This powerpoint talks about different valuation techniques including DCF, Comps, and P/E ratio.

1. How do you figure out how much
a company is worth?
By Cameron Fen

2. Table of Contents
• Present Value
• Discounted Cash flow
• Discounted Cash flow with growth
• Cash flow and WACC
• P/E and other metrics

3. What is Free Cash Flow
• Free cash flow is the cash that the company
has that is available to give back to
shareholders
• Companies don’t need free cash flow to
maintain the operations of the company
• The can pay dividends, buyback stock, make
acquisitions, invest in growth with free cash
flow

4. Stocks are cash flows
• The value of a stock is in the value of its
earnings
• The owner of a share owns the rights to
proportional share of a company’s cash flow
– If a company earns 100 million dollars and there
are 50 million shares outstanding each share owns
the rights to 2 dollars in earnings
• The company is going earn you a profit $2 or
more every year for the foreseeable future

5. Present Value of a stream of cash
• One share of Google is going to pay you $2.25
a share in dividends every year for perpetuity,
how much is the stock worth?

6. Present Value of a stream of cash
• One share of Google is going to pay you $2.25
a share in dividends every year for perpetuity,
how much is the stock worth?
• First we need to talk about interest rates
• If you put $100 in the bank and the interest
rate is 5% you get $105 at the end of the year

7. Discounting Future Value
• The Present Value of $105 a year from now is
$100 because you are indifferent from
receiving $100 now and $105 a year from now
• This makes sense because everyone would
rather have money now then money a year
from now so people have to pay us more if we
had to give up money now to receive money
in the future

8. Doing PV’s mathematically
• PV = Present value, i = interest rate, FV =
Future value
• Since PV * (1+i) = FV
• Dividing both sides by (1+i)…

9. Doing PV’s mathematically
• PV = Present value, i = interest rate, FV =
Future value
• Since PV * (1+i) = FV
• Dividing both sides by (1+i) =
• PV = FV/(1+i)
– This is called discounting

10. Doing PV’s mathematically
• PV = Present value, i = interest rate, FV =
Future value
• Since PV * (1+i) = FV
• Dividing both sides by (1+i) =
• PV = FV/(1+i)
– This is called discounting
• $100 = $105/(1+.05)
– This is how we convert from future value to
present value

11. PV for two periods
• If I put 100 in the bank account for 2 years I
get 5% interest for two years
– But I also earn interest on the interest that I
earned the first year
• PV*(1.05) = FVyear 1 = 105
• FVyear 1 * (1.05) = 105 * 1.05 = FVyear 2 =110.25
• PV * (1+i)^2 = FVyear  2
PV = FVyear 2/(1+i)^2

12. Generalizing PV for any number of
periods
• If you put $100 in the bank account for n
years you will have $100 * (1+i)^n after those
years
• The present value of receiving a money n
years away is payment/(1+i)^n

13. Present Value of $1 for 30 years
• PV = 1/(1+i) + 1/(1+i)^2 +…1/(1+i)^30
• We are not going to calculate it that way
• This is a geometric series
– There is a nifty formula for calculating the sum of
a geometric series

14. Present Value of $1 for 30 years
• PV = 1/(1+i) + 1/(1+i)^2 +…1/(1+i)^30
• We are not going to calculate it that way
• This is a geometric series
– There is a nifty formula for calculating the sum of
a geometric series
• Formula: PVannuity =
1
푖
∗ (1 −
1
(1+푖)푛)
– In this case since the last term is
1
(1+푖)30, n is equal
to 30

15. Accounting for Company Cash flow
• Google will earn $2.25 a year for perpetuity
– DCF: 2.25/(1+i)+2.25/(1+i)^2...
– We can factor out the 2.25 so =
2.25*(1/(1+i)+1/(1+i)^2…)
• That is 2.25 times our formula for one dollar
• Here n is infinity
– Thus
1
(1+푖)푛 will be zero
• Thus the stock’s earnings will be worth 2.25*
1
푖

16. Formula to Remember: Value of
a Stream of Constant Cash Flow =
Cash Flow(each year) * (1/i)

17. Note: DCF is the underpinnings of P/E
and P/cash flow ratio
• Cash Flow * (1/i) when i << 1 is like Cash Flow
*P/E ratio
• Ex. i = 10% Cash Flow *1/.1 = 10 * Cash Flow
– Equates to a 10 P/Cash flow ratio

18. Accounting for growth
• What do we do if we want to model for the
fact that the company is growing?
• Let’s assume the growth rate is constant
• Lets say this year the company earns A dollars
• Next year the company will earn A * (1+g)
where g is the growth rate
• The year after that the company will earn A*
(1+g)^2

