Wendell’s Donut Shoppe is investigating the purchase of a new $47,300 donut-maki

Question

Wendell’s Donut Shoppe is investigating the purchase of a new $47,300 donut-making machine. The new machine would permit the company to reduce the amount of part-time help needed, at a cost savings of $6,300 per year. In addition, the new machine would allow the company to produce one new style of donut, resulting in the sale of 2,600 dozen more donuts each year. The company realizes a contribution margin of $1.50 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 to the nearest whole percent?

4. In addition to the data given previously, assume that the machine will have a $13,605 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.)

1 Annual cash flows ?    2 Discount factor ? 3 internal rete of return ? % 4 internal rate of return ? %

Explanation / Answer

Req 1: Annual cash inflows: Contribution earned from new product (2600 dozens donuts@1.50 per dozen) 3900 Add: Cost savings due to part time help not required 6300 Annual Cash inflows 10200 Req 2: NPV @10% Present value of annual cash inflows for 6 years (Annuity factor @10% for 6 yrs is 4.355) 44421 Less: Present values of cash outflows 47300 Net Present value -2879 NPV @7% Present value of annual cash inflows for 6 years (Annuity factor @7% for 6 yrs is 4.767) 48623.4 Less: Present values of cash outflows 47300 Net Present value 1323.4 Therefore, Discount rates used is 10% and 7% Req 3: IRR = Lower rate + NPV at lower rates / difference in NPV * difference in rates                 7% + 1323.4 /(1323.4+2879)   *3% = 7.945% Req 4: Salvage value at the end of Life $ 13605 NPV at 10% Present value of annual cash inflows for 6 years (Annuity factor @10% for 6 yrs is 4.355) 48623.4 Add: Present value of salvage value of $ 13605 at the end of 6th year (PV factor @10%i.e..564) 7673.22 Less: Present values of cash outflows 47300 Net Present value 8996.62 NPV at 15% Present value of annual cash inflows for 6 years (Annuity factor @50% for 6 yrs is 3.784) 38596.8 Add: Present value of salvage value of $ 13605 at the end of 6th year (PV factor @15%i.e.0.432) 5877.36 Less: Present values of cash outflows 47300 Net Present value -2825.84 IRR = Lower rate + NPV at lower rates / difference in NPV * difference in rates                 10% + 8996.62 /(8996.62+2825.84)   *5% = 13.805% 1. Cash Inflows Annual   $10,200 2. Discounts rates 7% -10% 3. IRR 7.95% 4. IRR 13.81%

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