 And welcome to the session. This is Professor Farhad in which we would look at the present value of growth opportunities, the plowback ratio, as well as the retention ratio. Before I start, I would like to remind you to connect with me only then. If you haven't done so, YouTube is where you would need to subscribe. I have close to 2,000 YouTube videos that covering accounting, tax, finance, auditing, as well as Excel. If you like my lectures, please like them and share them. If they benefit you, it means they might benefit other people as well. If you're a CPA candidate, I strongly suggest you check out my website, farhadlectures.com. At least you want to find out how well is your university performing on the CPA exam. I do have plenty of resources that will help you improve your grade by 10 to 15 points. So let's start this session by discussing two companies, Cascale, Inc., and Growth Prospects Inc. The expected earnings per share for both companies is $5. The payout ratio is 100%. The payout ratio means when they earn this $5, they distribute all of it in terms of dividend. If they distribute the $5 in dividend, what remaining is retained, and specifically from an accounting perspective, it's retained earnings, but here we're going to assume we pay out everything. The market capitalization rate or the required rate of return for both companies is 12.5. Now, based on this information, we can find out what's the stock price of the company, which is D1 divided by the required rate of return, which is $5 divided by 12.5. Remember, this is the expected, it means it's D1. Therefore, the stock price of the company is $40 based on this earnings and required rate of return. Now, growth companies, they would like to invest in a new project, maybe a new product, maybe expand geographically. To make the long story short, they can earn 15% on this new project, and they're going to change, they need some money, they need some money to invest in this project. The dividend payout ratio is 40%. What's going to happen is, remember they have this $5, and they pay all of it in dividend. What's going to happen is this, they're going to pay $2, and they're going to keep $3. So, the retention ratio is 3 divided by 5, which is 60%. The payout ratio is 40%. So, the plowback or the retention, another word for the retention ratio is the plowback ratio is 60. So, 60 plus 40 should equal to 100%. So, how much growth are we going to generate if the growth prospect decided to find a project that will earn them 15%. Well, here's what's going to happen. We're going to invest $100 million from equity, from equity means from earnings, in property, plant, and equipment to expand. We need this, we need, we need those equipment to start our new project. So, we're going to invest $100 million, and this $100 million, it's going to return 15%, which translates in $15 million return on the equity. We're going to assume we have 3 million shares. Here's what's going to happen. If 60%, now remember, we earned 15 million. If 60% of the 15 million is reinvested, then the value of the firm capital stock will increase. It's going to increase by 15 million times 60%. It's going to increase by 9 million or percentage-wise is 9%. So, the percentage increase in the capital stock is the rate at which income was generated times, so it's ROE, not I, times the plow-back ratio, which will be donated by B. So, ROE return on equity multiplied by B. What does that going to give us? Now, with a 9% more capital, the company earned 9% more income and pays out 9% higher dividend. Therefore, the growth rate of the dividend, how do we find the growth rate? It's ROI, which is return on equity is 15% times the ratio that we reinvest. Therefore, G, the growth is 9%. So, we have to know what is the growth. Now, the growth is 9%. Okay, now, we're using the money that we are making to reinvest in the business, and 60% of it, and that 60% is making 15%, which is given us a growth rate of 9%. So, if the stock price equal to its intrinsic value, and this growth rate can be sustained, then the firm stock should sell at how much? Now, we have a new price, P0 equal to D1, and rather than just divide it by K, now we have a growth rate minus the growth rate. So, K is 12.5 minus the growth rate. The stock price is $57.14. Now, remember, how much was the price if we did not invest? The price would have been $40, as we saw on the first slide, which was basically D1 divided by K, which was $5, keeping the whole, distributing the whole amount divided by 12.5, which gives us $40. So, notice, if we reinvest at 15%, to grow the company, the stock price will be higher, okay? So, when growth prospects pursuit a no-growth policy, no-growth policy means you are not reinvesting in the company, you're paying out everything, the stock price was only $40, and this is an important concept. You have to understand that's why certain companies pay dividend and others don't. So, why would the