Let's compare two bonds, one that pays coupons annually and one that pays coupons semi-annually. So in workout A, we're gonna price a bond that pays coupons annually. What should an investor pay for a 30 year 4.25% bond with a face value of a hundred, if the investor wants a 3% return? The bond pays coupons annually. Well, we are going to use the PV function here in Excel. So this function will ask us about the face value of the bond. That will be 100. It will ask us for the number of periods until maturity, that will be 30, would ask us for the required rate of return, which is 3%. And finally, we need to input the payment or the coupon rate. That is going to be 4.25% times the face value of the bond. That's 4.3 or 4.25.

What we've gotta do now is calculate the present value equals minus present value tab to select the function. Input the rate 3%, the number of periods, 30, the annual payments or the coupons, and finally, the face value of the bond. Close the brackets hit enter and the price is 124.5. So that's what this investor could pay, provided his required rate of return for this bond that pays coupons annually. Let's compare that in workout B to a semi-annual bond.

So in workout B, we're being asked, what should an investor pay for a 30 year 4.25% bond with a face value of a hundred if the investor wants a 3% return. So far, same question as before. However, this bond pays coupons semi-annually. In order to price this, we are going to use a different Excel function, namely the price function. The price function will first ask us to input a settlement date, and that is in this case a hypothetical date when the investor would pay for the bond if he or she bought it. So I'm just going to pick a random settlement date. The 1st of January, 2010.

The maturity date is 30 years after we bought this bond, plugin 1st of January 2040.

The coupon rate is 4.25%.

The yield or the required rate of return is 3%, and the redemption amount is 100.

Now let's use the price function to price this bond. So I'm gonna type in equals price tab to select this function. First thing we'll put in is the settlement date. Secondly, the maturity date. Third, the annual coupon rate. So be careful there. This is the coupon rate. Third, the yield the 3%, then the redemption amount. And finally, and you will see the dropdown up in the right hand corner.

The function will ask us for the annual coupon payment frequency, and I'm gonna pick semi-annual here in the dropdown tab to select that, close the bracket and hit enter. This bond is worth 124.6, and you'll notice that it's slightly more valuable than the example in workout A.

This is of course, because it pays coupons semi-annually, and the investor therefore receives cash flows earlier. Let's see what happens if we change that frequency to once a year and hit enter, and we will see that we get the same price as in the first example. So with the same frequency, this would be an annually coupon paying bond and it would have the same price as the bond, in example A, I'm just gonna change that back to semi-annual frequency again, and the price is 124.6 again.

So coupon paying bonds, you receive the cash flows earlier.