Question

Wendell’s Donut Shoppe is investigating the purchase of a new $48,300 donut-making machine. The new machine would permit the company to reduce the amount of part-time help needed, at a cost savings of $6,800 per year. In addition, the new machine would allow the company to produce one new style of donut, resulting in the sale of 1,700 dozen more donuts each year. The company realizes a contribution margin of $2.00 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 sales Annual cash inflows $0 2. Find the internal rate of return promised by the new machine to the nearest whole percent.

	Internal Rate of Return Choose Numerator: / Choose Denominator: = Factor Number of years Internal rate of return / = Factor / = %

3.	In addition to the data given previously, assume that the machine will have a $15,685 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.) Internal rate of return %

Answer 1

	Purchase	$    48,300.00
	Cost saving	$      6,800.00
	New donut sale	1700	dozen
	Contribution margin per dozen	$               2.00
	New machine life	6.00
1	Annual saving	$      6,800.00
	Added CM from expanded sale	$      3,400.00	(1700*2)
	Annual cash inflow	$    10,200.00
2	Numrator	Denominator	Factor	No. of years	IRR
	$ 48,300.00	$    10,200.00	4.7353	6	7%	(rounded off)
	At 7% Sum of PV for 7 years-1=	4.7665
	At 8% Sum of PV for 7 years-1=	4.6229
	IRR=Low Rate+((Sum of PVF at low rate-Sum of PVF at IRR)/(Sum of pvf at low rate-sum of pvf at higher rate))*Difference in rate	7.22	(7+((4.7665-4.7353)/(4.7665-4.6229))*(8-7))
3	IRR
	Yr		PV Factor@10%		PV Factor@15%
	0	-48300	1	$ (48,300.00)	1	$ (48,300.00)
	1	10200	0.9091	$      9,272.73	0.8696	$      8,869.57
	2	10200	0.8264	$      8,429.75	0.7561	$      7,712.67
	3	10200	0.7513	$      7,663.41	0.6575	$      6,706.67
	4	10200	0.6830	$      6,966.74	0.5718	$      5,831.88
	5	10200	0.6209	$      6,333.40	0.4972	$      5,071.20
	6	25885	0.5645	$   14,611.41	0.4323	$   11,190.80
		(10200+15685)	NPV	$      4,977.43		$   (2,917.22)
	IRR=Lower rate+((NPV at lower rate)/(NPV at lower rate-NPV at higher rate))*Difference in rate	13.15	=13% rounded off