Question

Problem Set 1

You are the owner of a large data-services firm and are deciding on the purchase of a new hardware cooling system that you expect will yield $233,300 in cost-savings per year for the next 15 years. The installation of this cooling system will cost $3,000,000.

1. At face value, does this system seem profitable? By how much?

2. Assume that your company uses a discount rate of 6%.

a. What is the Net Present Value (NPV) of this project?

b. How does the NPV of this project change as you assume a higher or lower discount rate? Why?

c. What is the IRR/ROI of this project? d. How much should the yearly cost-savings be in order to break even? i. (hint) use goal-seek/what-if analysis

3. Suppose that you decide to finance the purchase of this system through a loan from the bank. The bank is willing to loan this money over an 8 year term at an interest rate of 4% per year. a. Using a 70/30 debt-to-equity ratio, what is the NPV of this project? i. (hint) calculate the yearly payment using excel function “PMT” b. How does the NPV of this project change if a larger portion is financed through equity (e.g. debt-to-equity ratio of 60/40)? Why?

Answer 1

	1	At face value (without using discount factors ) this system seems profitable
	a	Total cost savings =233300*15=	$3,499,500
	b	System cost	$3,000,000
	c=a-b	Profit	$499,500
	2	Net Present Value (NPV)
	Rate	Discount rate	6%
	Nper	Number of years	15
	Pmt	Annual Savings	$233,300
	PV	Present Value of annual savings	$2,265,868	(Using PV function of excel withRate=6%, Nper=15, Pmt=-233300)
	I	Initial Investment	$3,000,000
	NPV=PV-I	Net Present Value of the project	($734,132)
	b	NPV will be lower if discount rate is higher
		NPV will be higher if discount rate is lower
		Because,
		Present Value (PV)of Cash flow:
		(Cash flow)/((1+i)^N)
		i=discount rate , N=Year of cash flow
		If I increases , PV decreases
		If I decreases , PV increases
		For example:
		If discount rate is 1%	1%
	PV	Present Value of annual savings	$3,234,717	(Using PV function of excel withRate=1%, Nper=15, Pmt=-233300)
	NPV=PV-I	Net Present Value of the project	$234,717
		If discount rate is 10%	10%
	PV	Present Value of annual savings	$1,774,498	(Using PV function of excel withRate=10%, Nper=15, Pmt=-233300)
	NPV=PV-I	Net Present Value of the project	($1,225,502)
c	PV	For Break Even, PV should be equal to I=	$3,000,000
	Rate	Discount Rate	6%
	Nper	Number of years	15
	PMT	Required Annual Savings	$308,888	(Using PMT function of excel with Rate=6%, Nper=15, Pv=-3000000)