Question

You are analyzing a proposal to build a new plant. Use the following information, a cost of capital of 14%, a capital gains tax rate of 5%, and an income tax rate of 40%. Land for the plant will be purchased today for $500. At the beginning of the second year (one year from today), $1,000 will be spent for the construction of the building. The equipment will be purchased at the beginning of the third year at a cost of $1,500. Operations will begin at the beginning of the fourth year, at which time a working capital investment of $500 will be required. Cash flows from operations will occur for 10 years and will be received at the end of each year. The building construction cost and the equipment will be depreciated on a straight-line basis, with zero expected salvage for each. Assume that you can't depreciate the building and equipment until you use them in operations. After 10 years of operation, you expect to sell the land for $600. Annual incremental revenue will be $2,000 for the first 5 years of operation, and $2,500 for the last 5 years of operation. Fixed operating costs (excluding depreciation) will be $200 each year. Annual variable operating costs will be 25% of annual revenue. The building and equipment both qualify for a 10% investment tax credit that can be received at the time each is purchased. This investment tax credit will not affect the amount you can depreciate.

1. Calculate the NPV

2. Calculate the IRR

Answer 1

		Present Value (PV) of Cash Flow:
		(Cash Flow)/((1+i)^N)
		i=Cost of Capital =14%=0.14
		N=Year of Cash Flow(End of year)
		Before tax sales value of land	$600
		Capital gain on   sale	$100	(600-500)
		Depreciation recapture	$500
		Tax on capital gain	($5)	(100*0.05)
		Tax on depreciation recapture	($200)	(500*0.4)
		Net Cash flow from sale of land	$395	(600-5-200)
		YEAR WISE CASH FLOWS
	N	End of Year	0	1	2	3	4	5	6	7	8	9	10	11	12	13
	a	Purchase of Land	($500)
	b	Construction of building		($1,000)
	c	Purchase of Equipment			($1,500)
	d	Cash flow for working capital need				($500)
		Annual Cash Flows:
	e=1000/10	Depreciation -building					($100)	($100)	($100)	($100)	($100)	($100)	($100)	($100)	($100)	($100)
	f=1500/10	Depreciation -equipment					($150)	($150)	($150)	($150)	($150)	($150)	($150)	($150)	($150)	($150)
	g	Annual incremental revenue					$2,000	$2,000	$2,000	$2,000	$2,000	$2,500	$2,500	$2,500	$2,500	$2,500
	h=-g*0.25	Annual variable cost					-$500	-$500	-$500	-$500	-$500	-$625	-$625	-$625	-$625	-$625
	j=g+h	Annual contribution					$1,500	$1,500	$1,500	$1,500	$1,500	$1,875	$1,875	$1,875	$1,875	$1,875
	k	Fixed operating cost					-$200	-$200	-$200	-$200	-$200	-$200	-$200	-$200	-$200	-$200
	l=j+k+e+f	Earning before tax					$1,050	$1,050	$1,050	$1,050	$1,050	$1,425	$1,425	$1,425	$1,425	$1,425
	m=-0.4*l	Income tax expense(40%)					-$420	-$420	-$420	-$420	-$420	-$570	-$570	-$570	-$570	-$570
	n=l+m	Net income					$630	$630	$630	$630	$630	$855	$855	$855	$855	$855
	p=n-e-f	Annual Operating Cash flow(Add Depreciation to net income)					$880	$880	$880	$880	$880	$1,105	$1,105	$1,105	$1,105	$1,105
		Other one time cash flows:
	q=-d	Release of working capital														$500
	r=-0.1*b	Investment tax credit -building		$100
	s=-0.1*c	Investment tax credit -equipment			$150
	t	Net Cash flow from sale of land														$395
	CF=a+b+c+d+p+q+r+s+t	NET CASH FLOW IN EACH YEAR	($500)	($900)	($1,350)	($500)	$880	$880	$880	$880	$880	$1,105	$1,105	$1,105	$1,105	$2,000	SUM
	PV=CF/(1.14^N)	Present Value (PV) of Cash Flow:	($500)	-$789	-$1,039	-$337	$521	$457	$401	$352	$308	$340	$298	$261	$229	$364	$866
	NPV=Sum of PV	Net Present Value(NPV)	$866
		Internal Rate of Return (IRR)	19.18%	(Using IRR function of excel over the NET CASH FLOWS)