lecture_20 firm valuation using dcf

8/17/2019 Lecture_20 Firm Valuation Using DCF

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Professor Sang Byung [email protected]

Firm valuation using DCF



FCF and DCF

•If we compute the FCF, and I give you the discountrate, you can value the operations of the firm.

•

This is called a “discounted cash flow” model (inshort, DCF).

• Two extreme cases

1. One period

2. Constant FCF growth

• A typical case (important!)

• During the forecast period, estimate each year’s FCF based on

financial statements.

• After the period, assume that FCF grows at a constant rate.



Extreme case 1: one period

•Using DCF is as easy as doing present values.

• For example, if your firm will have cash flows

of $50,000 next year, then cease to exist, and

the discount rate is 12% then

=

1

=$50,000

1.12 = $44,642.86



Extreme case 2: constant growth

•Unlike the previous examples, companies donot generally plan to cease existing.

• If we believe a firm is stable, and will remain

stable for the foreseeable future, we can use a

growth perpetuity to find enterprise value

=

<

• is the rate at which FCF will grow forever.



Example

•Company C is established, and has a stablefuture outlook. We expect next year’s FCF to be

$50 million. The discount rate is 8%, and we

expect C’s FCF to grow at a rate of 3% forever.

Use a growth perpetuity to find C’s enterprise value.

=

=$50

0.08 0.03

= $1,000



A typical case – four steps

• Few companies really qualify as “stable”

• How do we value a firm when we can’t forecast allthe future cash flows?

1. Choose a forecast period , (10 years is typical, but may

vary based on the context).

2. Forecast FCFs for all years based on projected financialstatements.

3. After the forecast period, typically assume that FCF grows

at a constant rate g.• Of course, you can assume differently if you have some reasons.

4. Calculate the present value of the FCF stream to find theenterprise value at time 0 ().



=

1

1 ⋯

1

1

1 +

1

1 + ⋯

PV of FCFs during theforecast period

PV of FCFs after the

forecast period

10(=H) 11 12

…

…13

0 1 2

…

…

0

3

11 12

…

…13

× ( 1 )

× 1

0 1 2

…

…3

× 1

Timeline

After the forecast period

During the forecast period

10(=H)



Terminal value

• Terminal value (aka continuing value)

• the present value (as of year ) for all cash flows after year

11 12

…

…13

× ( 1 )

× 1

…

…

× 1


H=10

×

( )

×

×

…

=

+

=

× (1 )

Since FCF grows at the

constant rate (g) forever

Terminal value =

Year-10 value ofFCFs after year 10



Timeline revisited

•

This is equivalent to

10(=H) 11 12

…

…13

0 1 2

…

…

0

3

11 12

…

…13

× ( 1 )

× 1

0 1 2

…

…3

× 1


During the forecast period

10(=H)

H=10 11 12

…

…13

0 1 2

…

…

0

3



Four steps revisited

• Four steps

1. Choose a forecast period , (10 years is typical, but

may vary based on the context).

2. Forecast FCFs for all years based on projected

financial statements.3. Compute a terminal value , : the present value (as

of year ) for all cash flows after year .

4. Discount the years of FCFs and the terminal

value to the present.



Final recap: DCF and enterprise value

0 FCF1

FCF2

FCF3

…

FCF10 +

TV

1 2 3 10…

• Enterprise value

=

1

1 ⋯

−

1 −

1

• To compute TV, assume a constant growth

perpetuity after year (10 in the timeline)

=+

= × (1 )



FCF example revisited

•Pretend it’s 2012 and you want to value thefollowing company.

• You’re given the income statement and balance

sheet for 2012, and projections for 2013 and

2014.

• Use these to find FCF for years 2013 and 2014.

• Assume a discount rate of 10% and a terminal

growth rate of 2%.

• Find the value of the firm’s operations.



Income statement

2012 2013 2014

Sales 2440 2800 3000

Cost of goods sold 1780 2020 2143

SG&A expense 467 542 580

Depreciation 61 78 88

Interest expense 38 38 29

Interest income 3 2 0

Income before taxes 97 124 160

Income tax 38.8 43.4 56Net Income/(loss) 58.2 80.6 104



Balance sheet2012 2013 2014

ASSETS

Cash and equivalents 12 13 31Receivables, net 46 44 58

Merchandise inventories 732 852 950

Other current assets 77 69 55

Total current assets 867 978 1094

Property and equipment at cost 636 726 827

Accumulated depreciation 202 245 312

Net property and equipment 434 481 515

Other non-current assets 70 90 95

Total assets 1371 1549 1704

LIABILITIES

Accounts payable 350 415 424

Accrued liabilities 200 255 275

Total current liabilities 550 670 699

Long-term debt 366 346 325

Total Liabilities 916 1016 1024

Shareholders’ equity

Common stock 445 470 525

Retained earnings 10 63 155

Total shareholder's equity 455 533 680

Total Liabilities and Equity 1371 1549 1704



FCF

•Previously, we calculated that the firm’s FCF in2013 and 2014 are $67M and $19.85M,

respectively.

• Need to calculate the terminal value given the

assumptions of 10% discount rate and 2%

growth.



Terminal value

•Terminal value in 2014 is therefore:

=( 1 )

=

19.85(1.02)

0.1 0.02 = $253.09

• What is the value of the firm’s operations then,

from the perspective of 2012?



Notes on terminal value

• How do we determine perpetual growth rate ‘g’?

• Make an informed guess based on the nature of the business, and link ‘g’ to

either a industry growth rate or some relevant macroeconomic variable.

• For example, in the long run Walmart can’t probably grow faster in real

terms than US population growth (~1.5%). Combining with inflation of ~3%

gives a long-run estimate of ‘g’ of ~4.5%.

• Unfortunately, valuation is highly sensitive to ‘g’

• A 1% change in ‘g’ can make a big difference to TV, which in turn, will make

a big difference to enterprise value and MV of equity!

• Always do a sensitivity analysis to understand how your answers vary with

key underlying assumptions.



DCF and MV of equity

•Once we find the enterprise value, we can alsocalculate the market value of equity using the

balance sheet identity:

= "ℎ"

• So using the DCF method, we can estimate the

stock price (per share value)

ℎ =

# ℎ



Example

•New startup Houston Inc believes it will havestable FCF growth, at a growth rate of 5%, after

5 years. FCFs for year 1 through 5 are expected

to be -$27M, -$11M, $0M, $6M, $33M.

• Houston Inc has $17M in cash, $19M in bank

debt, and a $8M loan from a supplier.

• Find the enterprise value, equity market value,

and share price for Houston Inc with a = 21%and 4M shares outstanding.



TV and EV

= × 1 = $33 × 1.05 = $34.65

=$34.65

0.21 0.05 = $216.56

= $27

1.21

$11

1.21

$6

1.21

$33 $216.56

1.21

= $.



MV of equity

= $. $17 $19 $8

= $.

ℎ =$59.19

4 = $.

lecture_20 firm valuation using dcf

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