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Welcome, everyone.

Â Now that you've attempted the quiz on bonds, I'm going to walk you through to

Â what the correct answers are and how to arrive at them.

Â So let's start with Question 1.

Â And think through each of these answers to the question

Â of what motivates negative interest rates.

Â Choice a is the least acceptable answer because negative interest rates

Â actually make money cheaper.

Â So banks lend more and

Â consumers borrow more which can help to kickstart a sluggish economy.

Â 0:44

Choice b is counter intuitive, since the countries that adapt negative

Â interest rates, were trying to weaken their currencies, vis-a-vis the Euro

Â to make their exports more competitive, and their imports more expensive.

Â 0:59

Choice c is the best answer because negative interest rates signal

Â to commercial banks that they will pay a penalty

Â to keep money with the central banks, which is what hoarding refers to.

Â And this should lead them to lend more money out to businesses,

Â again, to boost the economy.

Â 1:18

As mentioned in the video, negative interest rates are trying to do

Â the opposite of choice d, to avoid deflation when prices fall,

Â since this will just reduce national income and cause an economic contraction.

Â So the correct answer is c,

Â negative interest rates discourage banks from hoarding money.

Â Let's look at Question 2 now,

Â which asks what a typical corporate bond's coupon rate is quoted as.

Â Choice a and b speak to effective annual rates or EARs.

Â EARs convert the annual percentage rate, that is,

Â the APR, the rate which is advertised in the bond

Â issue into a rate that takes into account the effect of compounding.

Â This conversion is actually not done when the coupon rate is quoted.

Â 2:08

The correct choice is d, and not d, since the coupon rate simply advertise the APR,

Â or the stated rate, typically on semiannual basis.

Â So if the coupon rate, let's say is 6% compounded semiannually,

Â this means that keeping in mind the face value of a bond is $1,000.

Â The semiannual rate of 6% divided by 2, which is 3%,

Â will be $30 that will be paid out every 6 months.

Â Okay, let's look at Question 3 which asks whether the following statements

Â are true or false.

Â Statement a is false because, although it defines the current yield correctly,

Â the yield to maturity is not the same thing.

Â The yield to maturity is a market-determined rate that takes into

Â account both the coupon, the current price,

Â as well as the maturity of the bond which includes the time value element.

Â 3:41

Okay, let's look at Question 4.

Â Now this is an easy one to explain because all of these statements are correct, and

Â were explained in the video.

Â And the choice of course is d, which is all of the above.

Â Question number 5,

Â this requires us to pick out the relevant information in the problem and

Â then maybe depict it on a timeline, and then we can work through the calculations.

Â So let's isolate the important information.

Â First of all, we have the face value also known as the par value

Â of the bond with is $1,000.

Â We also have the coupon rate, and

Â the coupon rate is stated to be 10%.

Â And 10% of course of the par value which gives us $100.

Â The maturity of the bond, which is how long

Â it is outstanding, is given to be 8 years,

Â whereas the yield to maturity is stated as 12%.

Â Notice the difference between the coupon rate and the yield to maturity.

Â And very important to note that there is a frequency of compounding,

Â which as you remember from previous videos, is denoted by m.

Â In this case it is semi annual, so it is twice a year.

Â Now right away when we see the frequency is greater than one,

Â we should make adjustments to the coupon rate, to the majority and to the yield.

Â What will happen is this is paid annually, so if we're paying this semi-annually,

Â we must divide this by 2, which will give us $50 every 6 months.

Â Where as the maturity will now be 2 periods per year, we have 8 years, so

Â we multiply this by 2.

Â This gives us 16 periods and, of course, the yield again stated annually

Â must be divided by 2 which gives us a semi-annual rate of 6%.

Â So, why don't we put this up on a timeline?

Â And that we'll help us to visualize what exactly we're trying to do.

Â 5:58

And we have 16 periods to depict on this timeline.

Â So we can do that.

Â All the way to period 16.

Â And then we want to put these cash flows on this timeline so

Â we understand the valuation process.

Â The cash flows as you can see here, include, first off all

Â we have the $50 coupon payments every 6 months, so we can put that over here.

Â The $50 that we can expect to receive form the issuer all the way to the last period.

Â And then we also get back the phase value which is 1000, again in the last period.

Â And now our task is to simply discount these values back

Â at the very important market rate, known as the yield to maturity.

Â So here we can state now the equations to value the bond.

Â This is what we were after in the first place.

Â The bond price today, so this is the value we're after, right now,

Â today, is going to equal to the present value of these coupon payments.

Â So we can just write that.

Â Present value of the coupon payments.

Â 7:15

So the equation as you can see is quite simple.

Â All we have to do is plug some numbers in and off we go to the races.

Â So what are the numbers?

Â Well, we have here an annuity which we've already learned

Â is a series of equal numbers made in equal time intervals.

Â We have a discount rate, we have a time period, so this is easy.

Â So the market value is going to be the present value of this annuity,

Â which is $50 multiplied by the present value annuity factor,

Â which will be based on 6% interest for, as you can see, 16 remaining periods.

Â 7:57

And to this, we will add the second half,

Â which is a lump sum, 1 number, we have to zap back,

Â which is simply the present value of 1000 multiplied

Â by the present value factor 4 at 6% for 16 periods.

Â So, if you crunch the numbers, what do we get?

Â We get a value equal to $899, and

Â $899 corresponds to the correct answer.

Â All right, let's look at Question number 6.

Â Now given the information that these bonds are identical, and

Â we need the yield to maturity as we just saw to calculate the price.

Â What we can do is if first find the yield to maturity for bond A.

Â Now if we set the information up just like we did,

Â where we are given the bond price and that bond price is $885.30.

Â That's the price which we know is equal to the present value of the coupon.

Â We know the coupon is 50, and so the present value annuity factor for

Â again, this time we have 20 periods, but we don't know the yield.

Â So that is the missing variable that we're looking for.

Â Plus, we're going to have the $1,000 principal returned to us.

Â Again, present value 20 periods

Â at the yield to maturity which is what we're looking for.

Â So we have an equation with one unknown.

Â Now, mind you, the mathematics of this is a little bit tedious,

Â because the formula that we use actually to compute these values.

Â If I isolate that formula for you, which is this

Â annuity formula, the annuity formula is 1- 1

Â over 1 + r raised to the power t over r.

Â 10:20

Keep in mind that again we're looking for

Â a semi-annual yield because that's how the problem was set up.

Â And if you solve for that semi-annual yield, what you are going to get,

Â in this example.

Â The answer is going to be the yield to maturity,

Â on a semi annual basis, is equal to 6%.

Â Now, that's what we were looking for

Â to be able to solve the bond price for the next bond b.

Â And so all we have to do now is plug the numbers in for this kind of equation.

Â And this is going to be fairy straightforward.

Â So what do we know about Bond B?

Â We know the coupon instead of 50, for Bond B it is $70.

Â And again, we'll multiply this now with the present value

Â annuity factor at 6%, which we've figured out now, for

Â the 20 periods that it's going to be outstanding for.

Â Plus we're going to add again the face value component, the $1000,

Â for a lump sum factor, present value 6%, 20 periods, okay?

Â These, of course, can be calculated here, but If you have a financial calculator,

Â you're just laughing because you're punching in these values.

Â And you've seen that in the financial calculator tutorial,

Â you work this out and you get your answer which is $1,114.70.

Â Notice that this bond is selling at a premium

Â