14.15: Capital Gains

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It is interesting to note that, if G > 0, the model will automatically generate capital gains. Here again is our formula. Below is a problem whose resolution illustrates the model’s automatic generation of capital gains.

Question:

Formula:

P₀ = [D₀ (1 + G)] / (R – G)

P₀ = D₁ / (R – G)

Given:

D₀ = $1 The Last Dividend

R = 10% The Discount Rate

G = 5% The Dividend’s Constant Growth Rate

What is the price today?

What would the price be in one year?

Solution:

Price Today:

P₀= $1 (1 + .05) / (.10 – .05)

= 1.05 / .05

= $21

Price in One-Year:

P₁ = D₂ / (R – G)

P₁ = $1.05 (1 + .05) / (.10 – .05)

= 1.1025 / .05

= $22.05

We observe that $22.05 / $21 = 1.05. That is to say that next year’s price will be greater than last year’s by 5%, or the same as the stock’s growth rate (again, assuming a constant pay-out ratio).

We often say that a stock is “ahead of itself,” if the rate of growth in price exceeds the dividend – or earnings – growth rate (assuming a constant pay-out ratio).

Capital Gains, Dividend Growth: Some Practice Problems

The following should help summarize some relevant concepts.

1. Complete the empty cells, given the data noted below for a stock. The basic formula for the Dividend Discount Model is:

P₀= [(D₀) (1 + G)] ÷ [R – G]

2. Once again, complete the spreadsheet, given the data noted for a particular stock.

Given:

Solve:

Explain, in words, what is meant by the term, “G,” in question #2.

Assuming G is a constant (question #1), P₀ (1 + G) = P₁.

Capital Gains, Dividend Growth: Some Practice Problems (Solutions)

Problem 1:

Problem 2:

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Capital Gains, Dividend Growth: Some Practice Problems

Capital Gains, Dividend Growth: Some Practice Problems (Solutions)