There are many typical Net Present Value (NPV) problems. One is the “repair or replace” scenario. Here is a fictitious example.

Good Ol’ Amalgamated (GOA) of Arizona has an aging fleet of 1-ton trucks which are eating up profits because of high maintenance, unreliability, and bad fuel economy. GOA does inspections for the local phone company’s overhead facilities. Examine the assumptions below. One column is for the “Buy New Truck” alternative. The other is for the “Keep Old Truck” choice.

Should GOA repair the current trucks or replace them?

Use NPV to make your decision. Do it on a single truck analysis.

Is this an example of mutual exclusivity?

Yes. You will either buy and new truck or keep the old one, but NOT BOTH. This is the definition of mutually exclusive situation.

What is the rule for mutual exclusivity when doing NPV?

The rule is all alternatives, MUST BE ON THE SAME TIME FRAME. Note the life of the new truck is 10 years. The life of the old truck is five years.

Is this a problem?

How do you handle the different life expectancy?

One possible approach is to use a five year analysis and assume the old truck is a boat anchor after five years. Also assume the new truck is sold after five years. This makes both alternatives the same. At the end of the analysis you have no truck. That is fair.

To set up the spreadsheet, consider the line items shown below.

BBO PP36 Repair or replace. NPV

The line items in blue are cash and part of the “Net Cash Flows “line.

Why is there two lines at the bottom to calculate NPV, Year 1 thru 5 and the Initial Investment?

Excel has a quirk. The NPV Function formula “=NPV (rate,range)” moves the range one year back in time. So the range must not include the initial investment.

Why is there a line item for book Value?

This is necessary to keep track of the book value as depreciation eats into it. At Year 5, you will sell the new truck. The book value should be subtracted from the sales price to figure the capital gains. There is a 23.8% capital gains tax to pay. That is the last blue line item.

Assume the usual general assumptions: Tax Rate is 40%. Use straight line depreciation, not MACRS.  Use 10% as the Weighted Average Cost of Capital and use it as the opportunity cost of capital.

SOLUTION:

You should get a new truck NPV of about ($72.5K and a old truck NPV of a little north of ($78K). This means the new truck is less negative than than the old truck. Enjoy your new ride!

The solution spreadsheet is available here.