Chapter 9 - Valuing stocks Flashcards
(47 cards)
Recall the law of one price in regards to a stock
Says that the price of the stock MUST be equal to the cash flows that the investors expect to earn from it.
Name the two quantities of concern when valuing stocks
1) Cash flows we expect to receive
2) The discount rate
Recall the investment horizon ‘theorem’
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.
Name the sources (potential sources) of cash flows as far as shares are concerned
1) Dividends
2) capital gain
Which part of the shares cash flow is determined by the time horizon?
actually both.
Set up the 1-year cash flow statement of owning some random share that pays dividend
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)
What rate do we use to discount the cash flows from share ownership?
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”.
What is equity cost of capital?
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.
What is the buy rule for the 1-year valuation of shares
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.
if we decompose the 1-year fomrula, what result do we get?
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.
What is dividend yield
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”.
Difference between capital gain and capital gain rate
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.
What do we get if we sum capital gain rate and dividend yield?
Total return
Elaborate on total return
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.
How can we prove that the valuation of a stock is independent on time horizon
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 +
What is the dividend discount model?
extneded version of cash flows in terms of dividends and capital gain while discounting.
Works for any time frame
What is the simplest way of estimating future dividends?
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)
The constant growth dividend model has a very important result..?
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.
What determines the rate of growth of a firms dividends?
primarily two things, it turns out:
1) retention rate
2) return on new investments
elaborate on the simple model of growth (growht in terms of dividends)
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.
Elaborate on the term “sustainable growth rate”
sustainable growth rate refers to the rate that firms can grow using ONLY its retained earnings.
If a firm wants to increase its share price, should it pay more dividends or retain more earnings to invest?
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.
very generally, if a firm goes from no retained earnings to having some retained earnings, what happens?
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
Answer the question: when will cutting a firms dividend lead to a rise in share price?
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.
