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## Finance and capital markets

### Course: Finance and capital markets>Unit 6

Lesson 4: Corporate metrics and valuation

# P/E conundrum

A situation where the price to earnings ratio seems to not fairly price an asset. Created by Sal Khan.

## Want to join the conversation?

• At , Sal talks about the P/E ratio being 10? How did he get the number 10? Did he just choose it (I remember in a previous video he said 10 was a nice round number for the P/E ratio)? Because I thought that you had to calculate the P/E ratio based on the P and the E.
(27 votes)
• I think the confusion is that Sal was trying to show how just looking at P/E ration can skew the your analysis when you have two companies with different capital structures. If you wan t to show this how can you just randomly pick a P/E ration, when he was showing the Income he just picked 10. I'm confused by this, it would make sense if he said market price was x and so based on x P/E is y. Can someone please clear this up?
(11 votes)
• There seems to be a structural mistake in this example. If a company has a relation of 900% Net Debt / Equity, the cost of debt would be huge, wich means that the net profit would be much, much smaller... and using the same P/E, the Market Cap of the second company would also be much smaller, meaning that the asset value calculated by "the market" is also much smaller than the first company.
(6 votes)
• I believe he used this extreme amount of financing to end up with an extreme valuation difference. In real world applications, you are correct. However, the amount of overvaluation may not be as apparent. Also, companies have completely different capital structure mixes and growth fluctuations. Again, I believe the extreme amount of financing was just to easily show the fundamental problem with using solely p/e's.
(7 votes)
• At , The whole confusion is because of the assumption to take P/E as 10 for both companies, which has totally different price/share( book value). Shouldn't they have different P/E ratios? i mean why consider same P/E ratio when they are likely to have different price/share( huge difference)??
(4 votes)
• there is no such answer why people are ready to invest for such high p/e.. and there are plenty of individuals in market who does invest money without knowing b/s of companies.. they blindly follow rumors and invest their money in these stake expecting higher returns and creates demand which increases price of share.. after all . the only rule runs a market is demand and supply.
(2 votes)
• For the second company on the right, why the asset is taken to be 100K and not 110K?
(4 votes)
• It is 110 K of assets. The 10k is just cash on a bank account but it is stil assets of the company. The 10k is defined as non-operating assets.

Always compare the assets to the liabilities which in this case is 110K then the assets have to be 110K as well.
(1 vote)
• Both of the companies are paying 30% tax, question is why the second company is paying equal amount of tax beside having 100k dollars of debt?? second company should have more profit and it should enjoy tax benefit
(3 votes)
• The two PLCs will pay the same amount of corporation tax unless they use tax avoidance schemes etc. The second company is paying the percentage of tax (30%) on a lower amount - which means they will pay a lower amount in tax. This is due to the "interest expense" also known as the tax shield, which reduces the amount of money that can be taxed.
(1 vote)
• Would using the price to book ratio give some light to such a misvaluation?
(1 vote)
• when there is 10k in cash on top of 100k asset, wouldn't that mean total asset is 110k instead of 100k?
(2 votes)
• Yes. Company B has \$110K of assets. Remember A = L + E. Company B has \$100,000 in liabilities and \$10,000 in equity. In the video he lists the cash as distinct from the assets used to run the business, but they are both considered assets.
(1 vote)
• at wouldn't the net income for the first pizza place be 11k? Since 20k - 9k = 11k?
(1 vote)
• At , why does market value 189k means equity 10k instead of assets 100k?
(1 vote)
• what's the meaning of P/E Ratio: (Adjusted) ?
(1 vote)
• It depends on who is doing the adjusting. A popular measure is the Shiller P/E which is adjusted for the earnings cycle and inflation. A very simplified version would be to take the average earnings over the past 5 years to use as your E.
(1 vote)

