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CFA Level II Exam · Discounted Dividend Valuation

Present Value of Growth Opportunities (PVGO) Explained

Updated 7 October 2026 · Fact-checked

PVGO is the part of a stock's value that comes from future profitable investment. Compute it as value minus no-growth value: PVGO = V₀ − E₁/r. The no-growth value assumes all earnings are paid out forever. Dividing by E₁ links PVGO to the leading P/E.

Understand Present Value of Growth Opportunities

Start with a firm that invests nothing new. It pays out all its earnings as dividends, and earnings stay flat. Its dividend equals E₁ every year, a perpetuity. So its value is E₁ ÷ r. This is the no-growth value per share.

Most stocks trade above that number. The extra value comes from the firm investing retained earnings in projects that earn more than the required return r. This extra amount is the present value of growth opportunities (PVGO). So: V₀ = E₁/r + PVGO.

PVGO can be positive, zero or negative. It is positive only when new projects earn more than r (positive NPV). If the firm reinvests at exactly r, growth adds nothing and PVGO is zero, even though earnings grow. If it reinvests below r, PVGO is negative and growth destroys value. This is why growth alone does not mean higher value.

Divide both sides by E₁ and you get the justified leading P/E: P₀/E₁ = 1/r + PVGO/E₁. The first term is the P/E of a no-growth firm. The second term is the part of the multiple paid for growth. For the trailing version, divide by E₀ instead: P₀/E₀ = (1 + g) × (leading P/E) when growth is a constant g in a Gordon setting.

In vignettes, you usually get the price or a Gordon value, E₁ (or E₀ and g), and r. Your task is to find the data, compute E₁/r, and subtract.

Key formulas to remember

Value decomposition
V₀ = E₁ ÷ r + PVGO
E₁ is next year's expected EPS. E₁/r is the no-growth value per share.
PVGO
PVGO = V₀ − E₁ ÷ r
Use the market price if asked what the market implies; use the model value if asked for the intrinsic PVGO.
Justified leading P/E
P₀ ÷ E₁ = 1 ÷ r + PVGO ÷ E₁
1/r is the no-growth component. The rest is the growth component.
Gordon leading P/E
P₀ ÷ E₁ = (1 − b) ÷ (r − g)
b is the retention rate; g = b × ROE in the sustainable growth setting. Needs r > g.
Trailing P/E
P₀ ÷ E₀ = (1 + g) × (P₀ ÷ E₁)
Since E₁ = E₀ × (1 + g). Valid for constant growth.
Growth share of value
PVGO ÷ V₀
Fraction of price that depends on growth opportunities.

How to solve Present Value of Growth Opportunities questions

Use this method for any PVGO or P/E decomposition question in a vignette.

  1. 1Identify the value to decompose: the current price P₀ or a model value V₀ (for example from a Gordon model).
  2. 2Find E₁, the next-year EPS. If only E₀ and g are given, compute E₁ = E₀ × (1 + g).
  3. 3Find the required return r. Check whether it is given or must come from CAPM in the exhibit.
  4. 4Compute the no-growth value: E₁ ÷ r.
  5. 5Compute PVGO = V₀ − E₁/r. Keep the sign; a negative result is meaningful.
  6. 6If asked for P/E parts, divide by E₁: no-growth P/E = 1/r and growth component = PVGO/E₁.
  7. 7For trailing P/E, multiply the leading P/E by (1 + g), or divide by E₀ directly.
  8. 8Sanity check: does PVGO fit the story (ROE above or below r)?

Quickest way: Subtract the perpetuity

When to use it: When the vignette gives a price or Gordon value plus EPS and r, and asks for PVGO or its share of value.

  1. Compute E₁ ÷ r on the calculator.
  2. Subtract it from the price or value.
  3. Divide by the price if the share of value is asked.
  4. Check the answer type: per share amount, percentage, or P/E points.

