Calculating Bond and Stock Prices - Video Tutorials & Practice Problems
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Calculating Stock and Bond Price
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now let's see how we can use the time value of money to calculate the price of a bond today and the price of stocks today. So when we go to value and investment to say what is it worth today? We want to think of all the cash it's gonna bring in in the future. So we wanna think of it as the present value of the future cash flows. So we could think that in this first case a bond is going to pay us interest payments over the life of the bond and then finally pay off the principal. So a timeline for a bond might look something like this, let's say it's a three year bond. Just for simplicity. Most bonds are longer than three years, but this will give us the idea here. Okay, So what's gonna happen is we're gonna pay some amount and this will be the price today. So let me do it in a different color. We're gonna pay the price of the bond today, which is equal to what is going to be the cash flows in the future. So we're gonna see that after one year it's gonna make an interest payment. After another year it'll make another interest payment and in the final year it'll make another interest payment, right? But that's not all in the final year. They're also gonna pay back the principal the money that we lend to them, right? So we're also going to get the principal back. So if you think about our time value of money equation when we're looking for the present value, remember that present value equals the future value divided by one plus r to the end. So now we've got a few cash flows. We're looking for the present value of all these cash flows. We're not only gonna get one payment here, we're gonna get a payment here, a payment here, a payment here, right? There's multiple cash flows in this case. So to get the value of this bond today, we need to know the value of all of these payments together. So we're gonna add the value of all these payments together and that's exactly what's going on here in the bond price. So when we say coupon, that's the coupon interest, the interest that's being paid by the bond. So notice what's happening here, this first interest payment. We need to bring it back one year. So we're gonna take one plus the interest rate, right? I whatever the interest rate is on this bond, well we're gonna bring it back one year. Right? And then the second coupon payment will bring it back two years because we have to wait two years to get it. So what's the present value of uh of a two year payment. So notice all we're doing is using our present value equation from our time value of money and just having multiple payments all at once. And then finally we would do that every year, right the third year, fourth year depending on how long and then in the final year we would get one more coupon payment and we bring it back the number of years that it's been outstanding as well as the principal, the amount that we lent them in the first place, and once we find the value of all of those today, that is the price of the bond, the present value of those future payments. Cool. So the same thing happens here with a stock Except stocks don't pay interest and they don't have a principal amount. Right? When you buy a piece of stock, they're not gonna say, Hey, Alright, in 10 years I'm gonna pay you back that value of the stock. No, you're buying shares in the company. So what you're gonna get is dividends, you're gonna earn some dividends in the company. Okay. So the idea here is that the company that instead of cash flows being from interest and and um principal payments. The cash flows come from the dividends that you get from the from the stock. So you're gonna have dividends every year, right? You buy the stock now. So this would be the price of the stock today would come from the dividends that they're gonna play you in the future, right? So you're gonna get a dividend every year, let's say in a simple situation, you would get a dividend every year and that's what it would be worth today. However, when we think about a company, well the company we expect to grow over time, so we would expect the dividends to grow with the company. So when we do our calculation here, we actually do a little bit of a different calculation, it's it looks similar to what we had above with our time value of money, but we're accounting for the growth here without going into too much detail of how this is derived. It's good to just understand that what we're doing is basically finding the value of these dividends as they're growing. So this is dividend one and this is dividend to dividend three and we can expect that all of those are a little bit bigger. There's gonna be some growth in the dividends over time. So the way we calculate that is we're gonna take the value of the dividend and divide it. So this is the first dividend dividend dividend one, and then we're gonna divide it by the interest rate minus the growth rate. Right? So that this is these these numbers would have to be given to you, right? So it actually makes the calculation actually pretty easy, they'll tell you what the dividend is the interest and the growth rate. You just plug it into this formula and you get the stock price. Okay, so it takes into account those time value of money uh calculations, but it's at a little bit of a higher level. So for for this class it's good enough to just know the formula. Cool, alright. With that being said, let's go ahead and do a practice problem related to the.
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Problem
Stock Price = Divident (i - g) Where i = discount rate and g = dividend growth rate.
A stock currently pays a dividend of $1 per share. Dividends are expected to increase at a rate of 5% per year, while the discount rate is 8%. What is the current price of the stock?
