Question

Wendell’s Donut Shoppe is investigating the purchase of a new $40,000 donut-making machine. The new machine would permit the company to reduce the amount of part-time help needed, at a cost savings of $5,200 per year. In addition, the new machine would allow the company to produce one new style of donut, resulting in the sale of 2,000 dozen more donuts each year. The company realizes a contribution margin of $2.40 per dozen donuts sold. The new machine would have a six-year useful life. Click here to view Exhibit 14B-1 and Exhibit 14B-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 the nearest whole percentage.) 4. In addition to the data given previously, assume that the machine will have a $10,515 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.) (

Answer 1

Answer:

initial outlay $40,000

savings per year = $5,200

additional contribution margin = 2,000 x $2.40 = $4,800

machines useful life = 6 years

1) total annual cash flows (assuming no residual value)

Year₀ = -$40,000

Year₁ = $5,200 + $4,800 = $10,000

Year₂ = $10,000

Year₃ = $10,000

Year₄ = $10,000

Year₅ = $10,000

Year₆ = $10,000

2) to determine IRR we can use a financial calculator or the present value of an annuity formula:

PV = annual payment x annuity factor

PV = $40,000

annual payment = $10,000

annuity factor = $40,000 / $10,000 = 4

3) using present value of an annuity table:

we have 6 periods, and we must look for an interest rate that results in an annuity factor of 4 = 13% (the exact annuity factor is 3.998)

using a financial calculator, the IRR = 12.98%, which we can round to 13%

4) the cash flows will be:

Year₀ = -$40,000

Year₁ = $10,000

Year₂ = $10,000

Year₃ = $10,000

Year₄ = $10,000

Year₅ = $10,000

Year₆ = $20,515

We cannot use the annuity formula now because our annuities are not equal. Using a financial calculator, IRR = 16.99%