Chapter 9 - Valuing stocks

Question 1

Recall the law of one price in regards to a stock

Answer 1

Says that the price of the stock MUST be equal to the cash flows that the investors expect to earn from it.

Question 2

Name the two quantities of concern when valuing stocks

Answer 2

1) Cash flows we expect to receive
2) The discount rate

Question 3

Recall the investment horizon ‘theorem’

Answer 3

If two investors has the same beliefs/understanding of a stock, their investment horizon will not matter in terms of value and ultimately the price they would want to pay for the share.

Question 4

Name the sources (potential sources) of cash flows as far as shares are concerned

Answer 4

1) Dividends
2) capital gain

Question 5

Which part of the shares cash flow is determined by the time horizon?

Answer 5

actually both.

Question 6

Set up the 1-year cash flow statement of owning some random share that pays dividend

Answer 6

We purchase the share at time=0.
We then receive a dividend at time=1.
We also sell the share at time=1.

-P0 + div1 + P1

AS we know, the cash flows must be discounted.

In this simple case of 1 year etc, we can use a single discount term:

-P0 + (div1 + P1)/discountRate

Since the law says that the price must be equal to the expected PV of the investment, we get the equaiton:

P0 = (1/rate) (div1 + P1)

Question 7

What rate do we use to discount the cash flows from share ownership?

Answer 7

Earlier, as with most of the bonds, we used the risk free itnerest rate. however, this is not a good idea now, since shares have risk associated with them.

Therefore, we coin a term called “equity cost of capital”.

Question 8

What is equity cost of capital?

Answer 8

Equity cost of capital refers to the expected return of other investments available in the market with equivalent risk.

from the perspective of the equity investor, the equity cost of capital represent the rate of return required from investing in the firm. It reflects the return they would expect based on the risk profile of the firm.

Question 9

What is the buy rule for the 1-year valuation of shares

Answer 9

buy if the market price is lower than your expected cash flow returns from owning it. basically the law of one price says tht this is not possible, but here we are.

Question 10

if we decompose the 1-year fomrula, what result do we get?

Answer 10

We can get the equity cost of capiatal as a sum of two parts:

P0 = div1/(1+r) + P1/(1+r)

1+r = div1 /P0 + P1/P0

r = div1/P0 + P1/P0 - P0/P0

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

First part RHS is called dividend YIELD.
Second part RHS is called capital gain rate.

Question 11

What is dividend yield

Answer 11

Expected annual dividend (per share) divided by price. It is a percentage that says “for every buck we have invested, we receive the dividend yield in return as dividedn”.

Question 12

Difference between capital gain and capital gain rate

Answer 12

Capital gain = P1 - P0

Capital gain rate is the ratio where we also divide this difference on the P0. The result is a metric indicating growth.

Question 13

What do we get if we sum capital gain rate and dividend yield?

Answer 13

Total return

Question 14

Elaborate on total return

Answer 14

Total return is the expected return that the investor will earn. It should be equal to the equity cost of capital. this means, the expected return of the investment should be equal to the expected return of other investments in the market with similar risk.

This is a weird result, but it actually makes some sense.
The firm must deliver a cash flow/return similar to what the investor is “offered” elsewhere for the same level of risk.

Consider what would happen if this was not the case. If the firm offer less then the equity cost of capital/total return, the investors could earn more cash elsewhere. So they would go elsewhere. This would lower the demand for the stock, which would reduce the price, which would increase the expected capital gain rate. This is a process that continuosly work towards balance.

Question 15

How can we prove that the valuation of a stock is independent on time horizon

Answer 15

We can consider a two year horizon:

P0 = div1/(1+r) + div2/(1+r)^2 + P2/(1+r)^2

Then we consider the one-year horizon, but this dude wants to buy at P1.

P1 = div2/r + p2/r

Subsituting this inot the other one:

P0 = div1/r +

Question 16

What is the dividend discount model?

Answer 16

extneded version of cash flows in terms of dividends and capital gain while discounting.

Works for any time frame

Question 17

What is the simplest way of estimating future dividends?

Answer 17

Assume constant growth of dividends.

The benefit of this is that it is a perpetutiy, which means that we can use the constant growth perpetruity formula:

Price = div1 / (r_e - g)

Question 18

The constant growth dividend model has a very important result..?

Answer 18

We use the perpetuity formula, and rearrange it:

Price = div1 / (r_e - g)

r_e = div1 / Price + g

div1/price remains constant, because both quantitites are constant.

The interesting result is found by looking at what happens if we isolate g:

g = r_e - div1/p0

We know from earlier that r_e = div1/p0 + (P1-P0)/P0

Therefore, we have that g = (P1 - P0)/P0

this means, g equals the capital gain rate. What does this mean?
Capital gai nrate is the changes in share price.
If g is to be equal to this, it means that the share price must match the growth.

This means that if the dividends grow by 10% yerly, then the share price will grow by 10% yearly as well.

