Discounted distributions and sustainable growth

Learning goals

• Explain time and discounting using mechanisms and limitations.
• Explain growth stages using mechanisms and limitations.
• Explain consistency checks using mechanisms and limitations.

Draft · approximately 35 minutes, excluding further revision.

Time and discounting

A dividend-discount model values expected future dividends rather than accounting earnings; date each payment and use a discount rate consistent with risk and currency.

The constant-growth expression D1/(r−g) requires r greater than perpetual g and a sustainable stable-growth assumption; D1 is next-period dividend.

Growth stages

A multistage model discounts explicit early payouts plus a terminal value dated at the end of the explicit period; do not discount terminal cash twice or omit its time index.

Sustainable growth is retention times ROE under stable profitability and financing assumptions; reinvesting earnings creates value only when returns justify their required cost.

Consistency checks

FCFF is cash available before financing distributions; FCFE adjusts for after-tax interest and net borrowing under compatible definitions. Distinguish debt funding from operating value creation.

A small discount-rate change near r=g can dramatically move the terminal estimate; compare the implied growth and multiple to economically plausible long-run conditions.

Two-stage cash-flow valuation with explicit claim matching

Suppose equity cash flows FCFE1=3 and FCFE2=4 per share. Thereafter FCFE grows 2% perpetually and equity required return is 10%. Terminal equity value at year two is 4×1.02/(0.10−0.02)=51. The current estimate is 3/1.10+(4+51)/1.10²=48.1818. Year-two cash and terminal value share the same date; this prevents adding a year-two value without discounting.

For an enterprise bridge, assume EBIT100, usable tax rate25%, depreciation10, capex30 and operating working-capital increase5. FCFF=100×0.75+10−30−5=50. If interest8 and net borrowing3, FCFE=50−8×0.75+3=47. Match FCFF with overall capital cost and FCFE with equity cost; the tax treatment is a classroom assumption.

Perpetual preferred value and contingent features

A noncallable, nonconvertible perpetual preferred paying a fixed annual dividend 6 has value 6/.08=75 at an 8% required return under a perpetuity model. The model assumes the distribution continues and uses a risk-consistent discount rate; it does not make issuer credit or suspension risk disappear. A preferred with maturity instead requires discounting the redemption value as well.

An issuer call gives the issuer an option that can limit investor upside when rates fall; conversion can add equity participation; contingent or cumulative payment terms alter risk and valuation. Do not value these instruments solely as dividend/rate while ignoring the embedded rights. Read the actual priority and payment conditions.

Formula and assumptions

V0=D1/(r−g), r>g; sustainable g=retention×ROE

Original applied case: Discounted distributions and sustainable growth

1. Next dividend is 2.4, required return 9%, perpetual growth 3%; assume these inputs remain sustainable.
2. Value=2.4/(0.09−0.03)=40. At 10% required return it becomes 34.2857.
3. The drop reflects discount-rate sensitivity, not a change in the current cash distribution.

Errors to catch

• Do not assume: Past dividends alone determine all future value.
• Do not assume: Gordon growth remains finite when g exceeds r.
• Do not assume: Terminal value is always dated today.

Original knowledge check

Answer every question before checking. Review explanations after submitting; retry starts a new attempt.

Sources and coverage status

These original lessons are drafts. Public outlines are used to check scope; the official learning-outcome text and proprietary question banks are not reproduced here. Follow the source for exam-year requirements and updates.

• Reference · www.cfainstitute.org
• Reference · www.investor.gov