company pay dividend? The company pay dividend when they don't have internally a project that's gonna earn them something above the required rate of return. If that's not the case, then they're better off given the money to investors or the investors are better off getting the money because the company cannot earn more than the required rate of return, okay? So, when you have a no-growth, that's why no-growth, you pay out the dividend. But think of tech companies, think of startup pharmaceuticals. They need this money to reinvest, that's why they don't pay dividend. They keep everything, they reinvest everything. Simply put, the plow-back or the retention ratio for these companies is on the other extreme, they keep 100%. Like Twitter, Twitter keeps 100%. Obviously Tesla, they're barely making any profit of any. Those companies, they will need this money to reinvest. And it's a big deal when the company decide to distribute money. Therefore, you can think of the $40 value per share that has already in place as the no-growth price. So, the $40 is the no-growth price. Now, let's take a look at the growth opportunities, the present value of growth opportunities. The increase in the stock price, remember it, we went from 40 to $57.14, reflect the fact that planned investment provide an expected return greater than the required rate of return. This is important. In other words, the investment opportunity have a positive net present value. So, we have to make sure we understand this. And we're gonna mention this, that when you reinvest, you're gonna have to reinvest in a project that has a greater required rate of return than you are doing. So, the net present value is also called the present value of growth opportunities abbreviated as PV Go, PV Go. Therefore, we can think of the value of the firm as the sum of the value of the assets already in place or the no-growth firm, which is in our situation was $40, plus the net present value of the future investment of the firm will make, which is the PV Go. Dose together will give us the PV, the PV Go is 17.14 plus $40, will give us the $57 that we are discussing. So, simply put, this is the no-growth component of the price, which is the no-growth component is $40, plus we found a project that's gonna help us grow. And because of that, we added $17. And this is how you basically value the stock when the company has a new product. We have to find out if the new product or if the new project has a higher required rate of return. If it doesn't, then the stock will not grow. So not every time a company launches a product, obviously the company would launch a new project unless most companies will have a policy they have a required rate of return and they want to make more than that required rate of return for the company to grow. Therefore, when interest rate is low, what's gonna happen is your required rate of return should be lower, okay? Because your required rate of return is the cost of money, the cost of money. So let's assume you're borrowing. The cost of money is low. It's gonna give you a lower threshold to overcome. So if you have lower interest rate, therefore the stock price will go up because the companies will undertake more project. So hopefully this makes sense. It, you know, fit with everything that we learned so far in this course. Now we have to keep in mind not all growth is the same. So the growth only enhances the value if, again, the return on equity is greater than the required rate of return. This will be considered an attractive property. To justify the investment, the firm must engage in project with better prospective return than the shareholders can find somewhere else. This is why firm with considerable cash flow with limited investment prospect are called cash cows. For example, a company that does bubblegum, that they manufacture bubblegums. Well, there's not much they can do if that's all what they do. Therefore, they're called cash cow. These firm what they do, they make the cash and the cash is milled from the firm. It's milked out. It leaves the firm. Let's take a look at an example to see how this all fits together. Takeover is run by an entrenched management that insists on reinvesting 60% of its earnings in project that provide ROE of 10%. Despite the fact that the firm capitalization is 15%. So notice they have a policy, you know, we would like to invest 60%. Well, that's fine. But you're not having any project that's exceeding K, that's exceeding your capitalization rate. Therefore, they're investing at project that earned 10%. So the firm year end dividend will be $2 paid out out of the $5 per share earnings. So that's what they do. At what price will the stock sell? So we need to find out at what price will the stock sell? What is the present value of the value of growth opportunities PV go? Why would such a firm be a takeover target of another company? So let's look at these questions. So, well, giving the current