Question

1. (30%) ABC company can invest $10 million in a new plant for producing bread jam. The plant has an expected life of 5 years, and expected sales are 6 million jars of jam a year. Fixed costs are $2 million a year, and variable costs are $1 per jar. The product will be priced at $2 per jar. The plant will be depreciated straight-line over 5 years to a salvage value of zero. The opportunity cost of capital is 10%, and the tax rate is 40%. a) What is project NPV under these base-case assumptions? b) What is NPV if variable costs turn out to be $1.20 per jar? c) What is the NPV if fixed costs turn out to be $1.5 million per year?

Answer 1

A.

Cost of Plant		$10,000,000		Depreciation per year		$2,000,000	(COST OF PLANT/EXPECTED LIFE)
Expected life (Years)		5		Discount rate		10%
Sales per year (No of Jar)		6,000,000		Tax Rate		40%
Fixed Cost per year		$2,000,000
Variable cost (per jar)		$1.0
Price per Jar		$2
				Years
Item	0	1	2	3	4	5
Sales per year	0	$12,000,000	$12,000,000	$12,000,000	$12,000,000	$12,000,000	(NO OF JAR SOLD PER YEAR * PRICE PER JAR)
Fixed cost per year	0	$2,000,000	$2,000,000	$2,000,000	$2,000,000	$2,000,000
Variable cost per year	0	$6,000,000	$6,000,000	$6,000,000	$6,000,000	$6,000,000	(NO OF JAR SOLD PER YEAR * VARIABLE COST PER JAR)
Operating Income	0	$4,000,000	$4,000,000	$4,000,000	$4,000,000	$4,000,000	(SALES PER YEAR - FIXED COST PER YEAR - VARIABLE COST PER YEAR)
Initial outlay	($10,000,000)	0	0	0	0	0
Depreciation	0	$2,000,000	$2,000,000	$2,000,000	$2,000,000	$2,000,000
Taxable income	0	$2,000,000	$2,000,000	$2,000,000	$2,000,000	$2,000,000	(OPERATIN INCOME - DEPRECIATION)
Tax	$0	$800,000	$800,000	$800,000	$800,000	$800,000	(TAXABLE INCOME * TAX RATE)
Net Cash Flow	($10,000,000)	$3,200,000	$3,200,000	$3,200,000	$3,200,000	$3,200,000	(TAXABLE INCOME - TAX + DEPRECIATION)

NPV
Year	Net cash flow	Discount factor	Present value
0	($10,000,000)	0.10	-$10,000,000.00	((NET CASH FLOW/(1+ DISCOUNT FACTOR)^ YEAR)
1	$3,200,000	0.10	$2,909,090.91
2	$3,200,000	0.10	$2,644,628.10
3	$3,200,000	0.10	$2,404,207.36
4	$3,200,000	0.10	$2,185,643.06
5	$3,200,000	0.10	$1,986,948.23
NPV			$2,130,517.66

B.

Cost of Plant		$10,000,000		Depreciation per year		$2,000,000	(COST OF PLANT/EXPECTED LIFE)
Expected life (Years)		5		Discount rate		10%
Sales per year (No of Jar)		6,000,000		Tax Rate		40%
Fixed Cost per year		$2,000,000
Variable cost (per jar)		$1.2
Price per Jar		$2
				Years
Item	0	1	2	3	4	5
Sales per year	0	$12,000,000	$12,000,000	$12,000,000	$12,000,000	$12,000,000	(NO OF JAR SOLD PER YEAR * PRICE PER JAR)
Fixed cost per year	0	$2,000,000	$2,000,000	$2,000,000	$2,000,000	$2,000,000
Variable cost per year	0	$7,200,000	$7,200,000	$7,200,000	$7,200,000	$7,200,000	(NO OF JAR SOLD PER YEAR * VARIABLE COST PER JAR)
Operating Income	0	$2,800,000	$2,800,000	$2,800,000	$2,800,000	$2,800,000	(SALES PER YEAR - FIXED COST PER YEAR - VARIABLE COST PER YEAR)
Initial outlay	($10,000,000)	0	0	0	0	0
Depreciation	0	$2,000,000	$2,000,000	$2,000,000	$2,000,000	$2,000,000
Taxable income	0	$800,000	$800,000	$800,000	$800,000	$800,000	(OPERATIN INCOME - DEPRECIATION)
Tax	$0	$320,000	$320,000	$320,000	$320,000	$320,000	(TAXABLE INCOME * TAX RATE)
Net Cash Flow	($10,000,000)	$2,480,000	$2,480,000	$2,480,000	$2,480,000	$2,480,000	(TAXABLE INCOME - TAX + DEPRECIATION)

NPV
Year	Net cash flow	Discount factor	Present value
0	($10,000,000)	0.10	-$10,000,000.00	((NET CASH FLOW/(1+ DISCOUNT FACTOR)^ YEAR)
1	$2,480,000	0.10	$2,254,545.45
2	$2,480,000	0.10	$2,049,586.78
3	$2,480,000	0.10	$1,863,260.71
4	$2,480,000	0.10	$1,693,873.37
5	$2,480,000	0.10	$1,539,884.88
NPV			-$598,848.81

C.

Cost of Plant		$10,000,000		Depreciation per year		$2,000,000	(COST OF PLANT/EXPECTED LIFE)
Expected life (Years)		5		Discount rate		10%
Sales per year (No of Jar)		6,000,000		Tax Rate		40%
Fixed Cost per year		$1,500,000
Variable cost (per jar)		$1.0
Price per Jar		$2
				Years
Item	0	1	2	3	4	5
Sales per year	0	$12,000,000	$12,000,000	$12,000,000	$12,000,000	$12,000,000	(NO OF JAR SOLD PER YEAR * PRICE PER JAR)
Fixed cost per year	0	$1,500,000	$1,500,000	$1,500,000	$1,500,000	$1,500,000
Variable cost per year	0	$6,000,000	$6,000,000	$6,000,000	$6,000,000	$6,000,000	(NO OF JAR SOLD PER YEAR * VARIABLE COST PER JAR)
Operating Income	0	$4,500,000	$4,500,000	$4,500,000	$4,500,000	$4,500,000	(SALES PER YEAR - FIXED COST PER YEAR - VARIABLE COST PER YEAR)
Initial outlay	($10,000,000)	0	0	0	0	0
Depreciation	0	$2,000,000	$2,000,000	$2,000,000	$2,000,000	$2,000,000
Taxable income	0	$2,500,000	$2,500,000	$2,500,000	$2,500,000	$2,500,000	(OPERATIN INCOME - DEPRECIATION)
Tax	$0	$1,000,000	$1,000,000	$1,000,000	$1,000,000	$1,000,000	(TAXABLE INCOME * TAX RATE)
Net Cash Flow	($10,000,000)	$3,500,000	$3,500,000	$3,500,000	$3,500,000	$3,500,000	(TAXABLE INCOME - TAX + DEPRECIATION)

NPV
Year	Net cash flow	Discount factor	Present value
0	($10,000,000)	0.10	-$10,000,000.00
1	$3,500,000	0.10	$3,181,818.18
2	$3,500,000	0.10	$2,892,561.98
3	$3,500,000	0.10	$2,629,601.80
4	$3,500,000	0.10	$2,390,547.09
5	$3,500,000	0.10	$2,173,224.63
NPV			$3,267,753.69