[MUSIC]
We have been talking talking about the discount rate in the context of
calculating present and future values of different types of cash flows namely lump
sum, annuity and perpetuity.
The question is, what the discount rate is and what is a key factor or
factors that drive it?
Which is what we will cover in this video.
As part of understanding the discount rate, we will discuss how risk and
return are related.
We'll also cover the idea of a weighted-average cost of capital.
From a company's perspective, it needs to raise money from various sources to grow.
For example, money may come from bank loans, and from the insurance of bonds and
stocks.
The primary reason why various entities, individuals like you and me, banks and
other financial institutions,
provide money to companies, is to see that money grow over time.
In other words, they expect their wealth to grow over time.
As an investor, how much would you want as a rate of return
to be willing to invest in a company?
The answer is that it depends on the risk of the investment.
Most people think of risk as being a bad thing.
They relate it to the likelihood of losing money.
Risk is actually the uncertainty of outcomes, both good and bad.
In the context of investments, risk is the uncertainty of future returns.
This is usually measured using either the variance or standard deviation of returns.
Larger the variance or standard deviation, larger is the risk.
People think returns as a compensation for holding risk.
Normally, no one will hold risk without any compensation.
Let's look at a simple example to understand this idea better.
You have $100 and 2 investment choices to make.
The first investment will give you $105 guaranteed after 1 year.
Since there is no uncertainty or
risk on it's future pay off, this is what is called a risk-free investment.
The second investment will pay you either $115 after 1 year with
a 60% probability or $90 after 1 year with a 40% probability.
This investment is risky as your future payoff is uncertain.
The question is which investment should you invest in?
To answer this question, we need to compute the expected returns and
risk of 2 investment, for the first investment the expected return is
105- 100 divided by 100 which is 5%.
There is no uncertainty in this investment and hence it's risk is 0.
For the second investment we have to compute the expected return for
both possibly payoffs.
And the future payoff is $115, then expected return
is 115-100 divided by 100, which is 15%.
When the future payoff is $90,
the expected return is 90 -100 divided by 100 100, which is -10%.
With this investment, there's a 60% chance of a 15% return, and
a 40% chance of a -10% return.
So its expected return is 0.6 times 15% plus 0.4 times -10%, which equals 5%.
Both investments are expected to give you a return of 5%.
Though the first one gives you a guaranteed 5%,
whereas there is uncertainty or risk in the second one.
While it has a 60% chance of giving you a higher 15% return.
It also has 40% chance of yielding a -10% return.
Given their expected or anticipated returns are equal, I would prefer holding
the risk-free investment and earning guaranteed 5% return.
For the second investment to be attractive,
its expected return should be greater than 5%.
For example, a risky investment pays you $150 after 1 year with a 60% probability,
and $80 after 1 year with the 40% probability,
then it is expected to turn us 22%.
I will let you compute this and verify the number.
So this investment gives you an additional 17% over the risk-free
investments return of 5% to hold its risk.
A company or projects discount rate captures this
idea of compensating investors for the company's or project's risk.
Higher the risk company's investment, greater is the compensation that investors
would demand, and hence higher discount rates.
Remember, expected returns are not guaranteed to promised returns.
Actual realized returns will very likely be very different from expected returns.
They could be far higher or far lower than expected returns.
All they say is what an investor should anticipate as a return
from the investment.
Investors have various opportunities to invest their money and make it grow.
Given the same level of risk,
two investments should have the same expected return.
For a given level of risk, if 1 project has an expected return of say 15%,
another has an expected return of 20%.
No one will want to invest in the first project as the second one offers
a higher expected return.
So projects or company should offer the same expected return as
other investment opportunities available to investors with the same level of risk.
This is the concept of discount rate that we have been using until now to calculate
future and present values of various cash flows.
The discount rate is also referred to as the cost of capital or the hurdle rate.
It is called the cost of capital because it tells us how much it will cost
the company to raise capital from various sources.
However, the cost of raising capital from each of these sources won't be the same.
Investors, for
each source of capital, we have different expected returns from their investment.
Since stockholders are residual claimants in the company that is the good paid only
after everyone else is, their investment is the riskiest and
hence they expect the highest possible return on their investment.
Banks usually get paid first and so bank loans would typically cost the least.
Given the various sources of capital and their divergent cost.
The discount rate is computed as a weighted average of all these
different costs.
Hence, the discount rate is more commonly referred to as the weighted-average
cost of capital, WACC in short.
Now that we have understood what the discount rate is and
how it is related to risk, next time,
we will focus on what type of risk investors will be compensated for.
[MUSIC]
Ramabhadran ThirumalaiAssistant Professor