management investment policy, what is the dividend growth rate? Well, the dividend growth rate simply put return on equity times the blowback ratio or the retention ratio. To return on equity, they can earn 10% times the reinvesting 60%. Therefore, their growth is 6%. So now we can find the stock price. The stock price is the D1 divided by a required cap K minus G, which is 15% minus 6%. Therefore, the stock price is the intrinsic value is $22 and 22 cent. Now, what is the PV go? Well, the PV go is the price per share. And here we're gonna subtract, we're gonna subtract and you will see why in a moment, no growth value per share, okay? So we have $22 and 22 cent minus $5 divided by 15, okay? So it's negative. So the present value of no growth is negative. So basically by doing this reinvestment, we are in a sense losing value for the shareholders. We are losing $11 and $11 and 11 cent for the shareholders. So the PV go is negative in this situation, okay? Why? If you let the company grow, just by paying out all the dividend, don't reinvest, the company is better off. So PV go is negative. This is because the net present value of the firm's project is negative. So the rate of return on those assets is less than what we call the opportunity cost of capital. Such a firm would be subject to takeover, why? Because another firm could buy the firm for the market price. So if the price is 22.22, 22.22 and guess what? Just simply put, don't do anything. If the new management simply pay out all the earning as dividend, that's all. The value of the firm would increase to its no growth value. What's its no growth value? $5 divided by return on equity of 15% I'm sorry, capitalization rate of 15% or required rate of return will give us a stock price of $33.33. So if they don't do anything, if they don't reinvest, if they just kind of cross out this policy, the stock price should be $33.33. And this is what we say is not all growth policies are the same. So we have to make sure this return on equity is greater. So return on equity should be greater than K for the PV go is positive. Let's take a look at a couple more examples. Compute the price of a firm with a plowback ratio of 60% if it's ROE is 20%. Well, first we have to find the growth rate. Well, ROE times the plowback ratio or the retention ratio, which is 0.2 times 0.60 which will give us a growth of G equal to 12%. Now current earnings E1 will be $5 per share and required rate of return is 12.5. All right, that's fine, let's see. So we're gonna have $5 D1 divided by K which is 12.5, this is K minus G minus those are percentage. So we're gonna have $5 divided by 0.5 and that's gonna give us $400. Okay, so P0, that's what they're asking. Yes, P0, price zero is $400. Now, what if ROE is 10%, ROE is 10%. So we're gonna change ROE 10% which is less than the market capitalization. What would happen then? Well, what would happen is the stock price will fall. The stock price would fall. Compare the firm price in this instant to that of a firm with same ROE and E1 but a plowback ratio of zero. Basically, you don't keep anything. So what's gonna happen is this. So compare with the same ROE, okay, so let's see. So if we say growth, let's look at the growth rate. So the growth rate for, let's look at the 10% we're gonna look with this example here. So the growth rate is, I'm sorry, ROE equal to 10% times 0.6 and that's gonna give us 6% G, 6% G. That's fine. Now we're gonna have to find P0, what's P0? If that's the case, it's gonna be D1 which is 60%, if 60%, so we have $5, we're gonna keep $2, so $2 in dividend. So that's the dividend because we're keeping the $3, remember, they pay, the earnings is $5, $2. Now, 0.125 minus 0.06, minus 0.06 and this is gonna give us a stock price of $30.77. So if they invest 60% of their earnings and return on equity of 10%, the stock price will go down to $30.77. What if they don't do anything? What if they keep all the money? I'm sorry, not keep on the contrary, they distribute all the $5 in earnings and the return on equity here is 12.5, not the required rate of return, sorry, 12.5%. Well, the stock price now is $40. So notice here, so obviously this is the best option if they can find project that will earn them 20% because the stock price will be equal to 400. You know, if they should not invest at 10% and if they cannot, they should not invest at project that earn 10%, what should they do then if they cannot find those profitable project above earning above 12.5, don't do anything, just distribute everything, everybody will be better off. Hopefully this will make sense and once you complete the homework, it will make more sense. Again, I'm gonna invite you if you're studying for your CPA exam to check out my website for head lecturers.com and invest in your CPA career. The CPA is a long-term investment, 2030, maybe 40 years, we are living longer. Don't shortchange yourself, take it seriously. Good luck, study hard and stay safe.