Wendell\'s Donut Shoppe is investigating the purchase of a new $50,100 donut-mak

Question

Wendell's Donut Shoppe is investigating the purchase of a new $50,100 donut-making machine. The new machine would permit the company to reduce the amount of part-time help needed, at a cost savings of $5,900 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 $1.60 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? Annual savings in part-time help Added contribution margin from expanded sale:s Annual cash inflows

Explanation / Answer

1.Calculation of annual cash inflows associated with new machine

2.Calculation of internal rate of return

Internal rate of return (IRR) is the rate at which Net present value (NPV) is 0

NPV = Present Value of Cash inflows - Present value of cash outflows

Cash outflows = Cost of machine = $ 50100

Present value of cash outflow at time 0 would be $50100 x 1 = $ 50100

Let assume the discounting rate be 4 %

Present value of cash inflows at 4 % would be

PVAF (4%, 6years) x 10060 = 5.242 x 10060 = 52734.52

NPV= 52734.52 - 50100 = $ 2634.52

Now lets assume discounting rate be 6 %

Present value of cash inflows at 6 % would be

PVAF (6%, 6years) x 10060 = 4.917 x 10060 = 49465.02

NPV = 49465.02-50100 =($ 634.98)

Now by interpolation , IRR would be

4 % + (2634.52 - 0) x (6% - 4 %) / [2634.52 - (-634.98)]

= 5.61 %

3.Calculation of internal rate of return

Cash outflows = Cost of machine = $ 50100

Present value of cash outflow at time 0 would be $50100 x 1 = $ 50100

Let assume the discounting rate be 12 %

Present value of cash inflows at 12 % would be

[PVAF (12%, 6years) x 10060] + [PVF (12 %, 6 year) x 19000] = (4.111x 10060) + (0.506 x 19000)

= $ 41356.66 + $ 9614 = $ 50970.66

NPV= 50970.66 - 50100 = $ 870.66

Let assume the discounting rate be 13 %

Present value of cash inflows at 13 % would be

[PVAF (13%, 6years) x 10060] + [PVF (13 %, 6 year) x 19000] = (3.997x 10060) + (0.480 x 19000) =

= $ 40209.82 + $ 9120 = $ 49329.82

NPV= 49329.82 - 50100 = ($ 770.18)

Now by interpolation , IRR would be

12 % + (870.66 - 0)x(13% - 12 %) / [870.66 - (-770.18)] = 12.53 %

Particulars Amount ($) Annual savings in part time help 5900 Added contribution margin from expanded sales (2600 dozen x 1.6) 4160 Annual cash inflows 10,060

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