A Variable Growth Rate Model

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Lecture 5

• A Variable Growth Rate Model

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Outline

• Two stage growth model.
• Price sensitivity of high P/E stocks.
• Stocks with negative earnings.
• Three stage growth model.
• Comparative analysis.

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Useful Present Value Formulas

• The present value of an annuity of 1 per period
  for T periods.

• The first payment is at the end of period 1.

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Useful Present Value Formulas

• The present value of an annuity that grows at a
  constant rate g.

• The first payment is (1 g) at the end of
  period 1.

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Useful Present Value Formulas

• The formula will work for ggtk and gltk, but it
  will not work if gk.
• If gk, then the present value of the annuity is
  T.

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A Numerical Example

• g 35, k 15, and T 8 years.

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A Two Stage Growth Model

• Assumptions
• 1. Dividends per share and earnings per share
  grow at a constant rate g for T years.
• 2. After time T the growth rate slows down.
• 3. The stocks expected price-to-earnings ratio
  is PERT at the end of period T.

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A Two Stage Growth Model

• The value of the stock is
• gt the present value of the expected
  dividends from period 1 thru T plus
• gt the present value of the expected price
  at the end of period T.

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XYZ Stock Numerical Example

• Assumptions
• D0 .36 E0 1.20
• ROE 50 g 35
• T 8 years PERT 24
• k 15 PER0 90
• P0 108.00

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PV of Expected Dividends

• The present value of the expected dividends
  during the first T years is

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Expected Price in Period T

• The expected earnings at the end of year T is ET
  (1 g)T E0

• (1.35)8 (1.20) 13.24.

• The expected price at the end of period T is PT
  ET PERT

• (13.24)(24) 317.73

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PV of Expected Price in Period T

• The present value of PT is

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Value of the Stock

• The intrinsic value of the stock is

• The current price is 108.00.
• XYZ stock appears to be reasonably priced.

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Sensitivity Analysis

• Use the two stage growth model and an Excel data
  table to answer the following questions.
• What assumptions do I have to make to justify
  the current price of the stock?
• Are these assumptions reasonable?
• If not, the stock is probably over valued.

15
Price Sensitivity of High P/E Stocks

• The two stage growth model implies that the
  prices of high P/E ratio stocks are sensitive to
  changes in
• ROE
• Retention rate.
• Length of high growth period.
• Discount rate.

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Stocks With Negative Earnings

• Forecast the growth in sales.
• Estimate the net profit margin in period T.
• Estimate the price-to-earnings ratio in period T.
• Discount the price in period T back to today.

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Three Stage Growth Model

• Assumptions
• (1) The expected price-to-earnings ratio is
  PERT2 at the end of T2.
• (2) Earnings and dividends grow at the rate
  g1 from period 1 to T1.
• (3) The growth rate in earnings and dividends
  decrease linearly from g1 to g2 from T1 to T2.

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Three Stage Growth Model
Growth Rate
g1
g2
T1
T2
Time
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Example of Three Stage Growth Model

• Assumptions D0 0.40 T1 5 E0 2.00 T2
  10 g1 30 k 14 g2 8 PERT2 15

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Comparative Valuation

• Most analysts value stock using the relative
  value approach.
• The positive and negative aspects of a stock are
  compared with those of stocks with similar
  characteristics.
• Analysts then determine which stocks are
  relatively undervalued.

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Comparative ValuationRatios Compared

• ProfitabilityEBIT margin, net profit margin,
  ROA, and ROE.
• ActivityAsset turnover ratios.
• CreditDebt to equity ratio, interest coverage
  ratio.
• GrowthSales per share, cash flow per share,
  earnings per share.