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Introduction to Corporate Finance
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Course 4
Terms in this set (63)
Time value of money refers to the fact that money received or paid at different times is like different currencies. You can't add it. Money has a time unit.
Photo 1 - What you have to do is you have to convert to a common base unit in order to aggregate it, and to do that we need an exchange rate for time.
The tools: Time Line & Discount Factor
Photo 2
The way to think about R is just to ask yourself, what are the risks, or how risky are the cash flows that I'm going to be discounting here?
And then think about how that relates to investments in the capital markets
Photo 3 - You notice that riskier investments, as I move down the columns, riskier investments are met with higher returns.
Riskier investment, higher return.
So how do we use the tools? Well, we're first going to focus on bringing cash flows back in time and when we move cash flows back in time, that's called discounting.
Photo 4 - Discounting Cash Flows moves them back in time
Lessons of Time Value of Money
Photo 5
So compounding just refers to moving cash flows forward in time
Photo 6 - Now, these cash flows, once they've been moved forward are referred to as future values, right?
So, again, this is just notation, like with present values.
So, let's summarize this up. We use compounding to move cash flows forward. We apply a discount factor with a positive exponent to move them forward in time, and that gives us future values.
Photo 7
Useful Shortcuts - The first thing I wanna talk about is an annuity.
An annuity is a finite stream of cash flows of identical magnitude and equal spacing in time
Photo 8 - Lo primero de lo que quiero hablar es de una anualidad.Una anualidad es un flujo finito de flujos de efectivo de idéntica magnitud e igual espaciamiento en el tiempo
Annuity Example
Photo 9
Growing Annuity: Is a Finite Stream of Cash Flows that grow at a constant rate and that are evenly spaced through time
Photo 10 - (R is the Discount Rate, G the Growth Rate
Growing Annuity Example
Photo 11
Perpetuity: is just like an annuity except the cash flows go on forever,
all right? We get the same amount of money, equally spaced in time forever.
Photo 12
Growing Perpetuity - Dividend Streams are an example (Absent some event such as a bankruptcy or an acquisition or a takeover,
something like that.)
Photo 13 - All the requiriments for this operation should be satisfied
Savings with Taxes (Account) - The tax is applied on the INTEREST
Photo 14 - Taxes reduce the return on our investment
After-Tax Discount Rate
Photo 15
Savings with Taxes applied on the Discount Rate
Photo 16
So, let's understand it. How does inflation impact our returns?
Photo 17 - Inflation won't affect the money we earn (It will affect what we can buy with the money)
What inflation's going to do is it's going to affect what we can buy with the money we're pulling out, and it's going to affect the value of that money.
And so we'd like a way to quantify and understand the impact of inflation on that value, so I'm going to introduce the concept of a real discount rate.
I'm going to introduce the concept of a real discount rate.
I'm going to demote it by RR, and 1 plus the real discount rate equals 1 + the nominal discount rate / divided 1 + the expected rate of deflation, which I've denoted by pi.
And a commonly used approximation that you'll see, though I'll emphasize this is an approximation
Photo 18 - Is that the real rate equals the nominal rate, minus the expected rate of inflation.
Now, that's important, because even though the inflation is not impacting our account balance, how much money, how many dollars we have
It is impacting what we can do with that money, what we can buy with it. And that's ultimately what we care about
Savings with Inflation Example (Using the Real Rate instead of the Nominal Rate)
Photo 19
Savings with Inflation: Taxes Affect Money
Photo 20 - Inflation Affects Consumption, Not Money (Earn Nominal Return but can't buy as much)
We pull out $100, and what's going to happen is we're going to be left with this surplus, but that makes sense, right, because inflation doesn't affect the dollars.
It affects what we can do with these things that we pull out, okay?
Savings With Inflation, Yearly example
Photo 21 - So, let's think about what kind of cash flow
stream we might want to address inflation.
So, let's summarize this. Inflation does not affect dollar returns. It's not affecting the money in the bank account or the rate at which it's growing. What it's affecting is the purchasing power of that money.
Photo 22 - So, when I pull it out and go buy something, I can buy less of that good or that service with that same dollar year after a year after a year when we face inflation.
Any investment is ultimately judged by its rate of return, whether it's a certificate of deposit, a share of stock, or a government bond.
The rate of return is simply the percentage of growth in an investment over a specific period of time, usually one year.
But rates of return can be difficult to compare across different investments if they have different compounding periods.
One may compound daily, while another compounds quarterly or biannually.
Comparing rates of return by simply stating the percentage value of each over one year gives an inaccurate result, as it ignores the effects of compounding interest. It is critical to know how often that compounding occurs as the more often a deposit compounds, the faster the investment grows.
This is due to the fact that every time it compounds the interest earned over that period is added to the principal balance and future interest payments are calculated on that larger principal amount.
Banks in the U.S. are required to include the APY when they advertise their interest-bearing accounts. That tells potential customers exactly how much money a deposit will earn if it is deposited for 12 months.