19. Now what?
• Keep in mind the discounted cash flow model
is just PV = D1/(1+i)+D2/(1+i)^2+D3/(1+i)^3…
• D1, D2, D3… can be any numbers they are just
the value that you receive in cash flow on year
1, year 2, and year 3 etc.
• Plugging in D(n) = A* (1+g)^n gives us another
geometric series
– PV = A*(1+g)/(1+i)+A*((1+g)/(1+i))^2…

20. The formula for discounting with
growth
• PV = A *((1+g)/(i-g)*(1-((1+g)/(1+i))^n)
• If we assume earnings grow (and are
discounted with discount rate > growth rate)
to infinity this simplifies to PV = A*(1+g)/(i-g)
• Dividend Discount Model

21. Now what?
• Now that you have the present value of the
companies cash flow you have to subtract the
value of the companies debt
– Debt holders are senior to equity holders when it
comes to getting back there money so theoretically
the cash flow first goes to paying them back
• The present value of discounted free cash flows –
the value of the debt + total cash on balance
sheets should be approximately equal to the
market cap of your equity for a fairly valued
company

22. Exercise: Do a DCF model for
AAPL

26. What do you use for cash flow value
• What do you use for estimates of D0, D1, D2 ie
the amount of cash you receive each year from
the company
• Academic models use the dividend to evaluate
the value of a stock
• Generally most people use free cash flow (cash
from operations – capital expenditures)
• Don’t use earnings because you are double
counting growth and growth capital expenditures

27. What do you use for a discount rate?
• Personally I use the same discount rate for all
stocks
• Warren Buffet does the same
– He uses the interest rate on long term treasuries
• My hurdle rate for the return of a stock is the
same no matter the risk
– ie I want at least a 10% return on my stock a year
no matter how volatile (within reason) that 10% is

28. Weighted Average Cost of Capital
• The “correct” way is to use the company’s Weighted
Average Cost of Capital (WACC)
• This involves calculating the capitalization rate of a
company which is considered the rate of return of a
stock
– Market Capitalization rate = β*(expected return of the
market-risk free rate)+risk free rate
• Take Financial Economics if you want to understand why this is a
good way of estimating the return for stockholders
• Also you have to take the weighted average interest
rate on the bonds the company holds
– And multiply that by (1-tax rate) since that is the cost to
the company

29. Combining Debt interest and Equity
Return
• Next take the market value weighted average
of the rates of return on the equity and the
debt
• WACC = MV(e)/(MV(d)+MV(e))*Market cap
rate+MV(d)/(MV(d)+MV(e))*interest rate on
debt *(1-t)

30. Undervalued Stocks
• If you have a stock whose market
capitalization is significantly less the
discounted cash flow minus the debt your
stock might be undervalued and a good
investment
• Most investments should have a wide gap or
margin of safety between the intrinsic value
calculated by a DCF and the market cap

31. P/E ratio
• I don’t use a discounted cash flow to evaluate
stocks
• I used to but I have done it enough that with
the securities I buy I know the discounted cash
flow will yield a significant margin of safety
• Instead I use P/E ratio
• P/E is the ratio between the price of the stock
and the earnings per share of the stock

32. Things I know about DCF
• At a discount rate of 10% a company with no
growth and no debt should have a P/E of 10
• Companies with low single digit growth and no
debt should have a P/E of 12-17
• Debt reduces the suppose P/E ratio however
most of the time the markets don’t penalize a
company with a lower P/E unless the debt is
excessive
– This may be a mispricing although one can assume
that companies may be able to always roll over their
debt

33. Other Metrics
• Enterprise Value(EV), Earnings before interest
and taxes (EBIT), Earnings before interest taxes
depreciation and amortization (EBITDA), Price
to earnings divided by growth (PEG), Free
Cash Flow
• All these metrics are discussed in the
Accounting presentation

34. Company Valuation
• Another way to value a company is to look at
how comparable companies in the same
industry are being valued
• Also can look at recent acquisitions
• Compare using P/E or EV/EBIT or EV/EBITDA or
P/FCF or even more in depth look at the
company

35. Dangers of using industry comparables
• The whole sector maybe overvalued and you
are buying perhaps at best the least
overvalued (but still overvalued)
• Companies often overpay for acquisitions
– Goodwill write downs

36. Liquidation Value
• We can also valuate a company based on how
much all it’s assets will sell for if it closed
down the business and sold all it’s assets
• We can use tangible book value as one proxy
for liquidation value
• Tangible book value is Assets minus liabilities
minus intangible assets
– Goodwill etc.

37. Problems with Tangible Book Value
• Many companies own lots of specialized
equipment and machinery
• These things are hard to sell
• We need a margin of safety
– We need a value where we know if we liquidated
the company we would earn at least that much

38. Net Current Asset Value
• Net Current Asset Value was coined by
Benjamin Graham the father of value
investments
• Net Current Asset Value = Current Assets –
Total Liabilities