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Valuation
FIN449
Michael Dimond
UNDERSTANDING GROWTH
Michael Dimond
School of Business Administration
Most students can do this…
• V0 = CF1/(r-g)
:. r = CF1/V0 + g
and
:. g = r – CF1/V0
• This implies the growth of all cash flows after CF1
Michael Dimond
School of Business Administration
…but what if you don’t have CF1?
• CF1 = CF0 * (1+g)
:. V0 = CF0*(1+g)/(r-g)
• If you are only given CF0
• Could you solve for r?
• Could you solve for g?
Michael Dimond
School of Business Administration
Solving for r is pretty straightforward
• V0 = CF0*(1+g)/(r-g)
:. r = [ CF0*(1+g)/ V0 ] + g
Michael Dimond
School of Business Administration
Solving for g gives students more issues
• V0 = CF0*(1+g)/(r-g)
:. g = (r*V0 - CF0)/(CF0+V0)
• This implies the growth of all cash flows after CF0, including
the upcoming CF1.
Michael Dimond
School of Business Administration
Solving for growth can provide actionable insight
• Example: Your company was just acquired for $166.5 million.
The most recent free cash flow was $1.5 million. Assuming
the WACC was 12%...
• What is the growth of cash flows your new owners will expect from you every
year?
• How long can you keep that up?
Michael Dimond
School of Business Administration
Solving for growth can provide actionable insight
• What if the assumption is you can spend five years ramping
up volume & profits to improve free cash flows. Your plan
involves 15% average improvement to free cash flows over
the next five years and looks like this:
Year 0
1,500.000
Year 1
1,725.000
Year 2
1,983.750
Year 3
2,281.313
Year 4
2,623.509
Year 5
3,017.036
TV
279,111.499
• What is the long-term growth used in the terminal value? Assume the WACC
is still 12%
• How long can you sustain that terminal growth rate?
Michael Dimond
School of Business Administration
Solving for growth can provide actionable insight
• What if the assumption is you can spend five years ramping
up volume & profits to improve free cash flows. You manage
to insist on a long-term growth rate of 5%, but the new
owners still insist on improvements to make the value they
paid ($166.5 million) worthwhile.
• Assuming the WACC is still 12% and the growth in the terminal value is 5%,
what growth in FCF would be required for each of the next five years?
• What would next year’s FCF need to be to keep the plan on track?
• Do you feel confident you can achieve that plan?
Michael Dimond
School of Business Administration
Realistic growth expectations are key in valuation
• Cash flows are what we are valuing. We care about their
size, timing and uncertainty.
• What are the realistic parameters for risk and return?
• Growth expectations in your forecast imply decisions
management would have to make.
• Making a simple forecast (stable growth or even multi-stage model) does not
test the realism of the underlying assumptions
• Modeling the factors which create the cash flows allow us to examine
fundamental factors such as growth of sales and costs
• Use of the statement of cash flows forces an examination of the investment
decision management will face.
• The idea is to understand the cash flows and their value
• You cannot adequately value a cash flow if you do not know what it
represents and what drives it.
Michael Dimond
School of Business Administration
Growth expectations have value
• Value = PV(expected future cash flows)
:. Value = PV(non-growing perpetuity) + PV(expected growth)
• PV(non-growing perpetuity) = Value without earnings reinvestment
• PV(expected growth) = Value of anticipated earnings reinvestment
• PV(expected growth) is sometimes referred to as PVGO
• PVGO: Present Value of Growth Opportunities
Michael Dimond
School of Business Administration
PVGO: Present Value of Growth Opportunities
• PVGO is usually presented in relation to earnings per share:
P0 = EPS1/Ke + PVGO
PVGO = P0 - EPS1/Ke
Note: This relationship uses the expected EPS figure
• Since P0 is the market’s estimate of the value of the stock, we
could identify the value of expected growth if we know Ke and
the anticipated earnings per share. Here’s another
rearrangement:
P0/EPS1 = 1/Ke + PVGO/EPS1
Michael Dimond
School of Business Administration
PVGO in a real company
• The PE ratio is P0/EPS0, which means P0/EPS1 is the forward
PE ratio. If we are trying to get here:
PVGO = P0 - EPS1/Ke
we might need a little rearrangement to solve for EPS1
• Consider the example of Facebook (FB).
Data from finance.yahoo.com includes:
EPS0 = 1.11
P/E = 68.47
Beta = 0.85
Forward P/E = 29.70
• This means the price implied in PE is 76.002 and
EPS1 is expected to be 2.559
• If Rf = 2.57% and MRP = 5.5%, Ke = 7.245%
:. PVGO = 76.002 – 2.559/0.07245 = $40.68
Michael Dimond
School of Business Administration
PVGO in a real company
EPS0 = 1.11
Price implied in PE is 76.002
EPS1 is expected to be 2.559
PVGO = $40.68
Ke = 7.245%
• What percent of FB price comes from expected growth?
• What is the expected growth of EPS for next year?
• What is the average growth of earnings implied in the price?
• How do these figures look for your team’s company?
Michael Dimond
School of Business Administration