Friday, April 3, 2015

Working interest into the mix


Suppose I borrow $10, to be repaid as a lump sum after five years, with one dollar interest to be paid annually.

Year 0Borrow $10
Year 1Pay Interest $1
Year 2Pay Interest $1
Year 3Pay Interest $1
Year 4Pay Interest $1
Year 5Pay Interest $1 Principal $10

I pay back a total of $15 for $10 borrowed.

The graphs I've shown recently, comparing "nominal" to "real" Federal debt to GDP ratios, consider only the principal amounts. Not the interest. Now I want to consider the interest payments as well as principal.

Specifically, I want to see how well interest payments fill the gap between nominal and real on my graphs. Does interest make up the shortfall created by inflation? Does it more than make up for the shortfall? Or does a shortfall remain?

Suppose I borrow $10, to be repaid after five years pass, with one dollar of interest paid annually, and with inflation that reduces the dollar's value by ten cents each year. The "real" value of the dollar would be:

Year 0:$1.00
Year 1:90 cents
Year 2:80 cents
Year 3:70 cents
Year 4:60 cents
Year 5:50 cents

In year zero, when a dollar was worth $1.00, I borrowed $10. I received the value $10.

In year one, when a dollar was worth 90 cents, I paid $1 interest. I paid a year-zero value equal to 90 cents.

In year two, when a dollar was worth 80 cents, I paid $1 interest. I paid a year-zero value equal to 80 cents. The lender has received from me a total of $1.70 of year-zero value. Here, I don't need to type it all out:


Oh look at that. Open Office doesn't like the way I shortened the word accumulation.

So in this example, the  lender is repaid $8.50 out of $10 "real" value dollars. A better way to say it may be that, when we consider principal and interest and inflation, the lender received back 85% of the value lent out.

All of this of course assumes that it is reasonable to expect to be repaid at equal value rather than an equal number of dollars. In an inflationary world, that assumption may not be reasonable.

6 comments:

The Arthurian said...

Deflation is appealing to creditors, just as inflation is appealing to debtors. Justice demands a stable dollar.

jim said...

What does a stable dollar have to do with inflation/deflation?
You sound just like the Milton Freeman quote at the top of your blog.

Here is the way I look at inflation:

Before the early 70's the per capita consumption of petroleum doubled every 10 years. It is pretty obvious that trend could not continue (if it had all the oil would now be long gone)
By the 1980's per capita consumption had reached its maximum and has trended downward since.

So how do you get from an economy that is dependent on exponentially expanding consumption to one that can get by with less every year?

If you want to keep the economy open and free the only possible answer to that question is inflation.

The Arthurian said...

Oh, ouch. Good one, Jim!

Auburn Parks said...

Low and stable inflation is a stable dollar Art.

We had a "stable dollar" under the 19th century gold standard. After 50 years, the price index was essentially unchanged even though we had 10% inflation years and 10% deflation years.

That system is far inferior to a system where the nominal price level always increases yet at a low, slow, and predictable level.

Its much better to know prices will be higher nominally in 10 years and be able to predict the change than to know prices will be the same but to not know if we were going to have a large inflation or deflation in the short-term.

The Arthurian said...

Hi Auburn.

"Low and stable inflation is a stable dollar Art."

Yeah, I know. I was gonna say that to Jim. But you know me, I never disagree with anyone!
:)

Actually, I was responding to Jim's "You sound just like the Milton Freeman quote at the top of your blog." But instead of quotes I put a 'greater than' symbol in front of it like there used to be in old email. And Blogger ate the text following the 'greater than'.

Well I've done a lot with 'greater than' lately. I probably have comments all over the place that don't make sense.

So it goes.

//

I took Econ 101 in 1977. Robert Lucas and DSGE had not made it into the 1975-edition textbooks we were using. I learned that the two objectives of economic policy were price stability and economic growth.

Your perspective on inflation here is interesting, Auburn, but it would take some doing to convince me that you are right.

Actually... dunno if this will fit in a brief comment...
I'd say the dollar was stable in the 19th century because gold put limits on the expansion of bank money. I don't know, maybe people got nervous when they got home from shopping (??) and took the change out of their pockets and saw a lot of paper and very little gold. It would have been obvious, in those days, when there was a lot of bank money relative to hard money. And we got frequent, sudden, substantial shocks because people wanted hard money.

These days you can't tell bank money from base.

//

"That system is far inferior to a system where the nominal price level always increases yet at a low, slow, and predictable level."

Are you praising the 1985-2005± period (the "Great Moderation") ?

Auburn Parks said...

"Your perspective on inflation here is interesting, Auburn, but it would take some doing to convince me that you are right."

I was speaking from the perspective of the belief that uncertainty is bad for business planning. And the observation that the nominal price level is irrelevant. Life is not worse in Japan because a loaf of bread costs 1K yen instead of $1 dollar as long as the relative incomes are appropriate. From this POV, inflation is not inherently bad or good, its the rate of change and its relationship to income that matters.

I mean look how crazy volatile the rate of change was before the Fed was created:

http://en.wikipedia.org/wiki/Inflation#/media/File:US_Historical_Inflation_Ancient.svg

There were some 5 year periods where we'd have 50% net swings, hard to do business planning in that environment even though we had zero net change in the nominal price level over a 100 year period.

"Are you praising the 1985-2005± period (the "Great Moderation") ?"

Actually the great moderation has been happening since the modern Fed evolved in 1934:

http://inflationdata.com/articles/charts/decade-inflation-chart/

8 decades and 3.5% average inflation rate seems pretty stable and moderate to me. The only outlier coming from the Oil price crises of the 70s or the average would be even lower and more stable.