[HOW TO] NPV Tables For Making Decisions

[Millenial_Kid5K1]

Hello all,

I wanted to share one of my favorite tools for making financial decisions: Net present value (NPV) tables.

What you can do with an NPV table:

1. Compare two options where money is the only deciding factor, e.g.:
2. Deciding what car to buy
3. Deciding whether to buy a house or rent
4. Deciding whether to invest in product A or B(or neither)

Limitations of NPV tables:

1. You have to have some internal rate of return (IRR), which represents the best return on your money you think you'd get if you invested it somewhere else. This can represent the stock market, bonds, or the average rate of growth of your business.
   
2. You can't make conceptual decisions about your life where there are abstract variables, such as the decision to get a job or be an entrepreneur
3. You can't easily incorporate "odds" into your calculation, for much the same reason as point 2 above. There are ways to do math related to appetite for risk, but I've yet to see a way to rectify these with a simple NPV table.

Concepts:

Inflation - The percentage that your money becomes less useful year over year. This might be the average increase in cost of groceries since 1999, the consumer price index, or you could use a standard 3%.

Internal Rate of Return (IRR) - This is the percentage you could make on a baseline investment year over year with relatively little risk. Many companies use 9.8%, which is supposed to approximate the best investments available to large companies(unrelated to company growth). This is used to discount future money.

I will construct a concrete example to help you learn. Let's consider buying a car. In this case, we're only interested in what will get us from point A to point B for about 10 years. The two options we're considering are a 2007 Toyota Prius, and a 2003 Toyota Corolla, both with about 130,000 miles.

https://www.autotrader.com/cars-for-sale/vehicledetails.xhtml?listingId=460140381

Cars for Sale: Used 2003 Toyota Corolla CE for sale in Norcross, GA 30071: Sedan Details - 456638758 - Autotrader

The first thing with an NPV table is to define our parameters:

1. We'll take our IRR as 9.8%. It could be much, much higher if your business is growing quickly(e.g. 150%), and it could be lower if you're protecting your assets with very low risk investments(e.g. 5%). Remember that this is supposed to represent money you're actually taking away from another investment with IRR being the return of that other investment.
2. We'll take inflation as 3%
3. We'll say that we plan to keep either car for 10 years, driving it roughly 10,000 miles per year.
4. We'll say the Prius gets 45 mpg, while the Corolla gets 28 mpg.

Next we go about defining some financial aspects:

1. From the car listings, the prius is $5800 while the corolla is $3800.
2. We'll guess that the increase of gas stays just ahead of inflation, at about 4% per year.
3. From repairpal.com, we'll estimate average annual repair costs of the prius at $435/yr, and the corolla at $341 per year, increasing each year with inflation.
4. In addition, we'll assume that the Prius will need its battery replaced within the first 5 years of ownership(It's free if it happens in 2017, $2600 after that). We'll spread this cost over years 1-4.

CASH FLOW - For each year starting at 0(this is important mathematically), we'll add the gross profit and subtract the costs for that year. In year 0, the costs are the purchase price of the car, the price of gas, and the repair costs for each vehicle. The sum of these is your cash flow.

At this point our spreadsheet for the Prius option looks like this:



And the Corolla looks like this:


DISCOUNT FACTOR - This is the value of money in a given year relative to year 0. It is calculated by {(1 + Inflation)/(1 + IRR)}^year. What this tells you is the useful value of money in that year. In year 1 of our example, (1.03/1.098)^1 = .94, so we're saying that the value of money properly invested next year, should be worth only 94% of the same money invested today.

DISCOUNTED CASH FLOW - This is simply CASH FLOW * DISCOUNT FACTOR. This is the value of cash flow in a given year in today's dollars.

NET PRESENT VALUE - This is the sum of discounted cash flows for every year. This number will tell you whether or not the investment you're considering is worthwhile. In the case of a car, this number will be very negative, since it's a necessity and not an investment geared towards making money. Since you're comparing two options, you can pick the one which is less negative.

Our final spreadsheet for the Prius looks like this:

And this is the Corolla:


In this case, the Corolla would be a better choice, based on our initial assumptions(and assuming there are no other factors than money.)

I've attached the spreadsheet for those who would like to mess around with it. I hope this was useful to you, like I said it's been one of the main tools I've used in the past for making financial decisions.View attachment 15410

 

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