Common mistakes in Present Value of Growth Opportunities

  • Using E₀ instead of E₁ in E/r.

    The vignette shows current EPS prominently and the formula is written as E/r.

    Fix: The no-growth perpetuity starts next year. Use E₁. Convert E₀ × (1 + g) when needed.

  • Assuming growth always means positive PVGO.

    Students link earnings growth with value creation.

    Fix: PVGO is positive only when projects earn more than r. If ROE equals r, PVGO is zero despite growth.

  • Mixing leading and trailing P/E.

    Both are called P/E and the formulas look alike.

    Fix: Check which EPS is in the denominator. Trailing = leading × (1 + g).

  • Forgetting the payout in the Gordon P/E.

    Students write 1/(r − g) and drop (1 − b).

    Fix: Leading P/E = (1 − b)/(r − g). Dividends are E₁ × (1 − b).

  • Using the wrong r.

    Several rates appear in the exhibit, such as ROE, WACC and cost of equity.

    Fix: Use the required return on equity. Compute it by CAPM if only rf, beta and ERP are given.

Worked examples

Example 1

Vignette: Lumora Foods trades at €48.00. Next year's EPS is expected to be €3.00. The analyst's required return on equity is 8%. Questions: (1) What is the no-growth value per share? (2) What is PVGO? (3) What share of the price is PVGO?

Show the solution
  1. No-growth value = E₁ ÷ r = 3.00 ÷ 0.08 = €37.50.
  2. PVGO = 48.00 − 37.50 = €10.50.
  3. Share of price = 10.50 ÷ 48.00 = 0.21875, about 21.9%.

Answer: No-growth value €37.50; PVGO €10.50; PVGO is about 21.9% of the price.

Example 2

Vignette: Nordvik Marine has current EPS of €4.00, a payout ratio of 60%, ROE of 10% and required return of 9%. Growth is constant at g = b × ROE. Questions: (1) Find the justified leading P/E. (2) Find PVGO per share. (3) Find the justified trailing P/E.

Show the solution
  1. Retention b = 1 − 0.60 = 0.40. g = 0.40 × 0.10 = 4%.
  2. E₁ = 4.00 × 1.04 = €4.16. D₁ = 0.60 × 4.16 = €2.496.
  3. V₀ = 2.496 ÷ (0.09 − 0.04) = 2.496 ÷ 0.05 = €49.92.
  4. Leading P/E = 49.92 ÷ 4.16 = 12.0. Check: 0.60 ÷ 0.05 = 12.0.
  5. No-growth value = 4.16 ÷ 0.09 = €46.22 (rounded).
  6. PVGO = 49.92 − 46.22 = €3.70 (rounded). It is positive because ROE of 10% exceeds r of 9%.
  7. Trailing P/E = 49.92 ÷ 4.00 = 12.48, which equals 1.04 × 12.0.

Answer: Leading P/E 12.0; PVGO about €3.70 per share; trailing P/E 12.48.

Exam tips

  • Always check the timing of EPS. E₁ goes with E/r and the leading P/E.
  • If ROE equals r, expect PVGO of zero. Use this to check your answer quickly.
  • Read the question for price versus model value. Market-implied PVGO uses price.
  • Questions often ask which P/E component changes when r rises: both 1/r and PVGO fall.

Present Value of Growth Opportunities: frequently asked questions

What is PVGO in simple terms?

It is the part of a stock's value that comes from future investments earning more than the required return. The rest of the value is what the firm would be worth with no growth.

Can PVGO be negative?

Yes. If the firm invests retained earnings at a return below the required return, growth destroys value and PVGO is negative.

How do I get PVGO from the P/E?

Multiply the leading P/E by E₁ to get the price, then subtract E₁/r. Equivalently, PVGO/E₁ = leading P/E − 1/r.

What is the difference between leading and trailing P/E?

Leading P/E uses next year's expected EPS. Trailing P/E uses the last year's EPS. With constant growth, trailing = leading × (1 + g).