This workout is gonna get us to explore what happens to bonds as we change the yield. And you can see we've got four bonds and they have different maturities and coupons. And we're gonna figure out the initial price for these four bonds. Then you'll notice that from top to bottom, the yield is moving from 5 to 6%. That's gonna lead us to a new price. And then we can see how the different bonds respond to that different yield and we can draw some conclusions about what type of bonds are more or less sensitive to a change in yield.

Even the way the information is organized here, probably the most sensible way to get the price of this bond is by doing a present value of its future cash flows. And we'll do that by using the PV function. If you're ever in doubt about how a function works, one way to figure it out is to click the fx button. That's what I'm gonna do. This opens a dialogue and it suggests what we might be putting in and it also has a handy explanation of what is the meaning of each of these terms. So it tells us the rate, well, that's our yield.

It then asks us for the number of periods, that's gonna be the maturity. It then asks us for the payment. Now, it cannot change over the life of the investment. So if we had a bond that had different coupon over its life, we couldn't use PV. But here, the coupon appears to be the same every year. And so we put it in.

Now, the fair value will be the par value and we are not given that, but we have to assume that it's 100.

Now, we hit OK and we get an initial price, but you'll notice it's negative. The PV will give us a negative price if we feed it information the way we have here. And so let's just add a times minus one to the end of that, drag it to the right using control R, and then you can see the formula there if you missed it. And so we can see the different pricing of these bonds. And it makes sense that the third bond would be the most expensive because it's delivering a very high coupon, compared to the required yield. Now, if we fully understood row nine here, the nice thing is we can take that, copy it, and paste it down here. And because the organization is of the data's the same from top to bottom, it will copy down quite nicely and give us the new prices. You can see that all the prices have gone down, which makes sense because the required yield has gone up. So you'll have to pay less for these bonds for them to deliver you your 6% yield to maturity.

To finish things up, we would get the price drop. And so what we'd say is, okay, what's the closing position? Put it relative to the opening position, and then minus one. And you can see that we have a small price drop for the first bond and that price drop goes up as we go to the right. And this starts to demonstrate the ideas of duration and bond pricing in that the longest dated bond is the one that has the greatest sensitivity to change.