Chapter 9 - Valuing stocks

Question 1

‘elaborate on the law of one price in regards to stocks

Answer 1

The law of one price tell us that the price of the stock is equal to the present value of expected cash flow that the investor expect to earn from owning the stock.

Because of this relationship between law of one price and expected present value, the expected cash flows plays a very important part in the valuation of the stock.

Question 2

In addition to the cash flows, what do we need to “know” in order to value a stock?

Answer 2

We require the cost of capital, which we will use as the discount rate.

Question 3

the law of one price says that price of stock is equal to expected present vlaue of the cash flows. but why?

Answer 3

The value of the stock (price) will be equal (at least in theory) to the expected present value of the cash flows that the investor will receive from owning the stock. This is the case because of what would happen if there was a mismatch between the price and the expected net present value of the cash flows. In such cases, there would be arbitrage opportunities. If price too high, people will short it, or just simply lower the demand, which will cause the price to decrease. If price is too low, investors will buy it, which will increase demand and therefore the price as well

Question 4

The two ways to generate cash flows from stocks are..?

Answer 4

Dividends and sale of shares

Question 5

What is important regarding discounting the future expected cash flows, like dividends and future stock price?

Answer 5

We cannot use the risk-free rate to compute the discounted flows, because the investment is not risk-free.

instead, we must use something called “equity cost of capital”, typically denoted r_e.

Question 6

Elaborate on equity cost of capital, r_e

Answer 6

Equity cost of capital is an interest rate we use to discount risky investments, like stocks.

Specifically, equity cost of capital is the expected return we will get from other investments with the same risk-level.

By using this, we can develop a very simple formula for the 1-year investor:

buy if Price <= (Div1 + P1)/(1+r_e )

We can also flip this to get the selling requirements

Question 7

what is dividend yield?

Answer 7

Dividend yield is the percentage of dividends per year, in terms of stock price. So, you take the amount of money (dividend) and divide it by the stock price, P0.

Question 8

What is capital gain rate?

Answer 8

Capital gain rate is the capital gain the investor will get from the investment, divided by the stock price P0. And the capital gain is the difference between the “selling point” P1 and the “buying point” P0.

Formula:

Capital gain rate = (P1 - P0)/P0

Question 9

What is total return of the stock?

Answer 9

total return refers to the sum of dividend yield and capital gain rate.

The total return will equal the equity cost of capital. this makes a lot of sense, considering it basically means that the total return (one year) on the stock will equal to other investments in the market with the same risk level. classic law of one price case.

The book is very clear about the fact that total return is a percentage, and does not use “total return rate” or similar.

Question 10

How do we find the formula for total return?

Needs rework, not sure about the formula. It sort of makes sense if prices are given and we solve. Check book anyways

Answer 10

We start with the formula P0 = (div1 + P1)/(1+r_e)

which we can re-formulate to be.

r_e = div1/P0 + (P1-P0)/P0

Question 11

What happens with dividends during a short sale

Answer 11

the investor who borrow stock to short it must pay the dividends to the original owner of the stock.

Question 12

Does it matter if we have a one-year or a two-year perspective for our stock investment?

Answer 12

No. Intuition tells us that if we buy a one-year deal, the price that we can sell the stock for will of course be impacted by what the expectation is for the next year (or longer).

For instance, say we have a one-year in mind.
P0 = (div1 + P1)/r_e = div1/r_e + P1/r_e

P1, is equal to this: P1 = div2/r_e + P2/r_e

together, they become:

P0 = div1/r_e + (div2/re + P2/re)/re

P0 = div1/re + (div2+P2)/re^2

Now, we recognize that this last result is exactly the same as the P0 price level would be if WE originally had a two-year in plans. This result is directly generalizable to multi-years, and it shows that the time horizon of the single individual investor does not affect the price level. Very important result.

Question 13

Quickly explain the multi-year effect vs single-year on stock valuation

Answer 13

There is no difference. the value of the stock will be teh same regardless. this is because (efficient market) there will always be a buyer to a seller, which means that hte buyer takes over the responsibility of valuation etc.

Question 14

What is the dividend-discount model?

Answer 14

The dividend-discount model is the result of generalizing the value of a stock when taking dividends and stock re-sale value into account for an arbitrary time period. The model also allows for an infinite sum of dividends.

Question 15

What is the simplest way to forecast future dividends?

Answer 15

Assume that they will grow with constant rate, g, forever.

We would then receive a cash flow stream like this:
-P0
+d1
+d1(1+g)
+d1(1+g)^2
+d1(1+g)^3
…

this is a perpetuity, for which we have a formula. We will get the following resulting formula:

P0 = Div1 / (re - g)

This is called the constant dividend growth model.

