Question

V. Rahr and Sons is a Fort Worth brewery founded by Fritz Rahr, a Neeley undergraduate and MBA. Currently the company makes Rahr Blonde Lager, Rahr’s Red, and Ugly Pug brews. They are considering a new beer, Frog Princess, with which to celebrate their ties to TCU. The project includes an initial outlay of $750,000 for the purchase of capital equipment that will be depreciated straight line to zero over six years.

Sales are expected to be $400,000 in years 1-3 and $600,000 in years 4-6. Production costs during years 1-6 are as follows: fixed costs (not including depreciation) are expected to be $150,000 per year; variable costs per year will be 40% of sales. The project will require an initial investment in NWC of 200,000 in year 0.

Beyond year six, the company expects that sales and unlevered net income in year seven will be 4% higher than that in year 6, and will continue growing at 4% per year infinitely. Additionally, in year 7 and beyond, new capital expenditures net of depreciation, and increases in NWC, combined, will be 6% of sales. Assume the marginal tax rate is 21%. The appropriate discount rate is 8%.

What is the NPV of the project? What is the IRR? Should the project be undertaken?

Answer 1

		Year		0	1	2	3	4	5	6
	Initial Outflow			-750000
	Increase in NWC			-200000
		Sales			400000	400000	400000	600000	600000	600000
	Less:	Variable cost			160000	160000	160000	240000	240000	240000
	Less:	Fixed cost			150000	150000	150000	150000	150000	150000
	Less:	Depreciation			125000	125000	125000	125000	125000	125000
		PBT			275000	275000	275000	475000	475000	475000
	Less:	Tax @ 21%			57750	57750	57750	99750	99750	99750
		Post tax increase in earnings			217250	217250	217250	375250	375250	375250
	Add:	Depreciation			125000	125000	125000	125000	125000	125000
		Incremental cashflows			342250	342250	342250	500250	500250	500250
		PV Factor @ 8%%		1	0.925926	0.857339	0.793832	0.73503	0.680583	0.63017
		PV of cashflows		-950000	316898.1	293424.2	271689.1	367698.7	340461.7	315242.4
		PV of 1st 6 years FCF			955414.2
		PV of FCF beyond 6 years =			FCF7/(Kc-g)
		FCF7 =
		Sales (7th year)	600000 x (1.04) =		624000
		Variable cost			249600
		Fixed cost			150000
		Depreciation			0
		PBT			224400
		Tax @ 21%			47124
		Post tax increase in earnings			177276
		Depreciation			0
		Incremental cashflows			177276
		Less: Net Investments			37440
		FCF7			139836
		Kc-g =	0.08-0.04 =		0.04
		PV of FCF beyond 6 years =			3495900
		PV of cashflows =			4451314
		NPV =			4451314
		For IRR -
		At IRR NPV =0
		r		NPV
		52%		8014.404
		r		0
		53%		-9211.00
		Using linear Interpolation -
		r-52/53-52 =		0-8014.404/-9211-8014.404
		r-52 =		0.465267
		r =		52.46527
		Project is acceptable as it has positive NPV and the IRR is more then required return.