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Â All right.

Â Now we're going to deal with the cost of debt.

Â And, remember, for, for the cost of debt is RD, and

Â for what follows, we're going to forget about taxes.

Â We, we don't need taxes for this.

Â We already understood, the role that taxes play on the cost of debt.

Â So, what we're going to do, is to focus exclusively on the cost of debt.

Â And, and we're going to to assume that, that this is a company that issues a bond.

Â A bond is simply, a promise.

Â You give me some money today, and

Â I promise to pay you back over a number of years.

Â And let's consider a very simple example, because corporations issue bonds.

Â Government issued bonds there, there are many issuers of bonds out there and, and

Â all the bonds are more or less the same.

Â The, they, so,

Â so-called coupon bond, plain vanilla bond let's consider one in particular.

Â As you see there let's consider a bond, that is four years away from maturity.

Â Has a face value of 1000.

Â And has an interest rate of 10%.

Â What does this mean?

Â Well, being four years away from maturity means that in four years,

Â the bond will expire.

Â That might mean, that the bond was issued today.

Â And in four years it will expire, or that the bond was issued some time ago, and

Â it has four years of life still to go.

Â So it doesn't really matter, whether it is issued today or it was issued before.

Â The only thing that mattered is that four years from today.

Â That bond will expire.

Â What does it mean, that has a face value of 1000, $1000?

Â Well, that basically means, that is called, the face value of the, or

Â the principal.

Â And that means that the interest payments,

Â that the company is going to be making over time.

Â Are calculated, relative to that face value, relative to that principle.

Â And that is the amount, that the company will return,

Â when the bond expires five years, four years down the road.

Â So, $1,000 has two roles.

Â It determines the annual payments.

Â That investors are going to receive, and it determines, the final payment that

Â investors are going to receive, four years in our case, four years down the road.

Â And the interest rate and and

Â it's a very important difference between the interest rate and the return.

Â That investors get and we'll get to that in just a minute.

Â But the interest rate, is that the only role, is to determine the annual payment.

Â So if you have an interest rate of 10%,

Â that basically means that on the four years that the bond has to go until it

Â expires, you're going to be paying 10% of the principle.

Â So 10% of 1,000 is basically 100.

Â So you're going to be paying 100 or say 100 million, as time goes by,

Â at once a year, for the four years of the life of the bond.

Â So as you see there when we have a little, cash flows laid out there.

Â So if you buy this bond which is four years away from maturity, and

Â let's say that it cost you $1,000, that means that you're going to be

Â pocketing $100 one year down the road, $100 two years down the road,

Â $100 three years down the road, and $1,100 four years down the road,

Â because you will get the 10% interest which is $100.

Â Plus, the 1,000 of principle, all right?

Â So the cash flows are very simple.

Â You know whenever you buy a bond, you know exactly what you're going to get,

Â and you know exactly when, you're going to get it.

Â Bonds are slightly more complicated, because they pay interest twice a year,

Â typically, rather than once a year but

Â to understand what a bond is all about this is more than enough.

Â Now, once you issue a bond,

Â once a company, once a government issues a bond, the bond trades in the market.

Â And trading in the market basically means that people can buy the bond and

Â sell the bond and buy the bond and sell the bond.

Â And in the same way, that you're familiar, with how stock prices change it over time.

Â Well, bond prices also change over time.

Â Which means, that the promise that the company has made, is not going to change.

Â This company's always going to be paying $100 in the next four years and

Â $1000 at the end of the four years.

Â What does change, is the price, that people are willing to pay for

Â those promised cash flows.

Â And why is going to pre, the price is going to change?

Â Well, for the same reasons that we always exploring finance.

Â If you think that risk goes up, you will be actually, willing to pay less for

Â those cashflows, but if you think that risk goes down,

Â then you'll be willing to pay more for those cashflows.

Â Think, think about it in, in this way.

Â Require returns and willingness to pay, are always go, in opposite directions,

Â so if you perceive that a company becomes riskier, then you're going to require more

Â return and requiring more return and being willing to pay less for the cashflows.

Â Are exactly the same thing, if you think that a company has become less risky than

Â it was before, well your require return will go down, which means that we will be,

Â you will be willing to pay more, for

Â the cashflows that this bond promises, all right?

Â So now let's consider a particular example, let's suppose that for

Â whatever reasons they.

Â The risk of this company has gone up.

Â Maybe they have made bad investment decisions.

Â Maybe they have hired a bad CEO.