Question 16

What is the constant dividend growth model?

Answer 16

The constant dividend growth model is the result of assuming that dividends will grow with a constant rate forever, creating a perpetuity. Since perpetuity, we have the following simple formula:

P0 = div1 / (re - g)

Question 17

What can we conclude from the constant dividend growth model?

Answer 17

Recall that result:

P0 = div1 / (re - g)

We can re-arrange it:

re - g = div1 / P0

re = div1 / P0 + g

This tells us that g (growth rate of dividends) equals re - div1/P0 which actually equals the capital gain rate. Recall that capital gain rate = (P1-P0)/P0. So, we can conclude with the fact that if one assumes constant dividend growth, one also assumes that the share price will match the growth of the dividends, g.

Question 18

Quickly recap the important result of the constant dividend growth model

Not finished, do we compound using g or re or re-g?

Answer 18

Assuming constant dividend growth will lead to a matching growth in price of the stock.

Question 19

So, what two things primarily influence the share price?

Answer 19

The dividend amount we use as a starting point, and the expected growth in dividend. Div1 and g.

Therefore, to maximize share price, a firm will focus on improving BOTH.

Question 20

Elaborate on the tradeoff between dividend growth and dividend (g vs div1)

Answer 20

A firm want to maximize both. However, in many cases, maximiznig growth of dividends, g, require heavy investments, which will limit div1.

The constant dividend growth model can be used to offer some insight into this tradeoff relationship.

Question 21

What determines the size of a firm’s dividends?

Answer 21

Primarily three things:
1) Earnings
2) Shares outstanding
3) Dividend payout rate

We define the dividend payout rate to be the proportion of the earnings that are being payed out as dividends. All of these 3 things give the following formula:

div1 = (Earnings/sharesOutstanding) x DividendPayoutRate

Notice that the first part, Earnings/SharesOutstanding is equal to the EPS metric, called earnings per share. Therefore, we can say that in a very simple model of growth, the dividend is equal to EPS x dividendPayoutRate

Question 22

using the simple model of growth for dividends, what are the main results?

Answer 22

There are 3 ways a firm can increase dividends:
1) Increase earnings
2) Decrease the number of shares outstanding
3) Increase the dividend payout rate

The number of shares outstanding is usually not that interesting. It is more interesting to keep it fixed, and explore the relationship between earnings and payout rate (fraction of earnings being payed).

Question 23

What can a firm do with earnings?

Answer 23

A firm can pay earnings to investors, or it can re-invest the earnings (or combination).

In a very simplified model, we can consider the option of “no re-investing” as leading to zero growth in earnings, and thus zero growth in dividend (unless payout rate is changed). So, the simple model assumes that if no re-investment is made, the firm simply does not grow. The current level of earnings is expected to remain more or less the same. Theoretically: the same.

if all increases in future earnings come as a result of the previous re-investments, we can calculate it like this:
ChangeInEarnings = new investment x ReturnOnInvestment

new investment = earnings x retention rate

Retention rate is the proportion of earnings that the firm re-invests/retains.

We can set up the following equations:

Change in earnings = (earnings x retention rate) x return on investment

divide by earnings, and get:

Change in earnings / earnings = retention rate x return on investment

Re-arranged and re-formulated:

Earnings growth rate = (change in earnings)/(earnings) = (retention rate) x (return on investment)

So, in words, the growth in earnings will equal the percentage of earnings we re-invest multiplied by the percentage gain we get on these. Recall that the return on investment is a percentage, like 0.3, not 1.3.

if the firm choose to keep the dividend payout rate constant, the growth in dividends, g, will follow the same growth as the earnings, so we have that:

g = retention rate x return on investment

Question 24

if the firm choose to keep dividend payout rate constant, what can we say about dividend growth?

Answer 24

the growth in dividends will follow the growth in earnings.

g = retention rate x return on investment

For instance: If we retain 40%, and we expect 25% return on investment, we will get an increase in earnings (growth in earnings) of 0.4x0.25 = 0.1, which means that we get 10% increase in dividend.

Question 25

What is sustainable growth rate?

Answer 25

Sustainable growth rate is the rate that earnings and dividend can grow by only using its retained earnings.

Question 26

What is the general rule of stock price movements vs changes in payout rate (increasing investments in the firm instead of dividend)?

Answer 26

The general rule is that if the projects one use the retained earnings to invest in has a positive NPV, it will positively impact the stock price. If negative NPV, it will decrease stock price.

So, cutting the firms dividends to increase investments will increase stock price if, and only if, the new investments has a positive NPV.

Question 27

how do we find a firm’s equity cost of capital?

