Question

Aria Acoustics, Inc. (AAI), projects unit sales for a new seven-octave voice emulation implant as follows:

• ▪ The company has spent $150,000 for a marketing study to evaluate the project. The study shows that the company will sell 75,000 units per year for 6 years. In addition, the company will lose sales of 12,000 units per year of its high priced voice emulation implant.

• ▪ The variable production costs for new voice emulation implant are $260 per unit, and the units are priced at $380 each. Total fixed costs are $600,000 per year.

• ▪ The high-priced voice emulation implant has production costs are $440 per unit, and the units are priced at $640 each.

• ▪ Production of the implants will require $2,000,000 in net working capital to start, and that amount will be returned at the end of the project.

• ▪ The equipment will cost $20,000,000, and will be depreciated on a straight- line basis to $8,000,000 in 6 years. At the end of 6th year, the equipment can be scrapped for $7,000,000

• ▪ AAI is in the 20 percent marginal tax bracket.

• ▪ The cost of capital is 12% per year.

• ▪ The board of directors of AAI decided to only invest in those projects with

  less than 4.5 years of payback period.

  What is the NPV, IRR and payback period of this project? Should we accept or reject this project?

Answer 1

1]	INITIAL INVESTMENT:
	Cost of equipment	$      20,000,000
	+Increase in NWC	$        2,000,000
	=Initial investment	$      22,000,000
2]	INCREMENTAL ANNUAL OPERATING CASH FLOWS:
	Contribution margin from new implants = 75000*(380-260) =	$        9,000,000
	-Contribution margin lost on existing high priced implants = 12000*(640-440) =	$        2,400,000
	-Total fixed costs	$            600,000
	-Depreciation [(20000000-8000000)/6]	$        2,000,000
	=Incremental NOI	$        4,000,000
	-Tax at 20%	$            800,000
	=NOPAT	$        3,200,000
	+Depreciation	$        2,000,000
	=Annual operating cash flow	$        5,200,000
3]	TERMINAL NON-OPERATING CASH FLOW:
	After tax [tax shield] salvage value at EOY 6 = 7000000+(8000000-7000000)*20% =	$        7,200,000
	Recovery of NWC	$        2,000,000
	Terminal non operating cash flow	$        9,200,000
4]	Payback period = Initial investment/Annual OCF = 22000000/5200000 =	4.23	Years	Answer
5]	CALCULATION OF NPV:
	PV of annual OCF = 5200000*(1.12^6-1)/(0.12*1.12^6) =	$      21,379,318
	+PV of terminal non operating cash flow = 9200000/1.12^6 =	$        4,661,006
	Sum of PVs of cash inflows	$      26,040,324
	Less: Initial investment	$      22,000,000
	NPV	$        4,040,324		Answer
6]	CALCULATION OF IRR:
	IRR is that discount rate for which NPV = 0. It is to
	be found out by trial and error, by varying the
	discount rate, till 0 NPV results.
	Discounting at 17%:
	PV of annual OCF = 5200000*(1.17^6-1)/(0.17*1.17^6) =	$      18,663,761
	+PV of terminal non operating cash flow = 9200000/1.17^6 =	$        3,586,515
	Sum of PVs of cash inflows	$      22,250,276
	Less: Initial investment	$      22,000,000
	NPV	$            250,276
	Discounting at 18%:
	PV of annual OCF = 5200000*(1.18^6-1)/(0.18*1.18^6) =	$      18,187,533
	+PV of terminal non operating cash flow = 9200000/1.18^6 =	$        3,407,970
	Sum of PVs of cash inflows	$      21,595,503
	Less: Initial investment	$      22,000,000
	NPV	$          (404,497)
	As 0 NPV will lie between discount rates of 17%
	and 18%< IRR will also lie between those rates.
	By simple interpolation, IRR = 17%+1%*(250276)/(250276+404497) =	17.38%		Answer