Â Whatever is the reason, the risk of this company is perceived in the market,

Â as having gone up.

Â Well, that means that, the cash flows of the bond, will not change, but

Â now you will be willing to pay less, because you have more uncertainty.

Â You have more risk and therefore, you're willing to pay less.

Â It's kind of natural, you know.

Â Let's, let's make a quick parenthesis here, if I promise you, to pay you $100 in

Â each of the next four years and $1,000.00 at the end of that, and you thought that

Â I was fully, fully reliable, then you'd be willing to pay me ache even money for

Â those expected cash flows one, two, three, and four years down the road.

Â But if I told you, that in each of those years, I'm going to flip a coin and

Â if it's heads, I'll give you the promised cashflows but if it's tails.

Â I will not pay you, at that cashflow.

Â Then you'll say, but wait a minute, this is not the same proposition.

Â Now I have a risk, 50% you pay me and 50% you don't pay me.

Â So now you'd be willing to pay me less, for that promise that I'm making to you.

Â This is exactly, the same thing.

Â That is, the more risk you perceive, then the less you'd be willing to pay for

Â those cashflows.

Â So let me just in order, because we're going to be using these numbers, let me

Â just say that for whatever reasons, the perceived risk of the company has gone up.

Â And therefore you're willing to pay less.

Â Instead of being, being willing to pay $1,000, which is what we said before.

Â Let's suppose now, you're willing to pay $939 for those cash flows.

Â Now, let's go to the other side, let's assume the opposite.

Â And assuming the opposite is, from the Base Case,

Â that is from when, from a situation which you're willing to

Â pay $1,000 let's suppose that now the risk goes down.

Â And the risk might go down because, the company just came up with a new product,

Â and everybody thinks that it's going to be very profitable.

Â Or maybe, because they've hire a fantastic CEO with a great reputation.

Â For whatever reasons,

Â everybody seems to perceive that the risk of this company has gone down.

Â Now remember, the cash flows of the bond still don't change.

Â But now you'd be willing to pay more.

Â You bear less risk, so now you'd be willing to pay more.

Â And let's just put an arbitrary number.

Â Let's say that what you're willing to pay, is $1,000 and $66.

Â Right so, from the base case, when risk goes up,

Â you go from paying $1,000 to paying less, 9.30, 9.39.

Â When risk goes down, you're going from paying $1000 to paying more,

Â which is $1066 odd dollars.

Â Now, let's think of this from the point of view of the investor.

Â And let's think of this from the point of view of taking cash out of your pocket and

Â putting cash in your pocket.

Â In the first case, if you pay $1000.

Â And what you expect to get is 100, one year down the road.100,

Â two years down the road, three 100, three years down the road.

Â And 1100.

Â Four years down the road.

Â And there's a way to calculate the return that you get by taking $1,000 out of your

Â pocket and then pocketing 100 in the next four years and

Â another 1,000 four years down the road.

Â And we'll see in a minute how we calculate that number.

Â But, if you were to run the calculation.

Â If you were to ask the question, if I take $1000 out of my pocket today and

Â I receive 100, 1 year, 2 years and 3 years down the road and

Â then, on 4 years down the road, I pocket $1100, my mean annual return would be 10%.

Â And that is the number that you're seeing there.

Â So, if you take, again, $1,000.00 out of your pocket and you expect to get 100,

Â 100, 100 and 1100 in one, two, three, and four years.

Â Your mean annual return would be ten percent.

Â Now remember, let's take the, the we,

Â we look into two cases, one case in which the risk of the company went up and

Â one case in which the risk of the company went down.

Â Now let's think for a minute what happens when the risk goes up.

Â We had agreed that you'd be paying less for those cash flows.

Â And let's always compare everything to the base case.

Â The base case, you pay $1000.

Â And as we know now, you get a 10% return.

Â Mean annual return.

Â By buying this particular bond.

Â But if you pay less for those cash flows, then you're going to get more return.

Â The cash flows don't change.

Â But if instead of $1000, you pay $939.

Â Because you pay less for exactly the same cash flows, your return is going to go up.

Â And if you were to run a calculation and again in a minute we'll see how to

Â run that calculation, you'll see that your mean annual return now goes up to 12%.

Â Now compare.

Â The column that starts with more risk with the column right underneath,

Â that starts with minus 939 that number in parenthesis means minus 939.

Â Well, what that says it brings together the two things that we

Â said before when you perceive more risk you increase your

Â require return.notice that now our require return goes from 10% to 12%.

Â And that translate into paying less for that particular bond.