Unlike simple interest, compounding interest is calculated periodically and the amount is immediately added to the balance. With each period going forward, the account balance gets a little bigger, so the interest paid on the balance gets bigger as well.
APY standardizes the rate of return.
It does this by stating the real percentage of growth that will be earned in compound interest assuming that the money is deposited for one year.
For example, if you deposited $100 for one year at 5% interest and your deposit was compounded quarterly, at the end of the year you would have $105.09. If you had been paid simple interest, you would have had $105.
The APY would be (1 + .05/4)4 - 1 = .05095 = 5.095%.
Nominal interest rate refers to the interest rate before taking inflation into account.
To avoid purchasing power erosion through inflation, investors consider the real interest rate, rather than the nominal interest rate.
APY (annual percentage yield) is the effective interest rate which tends to be more relevant to borrowers and lenders than
the nominal, or stated, interest rate.
APR indicates the total amount of interest you pay on a loan account, like a credit card or an auto loan, over one year.
APR is based on the interest rate, but for some loans, it also takes into account points, additional fees, and other associated loan costs.
Difference between Rate (APR) & APY
Photo 23
EAR is a discount rate: Is what matters for computing interest and discounting cash flows
Photo 24 - APR is not a discount rate: APR is a means to an end, We use it to get a discount rate
Example of APR
Photo 25
Example of EAR
Photo 26
We can work in periods or in years
Photo 27
Interest rates vary with the term of the investment
Photo 28 - And you can see that as the term increases or changes, so to do the interest rate. Well, as the term of the investment changes, quite often, but not always,
quite often, the interest rate will change.
Term Structure is the relation between the investment term and the interest term
Photo 29
The yield curve is just a graph of that relation
Photo 30
The other thing I want to point out is that the relationship
between the short end of the yield curve, short term interest rate, and the long end of the yield curve, long term interest rates, that can vary over time as well.
Photo 31 - Here, at least in 2012, we see that the curve is upward sloping, so that interest rates, short term loans to the government, are less costly than long term loans.
Yields vary by maturity and risk
Photo 32 - Spot Rates
How should we make financial decisions? Well, a reasonable answer might be to undertake those actions that create value.
Value for those affected by the decision, value for the owners of a firm for example.
Which actions create value? And while that's a complicated question, a sort of general answer that seems reasonable
Would be to consider actions in which the benefits exceed the costs.
But here's a little wrinkle, what if the costs and benefits arrive at different times?
Photo 33 - Well actually, we're well equipped to deal with that wrinkle because we can compare the present value of the benefits to the present value of the costs.
Net Present Value Says
Photo 34
How Frequently do you use capital budgeting techniques (¿Con qué frecuencia utiliza las técnicas de presupuestación de capital)
Photo 35 - And what you can see is that there are actually a variety of responses. I've listed six here. But the majority or the predominant number of responses point to net present value and internal rate of return as the most popular decision criteria that CFOs use.
So we're going to move through this topic of DCF, discounted cash flow, emphasizing to a certain extent the NPV rule, because that is the optimal rule in terms of always leading you to making the decision that creates value.
That said, I'm going to take a much more practical perspective to corporate decision making, or financial decision making more broadly, and recognize that other rules are still informative.
So it's not surprising that we see their use by practitioners, whether it's PE, private equity investors, or investment bankers, or CFOs.
They're still informative, but the important thing to keep in mind is that these other rules have certain weaknesses that we need to understand and we need to recognize the limitations of these rules so that we can use multiple rules in conjunction to come to the best decision.
Two Components to NPV
Photo 36
Depreciation's just an accountant's way of recognizing the loss in value, the deterioration in value, of physical assets like plants and equipment.
But it's sort of an accounting notion that doesn't represent a true cash flow. When a plant depreciates it's not as though money is leaving the company.
You might wonder why we're even considering it. Well the reason we're considering it is because we're going to take this term In parenthesis that I've now bracketed and multiply it 1 times tc. Tc is the marginal tax rate.
Photo 37 - See even though depreciation doesn't represent any dollars flowing out of the company or away from a project. It's not a literal cost in terms of dollars. What it does is it does reduce our taxable income, it provides a tax shield.
Once we have this we're going to have to add back in depreciation and again that's just to net out the subtraction of depreciation here.
Photo 38 - It doesn't represent a true cash flow. What it does represent is a tax shield. So we add back in depreciation.
Well I'm getting them from a variety of different sources. I'm getting them from my marketing people and my strategy group within the company. I'm getting them from industry analysts as well.
Photo 39 - So there's a host of different sources of input that go into these numbers, but at the end of the day, they are just assumptions, and I'm going to emphasize that fact later on.
Forecasting Free Cash Flows Summary
Photo 40
Compute Internal Rate of Return Example
Photo 41
Compute NPV Example
Photo 42
NPV vs IRR
Photo 43
Portafolio
Conjunto de activos diversificados que generan rentabilidad con cierto riesgo
Riesgo
Es la medida de incertidumbre en torno al rendimiento que ganará una inversión, ó Es el grado de variación de los rendimientos relacionados con un activo específico
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