Wendell’s Donut Shoppe is investigating the purchase of a new $34,100 donut-making machine. The new machine would permit the company to reduce the amount of part-time help needed, at a cost savings of $5,600 per year. In addition, the new machine would allow the company to produce one new style of donut, resulting in the sale of 1,500 dozen more donuts each year. The company realizes a contribution margin of $2.50 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 $8,985 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.)
Explanation
1.
| Annual savings in part-time help | $ | 5,600 | ||||
| Added contribution margin from expanded sales (1,500 dozen × $2.50 per dozen) | 3,750 | |||||
| Annual cash inflows | $ | 9,350 | ||||
2.
| Factor of the internal rate of return | = | investment required | |
| Annual cash inflow | |||
| = | $34,100 | = 3.647 | |
| $9,350 | |||
3.
Looking in Exhibit 13B-2, and scanning along the six-period line, we can see that the factor computed above, 3.647, is closest to 3.685, the factor for the 16% rate of return. Therefore, to the nearest whole percent, the internal rate of return is 16%.
4.
The cash flows will not be even over the six-year life of the machine because of the extra $8,985 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 20%:
| Now | Years 1-6 | Year 6 | |||||
| Purchase of machine | $ | (34,100 | ) | ||||
| Reduced part-time help | $ | 5,600 | |||||
| Added contribution margin | 3,750 | ||||||
| Salvage value of machine | $ | 8,985 | |||||
| Total cash flows (a) | (34,100 | ) | $ | 9,350 | $ | 8,985 | |
| Discount factor (20%) (b) | 1.000 |
3.326
| 0.335 | ||||
| Present value (a) × (b) | $ | (34,100 | ) | $ | 31,098 | $ | 3,010 |
| Net present value | $ | 0 | |||||
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