Video 14 - Nominal vs Real Interest: the Fisher Equation - YouTube

Welcome back everyone. Up to this point, we've been discounting our future cash

flows using an interest rate that reflects our time value of money -- that is,

the return we require on our risk, inflation, and opportunity cost. Today,

we're going to focus specifically on inflation. First, we'll define inflation,

and explain the difference between real and nominal interest rates. Second, we'll

introduce the Fisher equation to explain the relationship between real, nominal,

and inflation rates, and lastly, we'll illustrate the importance of keeping

these rates consistent when we're discounting our future cash flows. Let's

get started! So what is inflation? Inflation is an

increase in the price of goods and services. It's why one dollar could buy

you 3 gallons of premium whiskey in 1810, and now you'd be lucky to get a sip of a

Hey Y'all. Inflation can be caused by a number of factors. It's most commonly caused by

an increase in the demand for goods and services, or an increase in the cost of

supplying those goods and services. Both of these effects can drive up prices. For

instance, if demand goes up, people will be willing to pay more, and if the cost

of supply goes up, people will be forced to pay more. While inflation is a complex

issue in the area of macroeconomics, as investors we don't have to dive too deep

into the complexities to understand how it affects our return. The annual inflation

rate tells us by how much prices have increased over a given year. We typically

measure inflation using the Consumer Price Index, or CPI, which tracks the

prices of a typical basket of goods in the market. Extreme cases of inflation

can hurt the economy by causing a currency to lose much of its value.

For example, during World War II, the rate of inflation was so high in Germany

that people would cash their paychecks in the morning, because the bread you

could buy in the morning would become unaffordable by noon. To avoid these

issues, most countries adopt monetary policies to try to control inflation. The

Canadian government sets an annual inflation target of 2%. For our

purposes, We'll take the rate of inflation as given. So let's say

inflation is 10%. If a llama costs $1000 today, after one

year it'll cost $1,100. Nothing has changed about

the llama -- he didn't get superpowers or anything -- and yet I would have to pay an

additional 10%, or $100, to buy him. What this means is that the true value of my

$1000 -- that is, my purchasing power -- has decreased. My $1000 can buy me a whole

llama this year, but only 91% of a llama next year. In other words, I can buy fewer

goods with my $1000 than I could have before. As investors, we don't like

inflation. Suppose I invest in a one-year bond that earns a 20% return. At the end

of the year, my money has grown by 20%. So I want to be able to go out and buy 20%

more things than I could have before. But if the inflation rate is 10%, my

purchasing power has actually fallen by 10%.

So the real return on my investment is only 9.1%, meaning that

my purchasing power has only increased by 9.1%. We can express

this logic as a general formula called the Fisher equation. our real return is 1

plus our nominal rate divided by 1 plus our inflation rate, where our real return

tells us by how much our purchasing power will increase. Recall that

purchasing power tells us how far our dollar can go to buy things. The nominal

rate is the percent return we earn on an investment, and the inflation rate is the

percent increase in the price level, like the CPI. If you're in a hurry, the

following formula will approximate the real rate of interest -- our percent

increase in purchasing power -- although it becomes less and less accurate as the

nominal and inflation rates increase. If you have a calculator handy, it's best to

just use the original formula. When evaluating an investment, you should

always consider your real return. This return should fully compensate you for

the remaining components of your cost of capital -- your risk and opportunity cost.

Unfortunately, investors often neglect real rates and instead base their

decisions on nominal rates. We call this the "money illusion." What can go wrong

with nominal rates? Well, let's say that you aren't overly concerned with growing

your money, so you choose to invest in a low yield investment that earns 3% each

year. But suppose the rate of inflation is 4%. Plugging these values into our

equation, we learn that the real rate of return

is actually negative! You're effectively losing value each year. This is why as a

smart investor, you should ensure that your investments can earn you a return

that's at least as high as the rate of inflation. Otherwise, you're actually

losing money. You would be better off spending your money on something today,

while you have greater purchasing power. Maybe that llama you've always dreamed

of? Next, let's talk about how to deal with inflation in our present value

calculations. When dealing with inflation, we have two choices: we can discount our

nominal future cash flows by our nominal interest rate to calculate the present

value of our investment, or we can discount our real future cash flows by

the real interest rate to calculate our present value. Regardless of which rate

we use to compound our cash flows, we will get the same answer for our present

value, since either way we must start with the same amount of money. We only

see a difference between our nominal and real cash flows over time, since they're

compounded at different rates. The farther into the future this cash

flow is, the greater this difference becomes, since there are more compounding

periods. The key here is being consistent. We should express all of our cash flows

and discount rates in either nominal or real terms, so that we can compare apples

to apples, the same way you'd convert cash flows into the same currency before

adding or comparing them. Let's try an example using these two different

methods -- discounting nominal returns and discounting real returns. Pause the video

and try this problem on your own.

Let's try it together. first, we'll solve for our present value using nominal cash

flows. We need to figure out how much the play house is going to cost in five

years. Prices are rising at two percent each year -- this is our inflation rate.

Thus, in five years, the play house will cost $4000 times

1.02^5, or $4,416.32

Next, we need to discount this nominal future value by 7%

for five years to determine how much we should invest today. We'll take

$4,416.32 divided by

1.07^5. This gives us

$3149. If we invest this amount today at 7%, we will

have enough money to buy this play house in five years. Now, let's compare by

solving for the present value using real cash flows. First, we'll calculate the

real rate of return. We can earn 7% each year, but inflation is 2%

each year; thus, our real return is1.07 divided by

1.02 -- 4.9%. Now, let's discount the price of the play

house, $4,000 in today's terms, by 1+4.9%

for the five years, or $4000 divided by 1.049^5,

which is also $3,149.

The important rule to remember is to always discount nominal

cash flows to their present values using the nominal interest rate, and real cash

flows to their present value using the real interest rate. Unless otherwise

stated, you can assume that cash flows and interest rates are in nominal terms.

Once cash flows are expressed in present value, you can compare and combine them.

Today, we talked about how inflation results in our real returns being lower

than our nominal returns. We can use the Fisher equation to solve for our real

return by dividing our nominal rate by the inflation rate. Lastly, when doing

time value calculations, remember to always discount nominal cash flows by

the nominal interest rate and real cash flows by the real interest rate. Thanks

for watching!