Wendell’s Donut Shoppe is investigating the purchase of a new $34,100 donut-maki

Question

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.

Exhibit 13B-2:

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

Find the internal rate of return promised by the new machine to the nearest whole percent.

In addition to the data given previously, assume that the machine will have a $10,000 salvage value at the end of six years. Under these conditions, compute the internal rate of return to the nearest whole percent. (Round your final answer to nearest whole percentage.)

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.

Explanation / Answer

1.  The total annual cash inflows associated with the new machine for capital budgeting purposes

= Cost savings per year + Sale of new style donuts

= $5600 + $3750 = $$9350

2. Internal Rate of Return = Low rate + (NPV at low rate / (NPV at low rate - NPV at high rate)*Difference of rates

= 10 + [6619.25 / (6619.25 - 3001.9)] * 10

= 28%

NPV at 10%

NPV = (Annual cash flows * Sum of PVF @ 10% for 6 years ) - Initaial Investment

= (9350 * 4.355) - 34100 = $6619.25

As the NPV is positive we should calculate NPV at higher rate, 20%

NPV = (Annual cash flows * Sum of PVF @ 20% for 6 years ) - Initaial Investment

= (9350 * 3.326) - 34100 = -$3001.9

3. NPV at 10% = (Annual cash flows * Sum of PVF @ 10% for 6 years) + Salvage value* PVF for 6th year - Initaial Investment

=  9350 * 4.355 + (10000*0.564) - 3410

= $12259.25

NPV at 20% = (Annual cash flows * Sum of PVF @ 20% for 6 years) + Salvage value* PVF for 6th year - Initaial Investment

= 9350 * 3.326+ (10000* 0.335) - 34100 = $348.1

Since the NPV is positive we have to take a higher rate say 25%

NPV at 25% = (Annual cash flows * Sum of PVF @25% for 6 years) + Salvage value* PVF for 6th year - Initaial Investment

=  9350 * 2.951 + (10000*0.262) - 34100

= -$3888.15

Internal Rate of Return = 10 + [12259.25 / (12259.25 - -3888.15)] * 15

= 21%

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