CF 2-3A – Internal and Sustainable Growth Rate – Corporate Finance

Let's take a look at problem two, three, a, we're going over a couple of growth rate calculations. The calculations themselves aren't too hard, but kind of understanding what's going on might be a little harder. So let's discuss the meaning of an internal growth rate and a sustainable growth rate as we solve the problem. So I'm going to distinguish the two immediately. The difference between an internal growth rate and a sustainable growth rate is this an internal growth rate is how fast a company can grow without taking on any new debt. So it's what percentage and growth the company can experience without taking on any new debt. A sustainable growth rate is the rate of growth a company can have while taking on some new debt, but maintaining the same debt to equity ratio. In other words, as the equity grows, the debt is allowed to grow along with it, where an internal growth rate, the equity grows, the debt has to stay at the same level. So we're going to project that a sustainable growth rate will always be larger than an internal growth rate. Let's get to the problem and hopefully it sort of clears itself up as we go. So we were given financial statements, given a dividend payout ratio, and it says compute the company's internal growth rate. Now there's just a formula for this. At the end of the video, I'll show you, I'll prove that this does indeed work. But at this point, you just want to kind of know the formula. So the formula for an internal growth rate is ROA, return on assets, times B, I'll explain what B is, divided by 1 minus ROA times B, so lowercase b, 1 minus the numerator. Okay. So ROA is return on assets. We learned to compute that last chapter. It's net income divided by total assets. So here it's net income divided by total assets. We can do the math. In fact, let's do the math, 350 divided by 2000, 17.5%. Okay. So I'll put 0.175, 0.175, that's our ROA. What is the B? The B is called the plowback ratio or the plowback. So if we have a dividend payout ratio of 30%, so it means of our profits, 30% is getting paid out. It's our policy to pay out 30% of our profits in the form of dividends. How much are we plowing back in the company? How much are we keeping in the company? How much are we retaining in our company's retained earnings? Well, the answer is the inverse, right? If our dividend payout ratio is 30%, the plowback rate or the plowback ratio is going to be 70%. That's how much we are plowing back into the company. So that's B. B is the plowback. So 0.175 times B, so it's 0.175 times 0.7 divided by 1 minus 0.175 times 0.7. Okay. So let's crunch all the numbers. So 0.175 times our plowback, which is 0.7, it's 0.1225. That's my numerator, 1225. My denominator is 1 minus 0.1225. So 1 minus 0.1225, 0.8775. So 0.1225 divided by 0.8775, and it's going to give us a percentage, 0.1225 divided by 0.8775 equals, whoa, I messed that up. I missed the decimal, 0.1225 divided by 0.8775. There it is, 13.96%, 0.1396 or 13.96%. Okay. So that is our internal growth rate. And that just means no more debt. How quickly can I grow? What's the maximum this company can grow without taking on new debt, without taking on leverage? That's the answer. That's the internal growth rate, and it's about 14% for this company. Now I'm going to prove that, but I'll prove it a little later. So let's compute the sustainable growth rate, then we'll come back to that concept. So the sustainable growth rate, almost the exact same formula, we just changed one letter. We changed the A in ROA to E, so we use return on equity, exact same formula otherwise. So the formula is ROE times B divided by one minus ROE times B. So what's our return on equity? Well, it's our net income divided by our equity. So net income divided by equity, 350 divided by a thousand is 0.35. So 0.35 times B, same B as before, which was 0.7, 0.5, 0.35 times 0.7 divided by one minus, oops, one minus 0.35 times 0.7. Okay. So now let's crunch the numbers, 0.35 times 0.7 is 0.245 divided by one minus 0.245. One minus 0.245 is 0.755, so 0.245 over 0.755, and let's at long last get a number, 0.245 divided by 0.755, we get 32.45%. So remember what this ratio was. The first ratio I think is very clear, at least in my mind. The internal growth rate tells us how quickly can this company grow without taking on a single dollar of debt. So the company can grow about 14% per year. The sustainable growth rate is how quickly can the company grow while maintaining the same debt to equity ratio? That means it takes on more debt, but the debt grows in proportion with the equity. So the fastest it can grow there is 32%. So it can grow faster. The sustainable growth rate is always going to be higher than the internal growth rate. Okay. If you want to stop there, I think this is a great place to drop out. I'm going to keep going though, but if you want to stop there, no hard feelings. As long as you smash one of those buttons, no hard feelings. But if you want to keep going, I just kind of want to prove this one. We won't go through both. You definitely could do both. I just want to prove this one. So if we grow at 14%, 13.96%, what does our company look like? And the answer is it looks like it grew by 14%, but we don't take on new debt. Let's do some math here. So again, we'll recast our income statement plus 13.96%, right? Assume we grow by about 14%. So 3,000 times 1.1396, 3418.8, 2,500 times 1.1396, 2849. 3418.8 sales minus our costs, 2849, 569.8. Taxes will be 30% of that, 170.9 say, and profits 569.8 minus 170.9, and we get 398.9. Okay, so our income statement has now grown by about 14%. Let's contemplate what that looks like for our balance sheet now. So our income statement's grown by 14%. What about when our balance sheet grows by 14%? But we, again, want to maintain the same level of debt. That's the whole idea here. So our current assets are going to grow by 14%, 200 times 1.1396, 13.96%. 227.9, 1,800 times 1.1396, our fixed assets grow, 2051.3. Totaling up here to, oh, sorry, 227.9 plus 2051.3 gives us total assets of 2279.2. That's going to be our total liabilities and equity, 2279.2. Let's figure out what our equity is going to be after having this happen. Okay, so our old equity was 1,000. We're going to add the net income, add the profit, 398.9. We're going to take out a dividend now. Dividends are 398.9 times 0.3, 119.7, and that's going to give us our new equity. So 1,000 plus three, our net income, 398.9 minus our dividend of 119.7. This gives us our new equity next year of 1279.2. Okay, so there's our new equity, 1279.2. Okay, so now we know our liabilities, or we know our equity rather. We know our liabilities plus equity. We're just going to solve for liabilities. And you can see the answer here. What's the missing number? Well, it's something plus 1279 equals 2279. It's 1,000. The whole point of this exercise was to say, if we grew by 14%, we're not going to need to take on any new debt. And guess what? I crunched numbers. It's true. If we grow by 14%, exactly, well, 13.96%, we don't need to take on any new debt. That last part of the video, there's a reason I said goodbye to a lot of the students, because generally speaking, you're not going to be asked to prove that. You're just going to be asked to like crunch the number, right? And so crunching the number is a lot shorter, but I just wanted to prove to you that this does in fact work. So it worked for me. If it worked for you, hit one of those buttons. Have a great day. Thanks for watching. Bye bye.