# PBR and Evaluating the Stock Price of Tesla and Toyota

PBR (Price to Book Value Ratio) refers to how many times the market evaluates about the book value of equity for a company. The market will trade it at a higher price when it expects the company to generate more cash flows with equity capital in the future. Suppose company A and company B have the same amount of equity capital of 100. If the market expects A to generate profits of 3 and B to create 10 in the future, it will appreciate B’s share price higher. Another one. Assume that X and Y generate the same profits of 5 with the same equity capital of 100. However, if X shows the growth rate of 3% and Y shows 20%, the market will also trade Y’s stocks at a higher price. The higher the market expectation, the higher the market value compared to the book value of equity. In other words, the PBR multiple is more elevated.

Analysts use PBR for the following reasons.

• First, it is more intuitive than DCF model and is stable because it doesn’t contain many assumptions.
• Second, it is possible to judge undervalued or overvalued across companies within the same sector.
• Third, you can apply PBR to companies that don’t have PER due to the deficit.

• First, sometimes the book value of equity does not reflect the ability to generate future cash flows with intangible assets such as brands, technologies, know-how, and IP rights.
• Second, book value could be different when accounting standards affect the size of assets and liabilities.
• Third, if equity capital impairment increases, the book value can also go to minus.

## Definition of PBR

### PBR = Price per share / Book value of equity per share

PBR is a multiple of the stock price divided by the book value per share. When calculating PBR, keep in mind the following:

• When a company has several types of stocks, the stock price varies depending on the type. In this case, carefully consider how to obtain the book value and allocate it according to their type.
• When considering only the market value of common stocks, you should subtract the value of preferred stocks from the book value.
• When comparing across countries, you need to look at the timing of the book value. That is because financial statements may be published quarterly, semiannually, or annually depending on the country.
• Some companies may have issued stock options or hybrid securities such as convertible bonds and convertible preferred stocks. In that case, you need to estimate the market value of all the options when exercised and incorporate it into the total market cap.

If you feel complicated in calculating the value per share considering all the types of stocks, you could get more comfortable by using the total value as follows.

### PBR = Market cap / Total book value of equity

In the above calculation, you should decide whether to include preferred stocks equally to the numerator and denominator or not.

## Intrinsic PBR and fundamental factors

Like PER, you can derive the formula of theoretical or intrinsic PBR from the Dividend Discount Model DDM. Then, you can identify the fundamental factors that compose PBR from it.

The above formula shows the disassembly of DDM sequentially. Dividend per share is the amount paid from earnings per share according to the payout ratio. And earnings per share is the profits created with the book value per share as much as ROE. When dividing the last formula above by BV0, the intrinsic PBR formula is derived.

From the above equation, you can see that the fundamental factors of PBR are ROE, growth rate, and cost of equity. When ROE is higher than the cost of equity capital, PBR is greater than 1, and when ROE is lower, PBR is less than 1.

### ROE > re → PBR is greater than 1, ROE < re → PBR is less than 1

It means that the higher the created return than the expected return from the invested capital by shareholders, the higher the PBR.

## Case: Evaluation of the stock price of Tesla and Toyota

As of September 2020, the news reported that Elon Musk became the third global billionaire as Tesla’s stock price soared. Tesla is currently the world’s number one automaker by market cap.

Tesla’s market cap is over \$400billion, and the share price is 42 times higher than the book value. Toyota, which has the second-highest market cap after Tesla, has a PBR lower than 1. Expectations for Tesla are very high in the market. If so, let’s evaluate the PBR formed in the market by using the fundamental factors that organise the intrinsic PBR.

For calculation purposes, it uses the last 12 months ROE  of each company and the expected growth rate over the next five years that Thomson Reuters has provided. And the cost of equity capital is calculated using the market premiums of the US and Japan and β of each company. With those three factors, Tesla’s PBR is close to 1 and Toyota’s 1.63.

##### When comparing the intrinsic PBR to the market PBR, you can see that Tesla is vastly overvalued and Toyota is undervalued.

Probably, it might reflect a big hope for Tesla because it has recorded a surplus in August 2020 as sales are rising and the deficit is diminishing after it recorded a deficit until 2019.

Intrinsic PBR also has some limitations in the calculation method. One of them is that it only considers the ROE of one point in time. For example, the intrinsic PBR of Tesla does not reflect the fact that ROE is free from a minus, turns into a plus, and grows. Nevertheless, it seems that the current stock price reflects a massive expectation for the company that has recently entered a surplus.