Question 19

What determines the rate of growth of a firms dividends?

Answer 19

primarily two things, it turns out:

1) retention rate
2) return on new investments

Question 20

elaborate on the simple model of growth (growht in terms of dividends)

Answer 20

We start by recalling the dividend formula:

div1 = (earnings/shares outstanding) x payoutRate

From this result, we know that there are 3 ways in which the firm can increase/grow its dividends:
1) Increase earnings
2) Reduce shares outstanding
3) Increase hte payout rate

The most interesting here is obviously the increase in earnings. But what is increase in earnings?
We can define increase in earnings as (very simple variant) return on new investment multiplied by the amount of the retained earnings (earnings that are not going to dividends).

change in earnings = ROI x retainment
This is a percentage, as ROI and retainment are percentages. It represent “for every buck we earn in earnings, we will grow with roi x retainment”. This reflects the fact that more retainment and more roi leads to more growth.

This result of g = ROI x Retention rate
is very important, as it produce the general results of what happens if we retain earnings vs ROI etc.

Question 21

Elaborate on the term “sustainable growth rate”

Answer 21

sustainable growth rate refers to the rate that firms can grow using ONLY its retained earnings.

Question 21

If a firm wants to increase its share price, should it pay more dividends or retain more earnings to invest?

Answer 21

The answer to this depends on the profitability of the investment that the firm would invest its retained earnings into.

If we consider a case of 100% dividend payment, and EPS of $6, current share price of $60:

We first find the equity cost of capital.
r_e = 6/60 + g
r_e = 0.1 + +
r_e = 10%

Now, if the firm start retaining some earnings, let us say 25%, we get a growth of g=0.25x0.12 (assuming 12% roi on the new investments) = 3%

Now we use the perpetuity formula

P0 = div1/(10% - 3%) = (6x0.75)/(7%) = 4.5/0.07 = $64.29

So, the choice of retaining earnings lead to an increase in the share price. And as we know, the share price is essentially ALL that matter now, because it reflect the present value of the share ownership.

The question is really: When will it not be beneficial in terms of the share price to retain? Intuitively, it is about the new investments. If we think about what happens to the money: If we retian earnings and invest in a project with shit ROI, the investors will value the share lower because the equity cost of capital means that they would get better returns elsewhere. Therefore, they want the dividends.
The breaking point is where the ROI on the new investments is equal to the equity cost of capital. In such a case, equity holders would be indifferent between receiving the dividend and investing the dividend in other projects, or just retaining it in the firm to achieve the growth.

Question 22

very generally, if a firm goes from no retained earnings to having some retained earnings, what happens?

Answer 22

The underlying assumption is that if the firm does not retain earnings at all, it will NOT GROW. Therefore, a firm that does not retain earnings will be able to pay the same amount of dividend every year, creating a perpetuity.

However, if it starts to retain some, it will experience growth. Recall the formula for a one year horiszon:

r_e = div1/P0 + g

Question 23

Answer the question: when will cutting a firms dividend lead to a rise in share price?

Answer 23

If the ROI on the new investment that we use the retained earnings for is greater than the equity cost of capital. In other words, the new investment must have a positive NPV when discounted with the equity cost of capital.

Question 24

Some firms are problemtic cases for the constant growth dividend discount model. Whcih ones and why?

Answer 24

Many young firms retain 100%, so there are no dividends. In addition, they usually have changing growth rates all the time until they mature, making it difficult to assume a constant growth.

However, we can work around this by considering the point where we assume the firm achieve maturity and will grow with a constant rate. WE use this point to comptue the future value (continuation value at this point).
Then we use the regular model. The point is to get to the point where we have the perpetuity

Question 25

Elaborate on limitations of the dividend discount model

Answer 25

Small changes in growth percentage leads to large changes in share price. Since it is difficult to estimate the growth g, the methods is kind of wack.

Question 26

Name the two models other than the dividend discount model

Answer 26

Total payout model

discounted free cash flow model

Question 27

It is common (for the uninitiated) to think that cash payment to equity holders takes the form of a dividend. Elaborate on this

Answer 27

It is not the only way. Share repurchase is also a way to do this.

Firm use its own excess cash to buy stock.

Stock repurchases make it difficult to use the dividend discount model because the shares outstanding change, while the earnings is not divided into dividends and new investments.

Question 28

What model can we use if the firm does stock repurchases?

Answer 28

Total payout model.

The total payout model considers all the firms equity as a whole, and not a single share. This makes it indifference towards shares outstanding.

The term “total” refers to the fact that we discount the total amount of payouts, which includes dividends AND stock repirchases. Finally, we divide on shares outstanding to get the share price.

It is kinda goofy. To find the present value of the total payout, we usually have to assume perpetuity of constant growth. The different rates (retention, payout, repurchase) must remain constant for this to work.