## Video transcript

Let's say we have two entrepreneurs. And they are both interested in buying a pizzeria and eventually turning it into a public company. So let's compare the two. So let me draw a dividing line here between the first and the second entrepreneurs. And they're actually going to buy identical assets. So they're going to buy a pizzeria with the ovens inside of them. And the same amount of cash in the cash register. Everything they need to operate the pizzeria and they may be in identical locations. Maybe right next to each other at the same intersection. Or across the street from each other. It's the same asset. Let me draw that out. I don't want to draw this box. So that's the asset. And it costs \$100,000. That includes the building. It includes the oven. It includes the places where the customers come sit. It even includes the cash needed to operate the business. So you need some cash to pay vendors just to get started and to pay for things like dough. And have some money in the cash register. And to have a little bit of a bank account. Things like that. So that's all inclusive. All of the assets needed to start the firm, the pizzeria. So this is the assets. And they both buy identical assets. So let me copy and paste that. They buy identical assets. Now, the first entrepreneur, he's very conservative and he's been saving all his whole life to do this. So he actually has \$100,000 of cash to buy his pizzeria, so he buys it outright. So he owns it outright so all of the \$100,000 of asset value is actually his equity. Let me do equity in a different color. It's all his equity. So that's all his equity. This guy here, maybe he's a little bit earlier in his career, or he's just not as good at saving money. So he doesn't quite have \$100,000. He actually only has \$10,000 in his pocket. But he's a smooth talker. So he goes to the local bank and says, hey I have this great idea for-- let me write this down, \$10,000 of equity, that's what he has-- but he tells the guy at the bank, and he buys him lunch, and he says, I have this great idea for a pizzeria. And they agree to give him not just \$90,000. This guy, he's a little ambitious too. He thinks not just beside a pizzeria. In the name of the pizzeria he's going to borrow some money and then maybe invest that in stocks or something. So he gets a sweetheart deal on the loan. And he's able to actually borrow a little bit more than what he even needs. He only needs \$90,000, but let's say he borrows \$100,000. So he borrows \$100,000 of debt. And so, he has \$110,000 to play with. He buys a \$100,000 pizzeria. And then he has another \$10,000 left over to do with what he wants. And he puts it in the pizzeria's name, in the pizzeria's bank account. Because he has to show the bank that it's going towards the pizzeria. But his real intent is to maybe gamble with it on the side in the pizzeria's name, and maybe invest in stocks or speculate on pork belly futures or something like that. But for all intents and purposes it's cash. And so they go off and they start their pizzeria. Let's see what happens. So let's look at them over the course of one year. So let's say, revenue. So let's say the first year they're identical. They both make \$100,000 in revenue. Let's say their cost of goods sold is roughly 50% of that. So it's \$50,000. I'll put a minus there because it's an expense. Minus \$50,000. So both of their gross profit is \$50,000. And then their SG&A is the same. If you've watched the video on depreciation and amortization, this might even include the depreciation on some of the physical assets they've bought, or maybe the amortization on the rights to the name Super Pizzeria. In either case. Maybe the brands are identical. So that's another \$20,000. Minus \$20,000. So far they look very, very identical. And that's because they have the same exact asset. So their operating profit. 50 minus 20 is \$30,000. And now we'll start to see a little difference. And this goes back to the very first video we saw. It says if you have an identical asset and it's being managed identically, which it is in this case, they will generate an identical amount of operating profit. But when I talk about the asset, I'm talking about only the operating assets. This guy has some non-operating assets, although it's officially part of the company. He doesn't need it to operate. This is cash above and beyond what's needed in the cash register. And we might have a little bit of cash here in this asset that's needed for the cash register. And I'll teach you more about working capital. But in order to pay vendors and things like this. This is cash above and beyond what's necessary. This guy has a little bit of cash just to operate the business. He just doesn't have this gambling cash out here. So now we add an interesting line. Non-operating income. This guy doesn't make anything. He's not gambling. This guy's pretty good with this \$10,000 of speculation cash. He makes, say, 20% on it in this first year. So he makes \$2,000. And then we have interest expense. This guy has no debt. Very prudent. He has no interest. So his pre-tax income is \$30,000. This guy, he does have interest. And let's say on that \$100,000 of debt, he got a really good deal. Let's say that the Fed thought that he was systemically important to the future of our financial system. So he gave him a sweetheart 2% debt deal, because he was afraid that if this pizzeria were to fail, it would bring down the entire financial system. So given that 2% on \$100,000 debt. That's \$2,000 of debt a year. So minus \$2,000. I'll make it a little bit more realistic. Let's say it's 5%. So 5% on \$100,000 is \$5,000 per year in interest. So that's his interest expense. Let me write that. This was interest. This was non-op income. This was operating profit. You just have to carry the lines over. And so his pre-tax income is now 30 plus 2 minus 5 is \$27,000. They both pay 30% in taxes. And so this guy's paying \$10,000. Well, actually, \$9,000 would be 30%. And this guy, 30% of 27. So let's see. Taxes. 