Question

Your firm is considering developing an apartment complex. The firm owns land that could be used for the project; it was bought last year for $500,000. Real estate has gone up sharply in the last year: the land could be sold today for $625,000. Real estate values are expected to increase at 5 percent per year going forward from today. The permitting fees and sewage infrastructure development required for development cost $250,000 (the bill is due now and the project could not have proceeded without this work).  This expense will be depreciated over the 30-year life of the project.

The apartment buildings will be four-plex townhouses (i.e. buildings that have four apartments each). Each apartment will rent for $1,000 per month. Initially, your firm will build 20 townhouses.

Each townhouse will cost $120,000 and will be depreciated straight-line to zero over the 30-year life of the project. In addition, the project will require a net working capital investment of $20,000 today—this amount will be recovered at the end of the project. At the end of the project, the townhouses will be completely trashed—the plan is to demolish them and sell the land. Demolition costs will be $150,000 before tax. Your variable cost is $1,250 per year per townhouse. Fixed costs are $130,000 per year. Your firm’s tax rate is 34% and the cost of capital is 10% .

Find the NPV

{Hint:   In year 30 the land will be unencumbered.

With increases of 5 percent per year, the land will be worth $2,701,213.98 After tax, our after-tax opportunity benefit is

$2,701,213.98 – (2,701,213.98 -500,000) ×.34 = $1,952,801.23.The demolition cost is$150,000×(1 –.34)}

Answer 1

	Cost of land after 30 years =			625000 x (1.05^30)
				2701214
	Tax on sale of land =
	Carrying value			500000
	Value of land			2701214
	Capital gain			2201214
	Tax on gain =			748412.8
	Post tax salvage value of land			1952801
	Post Tax cost of demolition cost			99000
			Initial cashflows	Annual operating cashflows	Terminal cashflows
	Cost of building townhouse	120000 x 20	-2400000
	Increase in NWC		-20000
	Rent from appartments	20 x 4 x 1000 x 12		960000
	Less: Variable cost	1250 x 20		25000
	Less: Fixed cost			130000
	Less: Depreciation	(250000+2400000)/30		88333.33
	EBT			716666.7
	Less: Tax @ 34%			243666.7
	Post Tax income			473000
	Add: Depreciation			88333.33
	CFAT			561333.3
	Post Tax cost of demolition cost				-99000
	Post tax salvage value of land				1952801
	Recovery of NWC				20000
	Net Cashflows		-2420000	561333.3	1873801
	PV Factors		1	9.43	0.057309
	PV of NCF		-2420000	5291641	107384.8
	NPV =		2979026