How do you figure out how much a company is worth?

By Cameron Fen

Table of Contents

• Present Value• Discounted Cash flow• Discounted Cash flow with growth• Cash flow and WACC• P/E and other metrics

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

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

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?

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

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

Doing PV’s mathematically

• PV = Present value, i = interest rate, FV = Future value

• Since PV * (1+i) = FV• Dividing both sides by (1+i)…

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

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

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

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

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

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 = )– In this case since the last term is , n is equal to 30

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 will be zero

• Thus the stock’s earnings will be worth 2.25*

Formula to Remember: Value of a Stream of Constant Cash Flow =

Cash Flow(each year) * (1/i)

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

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

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…

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

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

Exercise: Do a DCF model for AAPL

FCF = Cash from Ops - Capex

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

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

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

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)

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

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

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

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

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

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

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.

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

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