Question

Wendell’s Donut Shoppe is investigating the purchase of a new $18,600 donut-making machine. The new machine would permit the company to reduce the amount of part-time help needed, at a cost savings of $3,800 per year. In addition, the new machine would allow the company to produce one new style of donut, resulting in the sale of 1,000 dozen more donuts each year. The company realizes a contribution margin of $1.20 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? (Round your final answer to the nearest whole dollar amount.)

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 answer to whole decimal place i.e. 0.123 should be considered as 12%.)

4. In addition to the data given previously, assume that the machine will have a $9,125 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.) (Round your answer to whole decimal place i.e. 0.123 should be considered as 12%.)

Answer 1

1. Annual Cash flows of the machine

= Savings + Extra contribution

= 3800 + (1000 x 1.20)

= $5,000.00

2. Factor of the internal rate of return = Investment / Annual cash inflow
= $18,600 / $5000 = 3.720
Looking from the present value annuity table , look at a factor of 3.720 that falls closest to.

3. At IRR,

NPV is zero.

So let us calculate the NPV at different rates

NPV of the project @ 15% is:

Year	Total Benefits/ (Outflow)	PV of $1 @ 15%	P.V.
0	-18,600.00	1.0000	-18,600.00
1	5,000.00	0.8696	4,347.83
2	5,000.00	0.7561	3,780.72
3	5,000.00	0.6575	3,287.58
4	5,000.00	0.5718	2,858.77
5	5,000.00	0.4972	2,485.88
6	5,000.00	0.4323	2,161.64
	SUM (NPV)		322.41

NPV @ 16% is:

Year	Total Benefits/ (Outflow)	PV of $1 @ 16%	P.V.
0	-18,600.00	1.0000	-18,600.00
1	5,000.00	0.8621	4,310.34
2	5,000.00	0.7432	3,715.81
3	5,000.00	0.6407	3,203.29
4	5,000.00	0.5523	2,761.46
5	5,000.00	0.4761	2,380.57
6	5,000.00	0.4104	2,052.21
	SUM (NPV)		-176.32

IRR = 15 + 322.41 / (322.41 + 176.32) = 15.65% i.e. 16%

4.

Including the Salvage Value,

NPV @ 20% is:

Year	Total Benefits/ (Outflow)	PV of $1 @ 20%	P.V.
0	-18,600.00	1.000	-18600.00
1	5,000.00	0.8333	4166.67
2	5,000.00	0.6944	3472.22
3	5,000.00	0.5787	2893.52
4	5,000.00	0.4823	2411.27
5	5,000.00	0.4019	2009.39
6	14,125.00	0.3349	4730.43
	SUM (NPV)		1083.49

NPV @ 19% is:

Year	Total Benefits/ (Outflow) (a)	Discounting Factor (b ) = (1/1+r)^n	P.V. (c ) = (axb)
0	-18,600.00	1.000	-18600.00
1	5,000.00	0.8065	4032.26
2	5,000.00	0.6504	3251.82
3	5,000.00	0.5245	2622.44
4	5,000.00	0.4230	2114.87
5	5,000.00	0.3411	1705.54
6	14,125.00	0.2751	3885.60
	SUM (NPV)		-987.48

IRR = 20 + (1083.49 / (1083.49 + 987.48))x 4 = 22%