3, 6,000 plus-- 8,100. Minus \$8,100. Is that right? Yeah. That's \$9,000. And then if you have \$3,000 less, you should be \$900 less. Yep, that's right. And so, we're finally at the net income line. This guy makes \$21,000. This guy makes-- what is this? This is \$18,900 net income. And of course the difference is the money that he had to spend on tax. On interest expense. If you net out all of his little financial engineering, he had to pay \$3,000 more in interest, if you net out his profit he made on his little cash bets, his side bets. And that was able to be a tax deduction. So the actual effect ends up being \$2,100. Which is essentially \$3,000 of a 30% tax rate. So, fair enough. That's not what I want to do here. I don't want to focus too much on the tax savings on interest. What I want to do here is focus on valuation and see whether the price to earnings ratio holds up to scrutiny in this situation, where you have an identical asset but very different capital structures. So let's say they both have 10,000 shares. I'll arbitrarily switch colors. 10,000. So EPS. This guy made \$21,000 this year. Divided by 10,000 shares is \$2.10 per share. This guy, \$18,900 divided by \$10,000 is \$1.89 per share. And we could have modeled out their income statements further. And actually, this guy, even if the top line, even if the revenue grew the same and the operating profit grew the same, because of his leverage he would actually grow a little bit faster. I'll do another video on how that works with leverage. But let's say that someone looks at this and says, OK, it's the same business and everything. And if anything, this guy's growing a little bit faster because he's got that leverage, that extra juice from the financials, from the capital structure he's got. So they both deserve at least a price to earnings of 10. So you say, they both deserve a price to earnings of 10. So 10 price to earnings. You'd say, I'm willing to pay \$21 for this guy. And I'm willing to pay \$18.90 for this guy. Now what does that result in their valuation, or in terms of their market cap? So in this guy's case, market cap. \$21 times 21,000 times 10,000 shares, means that you are ascribing a-- 21 times 10-- you're saying that the equity in this company is worth \$210,000. In this case, you're saying that the equity in this company is worth \$189,000. So this one's worth a little bit more, because it's earning a little bit more money. Although I don't want to complicate it, but you might be willing to pay a higher multiple here. So something very interesting is happening. By applying the same price to earnings, we're saying that the market value of this equity is \$210,000, while the market value of this equity is-- what was it?-- \$189,000. Something doesn't seem to make sense. This guy put up \$100,000, and sure, they invested it and did all that. So now the market's willing to say, hey, you know what? This is a pretty profitable business, more profitable than most. You're making good margins. And I'll do a bunch of videos on margins in the future. We're willing to say that the market value of your equity is \$210,000. Which implicitly means that the market value of this asset is \$210,000. They're saying, this is worth \$210,000. That's because this must be worth \$210,000. But if you look here, by giving the same price to earnings, because they're the same business. And maybe this guy's even growing faster, so maybe they're being conservative by only giving this guy a 10 price to earnings. You get a \$189,000 market cap for this equity. Which, all of a sudden, this guy only put in \$10,000, and people are saying it's worth \$189,000? And if this little fraction right here is \$189,000, then it implies what about this asset? What does it imply about the value of that asset? You have \$189,000 as the value of this equity. The value of this debt is \$100,000. So the market is saying, the right-hand side of the balance sheet is what? It's \$189,000 plus \$100,000. It's \$289,000. And let's say this cash is still cash. It's worth \$10,000. So if you subtract it out, the market is saying, this is \$289,000 minus this \$10,000, \$279,000. So something is very bizarre right here. That the market-- just because of how this guy has capitalized his company-- if they just apprised a superficial price to earnings of 10 to both companies, it's willing to say that this asset is worth \$279,000, and this asset's only worth \$210,000, even though they're identical assets! So I've already used more than enough time on this video, so I'll let you ponder that a little bit. In the next video, I'll show you that the reason why this is kind of breaking down is because a price to earnings ratio does break down to a certain degree when you start comparing things with different capital structures. And in the next video, I'll introduce you to other ways of comparing things with a different capital structures, or essentially deleveraging them. That when you just talk about price to earnings or market capitalization-- when you just looked at market capitalization, it looked OK. Oh, they're similar businesses. This one's worth a little bit more because this one has debt. But when you actually back out the implicit value of the asset, all of a sudden you realize that you're really overpaying for this asset. So think about that a little bit. What's the conundrum here? What went wrong? And in the next video I'll give you some tools to actually do this right.