,691.53
6	24,040.00		0.35	8,461.56
			NPV	0.00

Thus IRR = 1.1901 - 1 = 0.1901 or 19.01%

This will be rounded off to 19%