# Valuation FIN449 Michael Dimond. Michael Dimond School of Business Administration UNDERSTANDING GROWTH.

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Valuation FIN449 Michael Dimond

Michael Dimond School of Business Administration Most students can do this… V 0 = CF 1 /(r-g) :. r = CF 1 /V 0 + g and :. g = r – CF 1 /V 0 This implies the growth of all cash flows after CF 1

Michael Dimond School of Business Administration …but what if you don’t have CF 1 ? CF 1 = CF 0 * (1+g) :. V 0 = CF 0 *(1+g)/(r-g) If you are only given CF 0 Could you solve for r? Could you solve for g?

Michael Dimond School of Business Administration Solving for r is pretty straightforward V 0 = CF 0 *(1+g)/(r-g) :. r = [ CF 0 *(1+g)/ V 0 ] + g

Michael Dimond School of Business Administration Solving for g gives students more issues V 0 = CF 0 *(1+g)/(r-g) :. g = (r*V 0 - CF 0 )/(CF 0 +V 0 ) This implies the growth of all cash flows after CF 0, including the upcoming CF 1.

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: 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: P 0 = EPS 1 /K e + PVGO PVGO = P 0 - EPS 1 /K e Note: This relationship uses the expected EPS figure Since P 0 is the market’s estimate of the value of the stock, we could identify the value of expected growth if we know K e and the anticipated earnings per share. Here’s another rearrangement: P 0 /EPS 1 = 1/K e + PVGO/EPS 1

Michael Dimond School of Business Administration PVGO in a real company The PE ratio is P 0 /EPS 0, which means P 0 /EPS 1 is the forward PE ratio. If we are trying to get here: PVGO = P 0 - EPS 1 /K e we might need a little rearrangement to solve for EPS 1 Consider the example of Facebook (FB). Data from finance.yahoo.com includes: EPS 0 = 1.11Beta = 0.85 P/E = 68.47Forward P/E = 29.70 This means the price implied in PE is 76.002 and EPS 1 is expected to be 2.559 If R f = 2.57% and MRP = 5.5%, K e = 7.245% :. PVGO = 76.002 – 2.559/0.07245 = \$40.68

Michael Dimond School of Business Administration PVGO in a real company EPS 0 = 1.11 Price implied in PE is 76.002 EPS 1 is expected to be 2.559 PVGO = \$40.68 K e = 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?