Answer 27

we can use the result of:

re = div1/P0 + g

what we typically do is to consider what happens if the firm invests nothing and therefore holds a constant growth of 0. Then we would get that re = div1/P0, which is metrics we usually have.

Remember that this formula, re = div1/P0 + g, comes from the constant dividend growth model and models this using formula for perpetuity.

Question 28

How can we use the constant growth dividend model to find the price of a stock of a firm that retain all of their earnings for multiple years to grow and invest, and eventually start to pay dividends?

Answer 28

We cant. They pay ZERO dividends when they are young, so the formulas doesnt work. Also, their earnings growth will change much from year to year until they eventually stabilize, which makes it difficult to use a growth measure of constant proportions.

However, the dividend-discount model with constant growth is not entirely useless here. We can use to to calculate the FUTURE price of the stock. The future price refers to the price at the point in time where the firm start to pay dividends, and the growth stabilize.

Question 29

elaborate on the process of using the dividend-dicsount model with constant growth to model a case where there is a period of no dividends, and 100% retention, followed by a period where the firm is stabilized and start paying dividends

Answer 29

We will use the dividend-discount model to find the future price of the stock at the point in time where the firm start paying dividends. We cannot do it earlier than this, because the dividends are zero etc. What i mean is: the formula we would want to use:

P0 = div/(re-g)

will not work since div is zero, and g is 0. What we do instead is to go to the point in time where we start paying dividends. At this point, we can use formula to find the price of the stock at this point in time.

P_N = div_n / (re - g)

Now we can also easily use this price to find the present value (stock price) P0. Recall that the present value will be equal to the cash flow that we expect from owning the stock. We can use the stock price for time point N as a resale-value we will get for the stock (continuation value/termination value). Then we need to add the cash flows from dividends. BUT: we have no dividends. Therefore, all we need to do is to discount the stock price at time point N so that it becomes present value.

P0 = P_N/(1+re)^N

Question 30

Summarize the result of constant growth dividend discount model when there is a starting period of 100% retention rate

Answer 30

Question 31

what is the main conclusion from the bit about the dividend-discount model of constant growth and uneven patterns of dividends?

Answer 31

The dividend-discount model is flexible enough to handle any pattern of dividends. All we need to do, is make sure we find the correct continuation/termination price in the future. then we backtrack using this price (discounting it) and including potential dividends that may occur at earlier dividends, but not in a regular pattern etc.

THe point is that we can find the stock price P_n at SEVERAL time periods n, and just keep reducing the time down to the present value time point.

NB: The formula we typically use require the far future to be a perpetuity.

Question 32

Main limitation of the dividend discount model?

Answer 32

Uncertainty in future earnings.

Relatively small changes in aspects like growth of dividends lead to extremely large changes in the present value stock price.

Question 33

Name something that may be used as an alternative to dividend payouts

Answer 33

Stock repurchases. Stock repurchases are also called stock buybacks.

In a stock buyback, the firm use its own money (earnings) to buy back shares it has previously issued out.

By doing so, the firm will not be able to pay as much dividends, but at the same time the dividend per share will increase in the future.

Question 34

What alternative model can be used in the case of stock repurchases?

Answer 34

A model called the Total payout model.

The total payout model accounts for dividends AND stock repurchases, as well as shares outstanding.

Question 34

What happens to the dividend-discount model when firms do stock repurchases?

Answer 34

The dividend discount model only use dividend per share, and takes present value of those cash flows.

Question 35

Answer 35

Question 36

What is key about the total payout model?

Answer 36

We do nto need to know the split between dividends and repurchases. We only need to know the amount in total that is used as payout equivalents.

Question 37

Elaborate on the discounted free cash flow model

Answer 37

THe discounted free cash flow model will determine the value of a stock by first estimating enterprise value from the cash flow, and then finding the market value of equity, which we use to divide by the shares outstanding.

Question 38

Recall the goal of the discounted free cash flow model

Answer 38

to valuate a stock price in present value terms.

Question 39

Elaborate on “market value of equity”, and what it truly is

Answer 39

You pay a price for a share which grant you equity. Owning this equity “can” grant you cash flows in various forms, but it comes with risk. A part of this risk is the debt part. Debt is not bad, but can be in the case of difficult times for the firm, which cause elements of risk. Therefore, the share price reflect the value of owning equity in the firm, combined with its specific risk level.

It is paramount to understand what we are buying with a share. We buy equity. equity grants ownership of the firm. Along with the equity, comes debt obligations of the firm (not shareholders). However, we are not (as investors) buying debt, we are buying equity, and only equity. The debt is associated with the equity.
When buying shares, the price reflect “what sort of present value can this piece of equity give me when I consider future cash flows and growth?”.

