Week 8
Chapter 9
There’s a few ways to figure out the share price, firm’s value etc. One of these ways is via the
dividend discount model. There’s a few formulas; v
General Dividend 𝐷𝑖𝑣 +𝑃1
Formula; 𝑃𝑜 =
Discount Model 1+𝑟𝑒
The basic idea is that the price now can be found using the price in one
year. It's a very simple time value of money equation.
Arbitrage →
There is no arbitrage as if the price is below what it should be then
people buy and it will rise.
Div yield and The div yield and capital gain rate can be found using the formula
Capital gain rate 𝐷𝑖𝑣1 𝑃1−𝑃𝑜
previously. Hence; 𝐷𝑖𝑣 𝑌𝑖𝑒𝑙𝑑 = 𝑃0
and 𝐶𝑎𝑝 𝑔𝑎𝑖𝑛 𝑟𝑎𝑡𝑒 = 𝑃𝑜
Total return →
Total return is thus Div Yield + Cap gain rate. A company must choose
between giving dividends or reinvesting! A company with similar risk
should have similar expected total returns as comparable companies in
the market.
Multiple years 𝐷𝑖𝑣1 𝐷𝑖𝑣2+𝑃2
𝑃𝑜 = + . If more years just add more of the first part. Like
Dividend Discount 1+𝑟𝑒 (1+𝑟𝑒)
2
Model a timeline… For infinite years we just add the sum of the first part from
n=1 till infinity.
With Constant 𝑃𝑜 =
𝐷𝑖𝑣
→ 𝑟𝑒 =
𝐷𝑖𝑣
+ 𝑔.
𝑟𝑒−𝑔 𝑃𝑜
growth
Other formulas 𝐷𝑖𝑣𝑡 =
𝑒𝑎𝑟𝑛𝑖𝑛𝑔𝑠
* 𝐷𝑖𝑣 𝑃𝑎𝑦𝑜𝑢𝑡 𝑟𝑎𝑡𝑒
𝑜𝑢𝑡𝑠𝑡𝑎𝑛𝑑𝑖𝑛𝑔 𝑠ℎ𝑎𝑟𝑒𝑠
𝑁𝑒𝑤 𝐼𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡 = 𝐸𝑎𝑟𝑛𝑖𝑛𝑔𝑠 * 𝑟𝑒𝑡𝑒𝑛𝑡𝑖𝑜𝑛 𝑟𝑎𝑡𝑒
𝐶ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑒𝑎𝑟𝑛𝑖𝑛𝑔𝑠 = 𝑁𝑒𝑤 𝐼𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡 * 𝑟𝑒𝑡𝑢𝑟𝑛 𝑜𝑛 𝑛𝑒𝑤 𝑖𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡
∆ 𝑒𝑎𝑟𝑛𝑖𝑛𝑔𝑠 𝑁𝑒𝑤 𝑖𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡 * 𝑟𝑒𝑡𝑢𝑟𝑛 𝑜𝑛 𝑛𝑒𝑤 𝑖𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡
𝐸𝑎𝑟𝑛𝑖𝑛𝑔𝑠 𝑔𝑟𝑜𝑤𝑡ℎ 𝑟𝑎𝑡𝑒 = 𝑒𝑎𝑟𝑛𝑖𝑛𝑔𝑠
= 𝑒𝑎𝑟𝑛𝑖𝑛𝑔𝑠
= 𝑟𝑒𝑡𝑒𝑛𝑡𝑖𝑜𝑛 𝑟𝑎𝑡𝑒 * 𝑟𝑒𝑡𝑢𝑟𝑛 𝑛𝑒𝑤 𝑖𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛
So when firms wonder if they should cut div to invest in a new
investment, they should only do this if the new investment has a
positive NPV.
repurchase: 𝐷𝑖𝑣+𝑟𝑒𝑝𝑢𝑟𝑐ℎ𝑎𝑠𝑒 𝑃
𝐼𝑓 𝑟𝑒𝑝𝑢𝑟𝑐ℎ𝑎𝑠𝑒 −−> 𝑟−𝑔
,Many new upcoming firms have a lot of good investment opportunities, hence they will often
have a lot payout ratio, once a firm becomes older they wont have that many opportunities so
they will have a bigger payout ratio. The limitation of this method is that it is not easy to forecast
growth rates, and a small change in growth rates can have a large impact on Po!
