Question

Problem 7 (20 points) Innovation Company is thinking about marketing a new software product Up-front costs to market and develop the product are $5 million. The product is expected to generate profits of $1 million per year for 10 years. The company will have to provide product support expected to cost $100,000 per year in perpetuity. Assume all profits and expenses occur at the end of the year. what is the NPV of this investment if the cost of capital is 6%? Should the firm undertake the project? (10 points) Repeat the analysis for discount rates of 2% and 11%. (10 points) a. b.

Answer 1

Cost to develop and market = $5 million

At 6% cost of capital,

Maintenance cost to perpetuity = 0.1/0.06 = $1.67 million

$NPV = -Initial Investment + \sum_{t=1}^{n} C_{t}/(1+r)^t - Cost of Maintenance$

NPV = $2.36 - 1.67

NPV = $0.69 million

At 2% cost of capital,

Maintenance cost to perpetuity = 0.1/0.02 = $5 million

$NPV = -Initial Investment + \sum_{t=1}^{n} C_{t}/(1+r)^t - Cost of Maintenance$

NPV = 3.98 - 5

NPV = -$1.02 million

At 11% cost of capital,

Maintenance cost to perpetuity = 0.1/0.11 = $0.91 million

$NPV = -Initial Investment + \sum_{t=1}^{n} C_{t}/(1+r)^t - Cost of Maintenance$

NPV = 0.89 - 0.91

NPV = -$0.02 million

Answer 2

Multiple Internal Rates of Return: Problem 6-13 in Berk   and DeMarzo (2010)
Cost of   capital	6%	Data Table: NPV of the   project as a function of the discount rate
upfront   costs	-$5.00
Annual   profits	$1.00		$0.69
Annual   support	-$0.10	1%	-$5.53
Production   period, Years	10	2%	-$1.02
		3%	$0.20
PV   support	-$1.67	4%	$0.61
PV of   profit before depreciation	$7.36	5%	$0.72
NPV	$0.69	6%	$0.69
		7%	$0.60
		8%	$0.46
		9%	$0.31
		10%	$0.14
		11%	-$0.02
		12%	-$0.18
		13%	-$0.34
		14%	-$0.50
		15%	-$0.65
		16%	-$0.79
		17%	-$0.93
		18%	-$1.06
		19%	-$1.19
		20%	-$1.31