Question 40

Elaborate on enterprise value

Answer 40

Recall the difference between “market value of equity” and “enterprise value”. Market value of equity tells us the worth of owning the equity. It is not debt related, but the debt is associated with the equity. What we usually say, is that equity has a risk involved. The risk is present in the share price, but not the debt. All that matters in regards to equity is that owning the piece of equity can produce cash for us. That is worth something.

Enterprise value takes the concept of the value of the equity, and considers what we can say about the “true” value of the assets of the enterprise. To do this, we add the debt to the market value of enterprise. We do this because we are interested in what the assets are worth, so we “repay” all debt.
Then we subtract cash (and equivalents) because the cash is not a part of the operating model, and we do not pay cash for cash.

Question 41

Elaborate on why cash is subtracted from the formula to find enterprise value

Answer 41

There are multiple reasons. One is that cash and cash equivalents are typically not a part of the operating model, and is therefore financing. The separation principle tells us that this does not matter to the operations.

We also do not want to pay for cash. It is common (before full acquisitions) to distribute the cash before the sale of the enterprise.

it is just generally more clean and easy to understand the value of a firm when considering the assets they are actibvely contributing to the operations, and not used to finance the operations. I suppose this is sort of the “separation principle” as well, where we distinguish investments and financing those investments into separate categories that are not really related.

The conclusion is that enterprise value is a measure that focus more on the operating model, and not on the financing aspect.

Question 41

Benefit of the “discounted free cash flow model”?

Answer 41

We do not have to estimate dividends, share repurchases or its use of debt.

Question 42

What is the formula for net investment when talking about the entire enterprise?

Answer 42

Net investment = Capital expenditure - depreciation

Question 43

What is the formula for free cash flow when talking about the entire enterprise?

Answer 43

FCF = EBIT(1-t) - net investments - ∆net working capital

Question 44

How can we loosely define/interpret the definition of net investments?

Answer 44

Recall net investments as “capital expenditure - deprecitation”.

We can interpret is as investments intended to increase the firms growth above and beyond the level needed to maintain the firms existing capital.

Question 45

According to the discounted free cash flow model, how do we find the current price of a stock?

Answer 45

We use the formula for free cash flow, FCF=EBIT(1-t) - net investments - ∆net working capital, where net investments is “capital expenditure - depreciation”.

Then we discount the cash flow using an appropriate rate so that we get the present value.

Now we need to take the free cash flow in its present value state, and add the debt and subtract the cash (to get the enterprise value).

Finally, we divide on the shares outstanding to get the price.

Question 46

What is important regarding the discounted free cash flow model?

Answer 46

The discount rate we use must account for both debt payments and equity investment alternatives.
With the dividend-discount model, we do not need this, as it is indirectly included in the cost of earnings. However, now we need to include it.

To do so, we use WACC: Weighted Average Cost of Capital.

If firm has no debt, the WACC equals the equity cost of capital.

Question 47

What is more risky, debt or equity?

Answer 47

Equity.
when we say that the discount rate for debt is typically lower than for equity ,it is because of the fact that debt holders are more prioritized (and therefore somehow more protected) than equity holders. From the perspective of the investor, buying a share in the firm, vs issuing debt (bond) to it, the equity is more risky.

Question 48

Elaborate on the discounted free cash flow model is typically applied

Answer 48

It is normal to compute the free cash flow of the firm each year up to some year where the firm is typically considered to be stabilizing. at this point, we usually compute the continuation/termination stock price value by assuming a constant growth, typically lower then previous years.

So, we can say that the point is to capture the “wild” cash flows from time 0 to time Stabilized to make value the firm.

When we have done the present value of these cash flows by using WACC, we add the debt at time 0, and subtract the cash at time 0. We only care about time 0 because it is NOW we want to acquire the firm.

Then we have the enterprise value, and we divide by shares outstanding to get the share price.

Question 49

How do we find continuation value?

Answer 49

We use perpetuity formula

Question 50

Elaborate on the price-earning ratio

Answer 50

P/E is equal to the share price divided by earnings per share.

there are different types of P/E:
1) Forward P/E, which try to use estimated forecasts
2) Trailing P/E, which use past results

Question 51

briefly elaborate on the method of comparables

Answer 51

We measure the value of the firm based on the value of other similar firms that we expect will generate a similar cash flow in the future.

In theory, if two firms were identical, and would produce the same cash flows, the law of one price would say that they are worth the same.

Question 52

What is a valuation multiple?

Answer 52

A valuation multiple is a metric that tells us something about the perofrmance of a firm that is relative to its size.

The various ratios are examples of valuation multiples, like the Price-earning ratio

Question 53

What is the immediate issue with comparable methods?

Answer 53

Identical comapnies are unlikely to exist. There will always be scale and size differences etc.