Â So, so this is the typical way that markets work.

Â And they promise in terms of cash flows from the point of view of the company

Â doesn't change, what you expect to get does not change, but because risk has

Â gone up, required return has gone up, and the bond price has gone down.

Â Now let's go to the other case.

Â In the other case, and remember we always compare to the base case, and

Â compared to the base case risk went down.

Â Something happened to this company.

Â They hire this fantastic CEO.

Â For whatever reason risk went down.

Â We said before that you're willing to pay more.

Â You're willing to $1000.00 and 66 in order to get those same cash flows and

Â remember the bonus cash flows actually never change but now you're paying more.

Â Before you were paying 1000 now you're willing to pay 1066,

Â which means that the return that you're going to get is going to

Â be lower than the 10% that you get when you pay 1000 dollars.

Â And if you actually were to run the numbers and once again.

Â In a minute we'll run those numbers, then your return would be 8%.

Â So that means if I take $1066 out of my pocket today,

Â and I expect to get 100 one, two, and three years down the road, and 1100.

Â Four years down the road, my mean annual return would be 8%.

Â So notice two important things about bonds.

Â And, and it's going to become important when we define rd.

Â When we define, the, the cost of debt.

Â What important thing number one, when risk, the perceived risk of the company

Â goes up, then your willingness to pay go down, and your required return goes up.

Â More risk implies more required return, and you pay less for the cashflows.

Â On the other hand when risk goes down then your require return goes down.

Â And what you're willing to pay goes up.

Â So there's always this negative relationship between how much you pay and

Â the return that you get.

Â And as it's kind of natural to assume or

Â to think about the more you pay the less return you get, The less return you, the,

Â the less you pay the more return that you're going to get.

Â Now, how do we calculate those 10%, 12%, and 8%?

Â Well, it's not that complicated, but it's not that simple either.

Â That is the general expression.

Â C are coupons.

Â Those are the interest payments.

Â In our case.

Â Those coupons are the 100, 100, 100 that the company promised to pay for

Â the first four years until the bond expires.

Â And P is the principal or the face value which in our case is $1,000.

Â Now the Y that is in the denominators that is what we solve for.

Â That is our mean annual return.

Â So let's put some numbers in this to make sure that you understand this idea.

Â We take 939 dollars out of our pocket.

Â Remember this was the situation in which we perceived the risk of

Â the companies going up.

Â We still expect to get exactly the same cash flows 100, 100, 100, and 11,000.

Â And the Y's that you see in the denominator that's what we need to

Â solve for.

Â Now you may be more.

Â Unless mathematically inclined but that is not an easy thing to solve.

Â It's not an easy thing that you can solve by hand.

Â Excel actually solves these very quickly and and there's a technical note that I

Â will recommend later on that you have to read that shows you

Â how to actually calculate that Number, and were going to do it exactly as we did in

Â sessions one and two, we're going to do it mostly through out these scores.

Â That is everything that is formal, everything that is mostly

Â a formal expression, We're going to delegate that to the technical notes.

Â And then we're going to do a little problem set, so

Â that you can test whether your understanding the concept or not.

Â But again, solving that equation is not that simple.

Â You actually need either a scientific calculation, calculator or you need Excel.

Â But if you asked Excel, if you threw those numbers in to Excel and you said solve for

Â x y, then Excel will find that 12% return.

Â That we mentioned before.

Â So that's the way we calculate the return that we obtain from bonds.

Â Now notice one important thing.

Â The cash flows of the bond never change.

Â So the numerator, so the expression that we have it will never change.

Â The promise that the company makes never change.

Â What does change is the market price.

Â What does change is people's willingness to pay.

Â For those cash flows.

Â When the company becomes riskier, they will be willing to pay less.

Â When the company becomes less risky, they will be willing to pay more.

Â And as that number on the left-hand side changes, the solution for

Â those y's will also change.

Â And so as the 939, you know, suppose now you see that

Â risk is actually decreasing as you're willing to pay more and more and more.

Â The 939, then the y that is going to solve is going to go down and down and down.

Â So the more you pay, the less return you're going to get and

Â the less you pay, the more return you're going to you're going to get.

Â This is, if you've never seen this before, this may not be entirely obvious.

Â But if you think about it for a little bit it's kind of natural that more dollars out

Â of your pocket will imply, everything else equal, that's very important.

Â Everything else equal, that will imply a lower return and the less dollars you take

Â out of your pocket again, everything else equal, that will imply a higher return.

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