# NET PRESENT VALUE Harvard Case Solution & Analysis

Revision : NET PRESENT VALUE

In this case, NPV is calculated by comparing the cost and saving result in the implementation of the new security system.

Cost

The following cost was incurred in the implementation of new security system.

• Initial investment of \$250,000 at the start of 2009
• Annual maintenance cost of \$25,000 from 2009 to 2013

Note: amount of initial investment and annual maintenance cost were given in the case (see Cost and Discount Rate heading in the case)

• Material cost of each new badge is \$7, whereas if the new security system implements so there will be no need to carry two badges; one for Terminal 2 and the other badge for the rest of the airport. So it will save \$2 per user because SFO will eliminate the need for duplicate badges. Net cost will show only \$5 (\$7-\$2) in calculating the net present value.
• Total material cost is calculated by multiplying the processing cost per badge of \$5 into total processing badge during the year (see Material Cost heading in the case).

Saving

Reduction in cost of processing the badge to \$35 (see Labor Costs heading in the case) and number of processing identity card is expected to grow at 5% per year in each year (see EXHIBIT 2 in the spreadsheet).

Present value

Cost incurred is subtracted from saving in order to get the present value of the project. Present value is calculated as:

Discount factor

Discount factor was given in question that is 10% (see Costs and Discount Rate heading in the case).

Net present value

NPV is calculated by multiplying the discount factor with the present value. Formula of NPV is:

Internal rate of return

IRR is calculated by taking a positive and negative NPV. Positive NPV has already been calculated when discount is 10%. It needs to discount that rate that gives negative NPV.

The formula of IRR is

Where

a = lower discount rate

b = higher discount

NPV(a) = positive net present value

NPV(b) = negative net present value

Steps to follow:

• Lower discount rate (a) was given in the case
• NPV(a) is already calculated as above
• Select appropriate rate in which NPV of the investment will be negative
• Calculate the NPV(b) at selected appropriate rate
• Put all the above values in IRR formula

See EXHIBIT 3 in the spreadsheet for IRR

Payback period

With Discount

Offsetting discounted saving of each year from the total cost, and when cost gets zero, so number of period will be counted in years.

Steps to follow: