BUS 313

Pay it out or plow it back?

Name: Business Tutor
Address: Burnaby, BC, CA
Telephone: +1-604-916-5838
Price range: C$30–C$129

A firm can hand its earnings to shareholders or reinvest them. See when reinvesting raises the share price, how much of a price is growth, and how to value a firm whose plans change or that has no price of its own.

Part 1 · Payout and growth · Step 1 of 10

A dividend that grows every year, forever

P₀ = $2.40 ÷ (r − g)g = r: no finite price

Part 1 · Payout and growth · Step 1 of 10

A dividend that grows every year, forever

A share is worth the present value of every dividend it will ever pay. Say next year's dividend is D₁ and it then grows at a steady rate g each year, forever. That stream is a growing perpetuity. Discount each dividend at r, the cost of equity (the return investors need for this stock's risk), and the endless sum shrinks to one short formula, the Gordon model: P₀ = D₁ ÷ (r − g). It only works when g is below r.

Try it: Slide g up towards r. The gap r − g shrinks and the price shoots up. At g = r there is no price at all.

Next year's dividend, D₁$2.40

Cost of equity, r12%

Growth rate, g9%

Price today, P₀

$80.00

r − g

First 10 dividends' share of P₀

23.8%

One more point of growth (10%) would make the price $120.00, 50% higher. Near r, small changes in g move the price a lot.

P₀ = D₁ ÷ (1 + r) + D₁(1 + g) ÷ (1 + r)² + … = $2.14 + $2.09 + $2.03 + …

Each dividend is one year bigger and one more year away.

P₀ = $2.40 ÷ (0.12 − 0.09) = $80.00

The growing perpetuity formula adds up all of them.

The first 10 dividends are worth $19.02 today, only 23.8% of the price. The rest comes from dividends further out.

Check yourself

r = 12%. Expected growth rises from 9% to 11%, with the same D₁. The price…

Midterm coming up and PVGO still feels slippery?

Bring your problem sets. We work through them together until every type feels routine.

Book a session Next toolNext: Valuing a business: free cash flow and the horizon value

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Pay it out or plow it back?

A dividend that grows every year, forever

A dividend that grows every year, forever

Pay out everything, or plow back: price and PVGO

Midterm coming up and PVGO still feels slippery?

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