NOTE the benefit of it though: there is no reason to know the split between dividends and stock repurchase. Total pay

Question 29

Elaborate on the discounted free cash flow model

Answer 29

The main thing about the discounted free cash flow model, is that it does not only consider equity holders. It also considers the debt holders.

Since debt holders are included, we cannot use market value of equity as the measure for “share price” (although it is not share price we are talking about here now).

We use the term “Enterprise Value”.

EV = Market value of equity + debt - cash

Recall that we are still interested in the share price. But we are taking a different approach. We use enterprise value as a baseline, and then later solve for market value of equity and then use shares outstanding to find the share price. THe reason why we can do this is because we can find the enterprise value from the discounted free cash flows of the firm.

Question 30

What is the benefit of the discounted free cash flow model?

Answer 30

It allows us to consider value without considering dividends, share repurchases, and the use of debt.

Question 31

Elaborate on the term “enterprise value”

Answer 31

so you would essentially be looking at what it would cost to buy all the shares from current equity holders, and then buy all the securities (debt securities) that are held by the debt holders, essentially removing the firm from all obligations.

Question 32

when talking about FCF in the discounted FCF model, what exactly are we referring to?

Answer 32

We are referring the FREE cash flow (the avilable cash) that the firm can use to pay its equity holders AND debt holders. We refer to this as “all investors”.

Therefore, the FCF obviously is the cash flow at hand before any interest is payed.

FCF = EBIT x (1 - taxRate) + depreciation - capEx - ∆NWC

This is the formula as before, but we make a change to it because it is common to refer to “capEx - depreciation” as net investments.

FCF = EBIT x (1-taxRate) - net investments - ∆nwc

Question 33

Talk through the discounted FCF model

Answer 33

We find the enterprise value. We can find this from finding the present value of all the future cash flows.
Given this value, we use the formula for enterprise value to solve for market value of equity. Finally we divide on shares outstanding to get the share price.

Question 34

What is “the” key difference between the dividend discount model and the disocunted FCF model?

Answer 34

The discount rate we use to find present value.

The dividend discount model use equity cost of capital. This is because the debt holders have already been payed at this point in time.
Whenever we consider “all” investors, we cannot discount using the equity cost of capital. Instead, we must use a discount rate that reflect equity cost and debt cost of capital. The result is WACC.

Question 35

What can we say about WACC rate?

Answer 35

It should be smaller than the equity cost of capital. This is because equity is generally more risky to hold than debt. Equity holders require to be compensated for this.

Question 36

elaborate on assumptions of debt in the discounted FCF model

Answer 36

the point is that while the model does not need the amount of debt to compute the free cash flows, it becomes difficult to discount them because the WACC requires the equity to debt structure.

therefore, if we are to consider constant WACC, this has implications of the debt generally.

Question 37

We have now used the law of one price to make computaitons of the present value of future cash flows to produce a share price. What other way can we use the law in this context for?

Answer 37

methods of comparables. The law is basically all about same level of risk = same level of value etc.

Question 38

elaborate on method of comparables

Answer 38

we want to use comparable firms to get some indication of value. However, even if firms are identical i nterms of industry etc, they are likely differnet scales and size. Therefore, we need to use mutliples that adjust for this shit.

We call such things “valuation multiples”.

Question 39

What are valuation multiples?

Answer 39

A ratio of the value to some measure of the firms scale.

The analogy for this is “price per square meter”. If we know the tendency of the price per square meter, we can find the value of a building by mulyping the “valuation multiple” by the size to get the total value.

Question 40

Elaborate on the most common valuation multiple in corporate finance

Answer 40

Price - Earnings ratio.

P/E.

Typically used as “forward P/E”,

Question 41

elaborate on forward P/E

Answer 41

We consider the result from the constant growth dividend discount model.

P = div1/(r_e - g)

Then we divide on earnings per share on both sides

forward P/E = (div/EPS) / (re - g)

Since the div is already a per share metric, we get:

forward P/E = (div/earnings) / (re-g)

firward P/E = payoutRate / (re-g)

Question 42

Why is it called “forward” P/E?

Answer 42

We use forward P/E when it is based on future earnings, which is the expected earnings.

Question 43

WHat are the underlying assumptions of using P/E as a valuation multiple?

Answer 43

The firms that we compare must have similar risk profile, payout rates and growth rates.

Question 44

Elaborate on a case using P/E to find value of share price

Answer 44

Say we have received the earnings of a firm. We know the shares outstanding.
We therefore have the EPS.
Then we find the average P/E for the similar industry.
EPS x P/E = share price.

HOWEVER: In order to use this, it is crucial to understand the assumptions. We assume that the industry aggregate is representable for the firm. This implies that the industry and the specific firm musth ave similar growht rate and payout rate.

The reason WHY we must assume this, is that the share price of those other firms in the industry will be determined based on their growth rate and payouts, like we have established earlier.

Question 45

what are the limitations of multiples?

Answer 45

obviously not able to capture what will make firms grow.

also, the entire industry may be overvalued, undervalued