Calculating coupon bond price via non-coupon bonds

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I’m.. so lost here. I saw in my investment class that a bond price can be calculated by adding the sum of non-coupon bonds discounted by their respective YTM.

I can’t even expand on this strategy to give you more details on what I dont understand. I just dont get it from the get-go and Im hoping someone here will know what Im talking about because I can’t even elaborate. Why would this be a good way to calculate a bond price?

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For all financial investments we calculate the current price as the sum of discounted cash flows the investment will produce. For bonds this is easy as all the cash flows are usually set permanently when the bond is created.

Starting with the very basics, if we see each other every day, and I offer you the choice of a $20 today or $20 a year from now, hopefully you agree that $20 today is better, because you can spend the $20 you get today or keep it and have $20 a year from now too, so getting the money today gives you everything getting the money in one year gives you and also the use of the money for a year, right?

That’s the basic principle behind discounting cash flows. If money today is better than money tomorrow, increasing the amount of money tomorrow will eventually reach a point where they’re equal (Maybe $21 is the right amount to make someone not care about whether they get $20 today or $21 in one year). That’s a lot of background, but it’s important to understand this principal because we’re going to use it a lot to price bonds (which are a trade of money today for money in the future).

So when pricing bonds we’ll have an agreed upon rate that we’ll use to make future money the same as today money. That’s called the discount rate. Most bonds create a whole bunch of future cash flows (often periodic interest payments and then the principal payment being returned in the last period).

Non-coupon bonds or zero coupon bonds are just a straight trade of money now for a single future payment (it can be any amount of time from literally tomorrow to 10 or more years in the future).

So to price a bond we could figure out when all the payments the bond will generate will happen and then apply our discount rate to them for the amount of time between the purchase date and the payments, to discount them all to the purchase date, and then add them up (or there are a number of functions that simplify standard bond types for people who have more to do today than enter bond payments in a long column).

For a non-coupon bond, we discount the one payment back to the purchase date.