Total Payout Model
We start with a set of simple formulas;
𝑃𝑉(𝐹𝑢𝑡𝑢𝑟𝑒 𝑇𝑜𝑡𝑎𝑙 𝐷𝑖𝑣 & 𝑟𝑒𝑝𝑢𝑟𝑐ℎ𝑎𝑠𝑒𝑠)
𝑃𝑉𝑜 = 𝑜𝑢𝑡𝑠𝑡𝑎𝑛𝑑𝑖𝑛𝑔 𝑠ℎ𝑎𝑟𝑒𝑠
𝐸𝑛𝑡𝑒𝑟𝑝𝑟𝑖𝑠𝑒 𝑉𝑎𝑙𝑢𝑒 = 𝑀𝑎𝑟𝑘𝑒𝑡 𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 𝑒𝑞𝑢𝑖𝑡𝑦 + 𝑑𝑒𝑏𝑡 − 𝑐𝑎𝑠ℎ
(advantage, don’t need to forecast div)
𝐹𝑟𝑒𝑒 𝐶𝑎𝑠ℎ 𝐹𝑙𝑜𝑤 (𝐹𝐶𝐹) = 𝑒𝑎𝑟𝑛𝑖𝑛𝑔𝑠 𝑏𝑒𝑓𝑜𝑟𝑒 𝑖𝑛𝑡𝑒𝑟𝑒𝑠𝑡(1 − τ) + 𝐷𝑒𝑝𝑟𝑒𝑐𝑖𝑎𝑡𝑖𝑜𝑛 − 𝑐𝑎𝑝 𝑒𝑥𝑝 − 𝑖𝑛𝑐 𝑛𝑒𝑡 𝑤𝑜𝑟𝑘
𝑉𝑜+ 𝑐𝑎𝑠ℎ − 𝑑𝑒𝑏𝑡
𝑉𝑜 = 𝑃𝑉(𝑓𝑢𝑡𝑢𝑟𝑒 𝐹𝐶𝐹) → 𝑃𝑜 = 𝑠ℎ𝑎𝑟𝑒𝑠 𝑜𝑢𝑡𝑠𝑡𝑎𝑛𝑑𝑖𝑛𝑔
.
We find Vo by making use of the following;
𝐹𝐶𝐹𝑁+1 1+𝑔𝐹𝐶𝐹
Vn is found using the perpetuity 𝑉𝑛 = 𝑟𝑎𝑣𝑟𝑔−𝑔𝐹𝐶𝐹
−−> 𝑟𝑎𝑣𝑟𝑔−𝑔𝐹𝐶𝐹
* 𝐹𝐶𝐹𝑁. Its a basic perpetuity.
See paper notes/slides for an example!
Valuation based on comparable firms;
We use the price/earnings ratio. Firms naturally want to maximize this, as their earnings go up
they want their price to be as high as possible.
, 𝑃/𝐸 𝑟𝑎𝑡𝑖𝑜 = 𝑠ℎ𝑎𝑟𝑒 𝑝𝑟𝑖𝑐𝑒(𝑃𝑜)/𝐸𝑃𝑆
𝑃0 𝐷𝑖𝑣/𝐸𝑃𝑆 𝑑𝑖𝑣 𝑝𝑎𝑦𝑜𝑢𝑡 𝑟𝑎𝑡𝑒
We can ofcourse find the forward P/E ratio as follows; = 𝐸𝑃𝑆1
= 𝑟𝑒−𝑔
= 𝑟𝑒−𝑔
. We got
this formula using a few of the previous formulas before. When using values of other firms to our
own, we make the assumptions that the companies have similar risks, future cash flows, growth
rates, etc. If these differ a lot then we can’t use this as it wouldn't be reliable!
Enterprise Value Multiple
In this multiple we use the EBITDA; this means the earnings before interest, depreciation and
amortization. Below is the following formula;
𝑉𝑜 𝐹𝐶𝐹/𝐸𝐵𝐼𝑇𝐷𝐴
𝐸𝐵𝐼𝑇𝐷𝐴
= 𝑟𝑎𝑣𝑟𝑔−𝑔𝐹𝐶𝐹
Again, she uses an example on the slides. In this example they give the EBITDA multiple. The
way she solves it (as she’s looking for the share price) she sets the multiple equal to the left
hand part. Then using the EBITDA value she can find Vo, then Po since she also has debt, cash
and # shares outstanding. It's interesting as you wouldn't think of setting the whole right side as
the multiple but it makes sense!
There’s ofcourse many other multiples, like the multiple of sales, etc. But we only need to know
these. The limitations? What’s better?
Valuation Multiples Discounted Cash Flow Methods
Simple Incorporates specific info about firm’s coc or
g.
Shortcut
Many assumptions about future growth, coc,
Deals with real market data etc.
Based on market assessment on other firms Potentially more accurate
Hence, no specific technique is better, we use assumptions in all of them. In the real world
people use a bunch of combinations and see if they are similar, if so, then they have a good
idea of the value.
Information:
Information is also a big part, a good example is Tesla, when Elon Must said he might go
private. When information is public it is easy to interpret, we find it in the news, financial
statements, etc. When it is the efficiency market hypothesis (EMH) holds. Info is easily shared
so investors can determine the effect of this info on value. When information is private there is
