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Â We have been talking talking about the discount rate in the context of

Â calculating present and future values of different types of cash flows namely lump

Â sum, annuity and perpetuity.

Â The question is, what the discount rate is and what is a key factor or

Â factors that drive it?

Â Which is what we will cover in this video.

Â As part of understanding the discount rate, we will discuss how risk and

Â return are related.

Â We'll also cover the idea of a weighted-average cost of capital.

Â From a company's perspective, it needs to raise money from various sources to grow.

Â For example, money may come from bank loans, and from the insurance of bonds and

Â stocks.

Â The primary reason why various entities, individuals like you and me, banks and

Â other financial institutions,

Â provide money to companies, is to see that money grow over time.

Â In other words, they expect their wealth to grow over time.

Â As an investor, how much would you want as a rate of return

Â to be willing to invest in a company?

Â The answer is that it depends on the risk of the investment.

Â Most people think of risk as being a bad thing.

Â They relate it to the likelihood of losing money.

Â Risk is actually the uncertainty of outcomes, both good and bad.

Â In the context of investments, risk is the uncertainty of future returns.

Â This is usually measured using either the variance or standard deviation of returns.

Â Larger the variance or standard deviation, larger is the risk.

Â People think returns as a compensation for holding risk.

Â Normally, no one will hold risk without any compensation.

Â Let's look at a simple example to understand this idea better.

Â You have $100 and 2 investment choices to make.

Â The first investment will give you $105 guaranteed after 1 year.

Â Since there is no uncertainty or

Â risk on it's future pay off, this is what is called a risk-free investment.

Â The second investment will pay you either $115 after 1 year with

Â a 60% probability or $90 after 1 year with a 40% probability.

Â This investment is risky as your future payoff is uncertain.

Â The question is which investment should you invest in?

Â To answer this question, we need to compute the expected returns and

Â risk of 2 investment, for the first investment the expected return is

Â 105- 100 divided by 100 which is 5%.

Â There is no uncertainty in this investment and hence it's risk is 0.

Â For the second investment we have to compute the expected return for

Â both possibly payoffs.

Â And the future payoff is $115, then expected return

Â is 115-100 divided by 100, which is 15%.

Â When the future payoff is $90,

Â the expected return is 90 -100 divided by 100 100, which is -10%.

Â With this investment, there's a 60% chance of a 15% return, and

Â a 40% chance of a -10% return.

Â So its expected return is 0.6 times 15% plus 0.4 times -10%, which equals 5%.

Â Both investments are expected to give you a return of 5%.

Â Though the first one gives you a guaranteed 5%,

Â whereas there is uncertainty or risk in the second one.

Â While it has a 60% chance of giving you a higher 15% return.

Â It also has 40% chance of yielding a -10% return.

Â Given their expected or anticipated returns are equal, I would prefer holding

Â the risk-free investment and earning guaranteed 5% return.

Â For the second investment to be attractive,

Â its expected return should be greater than 5%.

Â For example, a risky investment pays you $150 after 1 year with a 60% probability,

Â and $80 after 1 year with the 40% probability,

Â then it is expected to turn us 22%.

Â I will let you compute this and verify the number.

Â So this investment gives you an additional 17% over the risk-free

Â investments return of 5% to hold its risk.

Â A company or projects discount rate captures this

Â idea of compensating investors for the company's or project's risk.

Â Higher the risk company's investment, greater is the compensation that investors

Â would demand, and hence higher discount rates.

Â Remember, expected returns are not guaranteed to promised returns.

Â Actual realized returns will very likely be very different from expected returns.

Â They could be far higher or far lower than expected returns.

Â All they say is what an investor should anticipate as a return

Â from the investment.

Â Investors have various opportunities to invest their money and make it grow.

Â Given the same level of risk,

Â two investments should have the same expected return.

Â For a given level of risk, if 1 project has an expected return of say 15%,

Â another has an expected return of 20%.

Â No one will want to invest in the first project as the second one offers

Â a higher expected return.

Â So projects or company should offer the same expected return as

Â other investment opportunities available to investors with the same level of risk.

Â This is the concept of discount rate that we have been using until now to calculate

Â future and present values of various cash flows.

Â The discount rate is also referred to as the cost of capital or the hurdle rate.

Â It is called the cost of capital because it tells us how much it will cost

Â the company to raise capital from various sources.

Â However, the cost of raising capital from each of these sources won't be the same.

Â Investors, for

Â each source of capital, we have different expected returns from their investment.

Â Since stockholders are residual claimants in the company that is the good paid only

Â after everyone else is, their investment is the riskiest and

Â hence they expect the highest possible return on their investment.

Â Banks usually get paid first and so bank loans would typically cost the least.

Â Given the various sources of capital and their divergent cost.

Â The discount rate is computed as a weighted average of all these

Â different costs.

Â Hence, the discount rate is more commonly referred to as the weighted-average

Â cost of capital, WACC in short.

Â Now that we have understood what the discount rate is and

Â how it is related to risk, next time,

Â we will focus on what type of risk investors will be compensated for.

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