Friday, 3 June 2016

Is it worth it? Present value factor

Building a house is a series of decisions, and a lot of these decisions put one-off capital costs against month-on-month running costs.

For example you could add insulation somewhere that will save 10,000 yen every year in heating and cooling bills, and cost 150,000 yen.

The first thing to think about is how far into the future you are going to be making savings. Let's say it's thirty years.

So if you're going to save 10,000 yen every year for the next 30 years, how much is that worth? 
Well, at first sight you'd think it's 300,000 yen. But it's not that simple. You have to think about inflation and interest.

First, imagine you don't have the money. In that case to make the capital investment you're going to have to borrow it, probably from a bank who will charge interest. This means the capital will cost more than its face value. In other words the saving from the running cost is worth less.

Second, imagine that you do have the money. In that case, spending it means you can't invest the money somewhere else, so you lose out on the opportunity for earning interest. So again the value of the cash in hand, or wherever it is, is more than its face value, in the long run.

This can all be expressed as the present value factor, which can be calculated by this equation:
 Fpv = 1-(1+P) -n / P
Where P is the interest rate, and n is the number of years.

But what if you're bad at making investment decisions, and would probably have lost all the money? In that case, you will probably make the wrong decision here, too, so you can stop reading, if you haven't done so already. You probably stopped reading before the equation.

And what about inflation? If the prices are going to go up, then that 10,000 yen per year is going to be increasing. Won't that balance out the interest? Can't we just multiply the annual saving by the number of years after all?