This document provides an overview of various methods for valuing companies, including discounted cash flow (DCF) modeling. It discusses key DCF concepts like present value, free cash flow, growth rates, and weighted average cost of capital (WACC). Other valuation metrics mentioned include P/E ratios, comparable company analysis, and liquidation value based on tangible book value or net current assets. The document aims to explain the theoretical underpinnings of intrinsic stock valuation.

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