Question

Please show all work.

Mahya Fashions Inc. can invest $5 million in a new plant for producing invisible makeup.  The plant has an expected life of 5 years, and expected sales are 5 million jars of make-up a year.  Fixed costs are $2 million a year, and variable costs are $1 per jar. The product will be priced a $2 per jar. Plant requires $50,000 in additional net working capital. The plant will be depreciated straight-line over 5 years to a salvage value of $50,000. Using the WACC you have found above and the tax rate of 20 percent, please answer the following:

            a.         What is project NPV and IRR under these base-case assumptions? Accept or Reject?

            b.         What is NPV if variable costs turn out to be $1.20 per jar?

            c.         What is NPV if fixed costs turn out to be $1.5 million per year?

            d.         At what price per jar would the project NPV equal zero?

WACC is 10.5%

Answer 1

a]	INITIAL INVESTMENT:
	Cost of the plant	$      5,000,000
	+Net working capital	$            50,000
	=Initial investment	$      5,050,000
	ANNUAL OPERATING CASH FLOWS:
	Sales =5000000*2 =	$    10,000,000
	-Variable costs =5000000*1=	$      5,000,000
	-Fixed Costs	$      2,000,000
	-Depreciation = (5000000-50000)/5 =	$          990,000
	=NOI	$      2,010,000
	-Tax at 20%	$          402,000
	=NOPAT	$      1,608,000
	+Depreciation	$          990,000
	=Annual operating cash flow	$      2,598,000
	TERMINAL NON-OPERATING CASH FLOWS:
	After tax salvage value	$            50,000
	[No tax as Book value=Sale value]
	Recovery of NWC	$            50,000
	Terminal non-operating cash flows	$          100,000
	CALCULATION OF NPV:
	PV of annual cash flows = 2598000*(1.104^5-1)/(0.105*1.105^5) =	$      9,723,946
	PV of terminal non-operating cash flows = 100000/1.105^5 =	$            60,700
	Total PV of cash inflows	$      9,784,646
	Less: Initial investment	$      5,050,000
	NPV	$      4,734,646
	CALCULATION OF IRR:
	IRR is that discount rate for which NPV = 0. It has to be found out
	Discount rate of 43%:
	PV of annual cash flows = 2598000*(1.43^5-1)/(0.43*1.43^5) =	$      5,031,467
	PV of terminal non-operating cash flows = 100000/1.43^5 =	$            16,723
	Total PV of cash inflows	$      5,048,190
	Less: Initial investment	$      5,050,000
	NPV	$            (1,810)
	Discount rate of 42%:
	PV of annual cash flows = 2598000*(1.42^5-1)/(0.42*1.42^5) =	$      5,114,323
	PV of terminal non-operating cash flows = 100000/1.42^5 =	$            17,320
	Total PV of cash inflows	$      5,131,643
	Less: Initial investment	$      5,050,000
	NPV	$            81,643
	As 0 NPV falls between 42% and 43%, IRR also falls between those
	rates.
	By simple interpolation, IRR = 42%+1%*81643/(81643+1810) =	42.98%
b]	ANNUAL OPERATING CASH FLOWS:
	Sales =5000000*2 =	$    10,000,000
	-Variable costs =5000000*1.2=	$      6,000,000
	-Fixed Costs	$      2,000,000
	-Depreciation = (5000000-50000)/5 =	$          990,000
	=NOI	$      1,010,000
	-Tax at 20%	$          202,000
	=NOPAT	$          808,000
	+Depreciation	$          990,000
	=Annual operating cash flow	$      1,798,000
	PV of annual cash flows = 1798000*(1.105^5-1)/(0.105*1.105^5) =	$      6,729,659
	PV of terminal non-operating cash flows = 100000/1.105^5 =	$          600,930
	Total PV of cash inflows	$      7,330,589
	Less: Initial investment	$      5,050,000
	NPV	$      2,280,589
c]	ANNUAL OPERATING CASH FLOWS:
	Sales =5000000*2 =	$    10,000,000
	-Variable costs =5000000*1=	$      5,000,000
	-Fixed Costs	$      1,500,000
	-Depreciation = (5000000-50000)/5 =	$          990,000
	=NOI	$      2,510,000
	-Tax at 20%	$          502,000
	=NOPAT	$      2,008,000
	+Depreciation	$          990,000
	=Annual operating cash flow	$      2,998,000
	PV of annual cash flows = 2998000*(1.105^5-1)/(0.105*1.105^5) =	$    11,221,089
	PV of terminal non-operating cash flows = 100000/1.105^5 =	$          600,930
	Total PV of cash inflows	$    11,822,019
	Less: Initial investment	$      5,050,000
	NPV	$      6,772,019
d]	For 0 NPV, the PV of total after tax annual sales for
	the 5 years should be lower by the NPV of $4860556.
	Therefore, annual after tax sales should be lower by = 4860556*0.105*1.105^5/(1.105^5-1) =	$      1,298,621
	Before tax annual sales should be lower by = 1298621/0.80 =	$      1,623,277
	Price per jar should be lower by 1623277/5000000 =	$            0.3247
	Therefore, price for NPV = 2-0.3247 =	$            1.6753
	VERIFICATION:
	ANNUAL OPERATING CASH FLOWS:
	Sales =5000000*1.68 =	$      8,400,000
	-Variable costs =5000000*1.0=	$      5,000,000
	-Fixed Costs	$      2,000,000
	-Depreciation = (5000000-50000)/5 =	$          990,000
	=NOI	$          410,000
	-Tax at 20%	$            82,000
	=NOPAT	$          328,000
	+Depreciation	$          990,000
	=Annual operating cash flow	$      1,318,000
	PV of annual cash flows = 1318000*(1.105^5-1)/(0.105*1.105^5) =	$      4,933,087
	PV of terminal non-operating cash flows = 100000/1.105^5 =	$            60,700
	Total PV of cash inflows	$      4,993,787
	Less: Initial investment	$      5,050,000
	NPV	$          (56,213)
	NPV is negative due to rounding off of price per unit for 0 NPV.