Question

Procter and Gamble? (PG) paid an annual dividend of

$ 1.73

in 2009. You expect PG to increase its dividends by

8.4 %

per year for the next five years? (through 2014), and thereafter by

2.9 %

per year. If the appropriate equity cost of capital for Procter and Gamble is

7.3 %

per? year, use the? dividend-discount model to estimate its value per share at the end of 2009.

Answer 1

This question requires application of dividend discount model, according to which current value of share is present value of all dividends expected in future.

We would use the following mathematical function:

where V5 is terminal value, which is the value in year prior to year when constant growth in dividend expected in future. Mathematically terminal value is represented as:

Now, in order to apply this mathematical relation, we need to calculate expected values in dividends.

D1 = D0 * (1 + g) = 1.73 * (1 + 8.4%) = 1.8753

D2 = D1 * (1 + g) = 1.8753 * (1 + 8.4%) = 2.0328

D3 = D2 * (1 + g) = 2.0328 * (1 + 8.4%) = 2.2036

D4 = D3 * (1 + g) = 2.2036 * (1 + 8.4%) = 2.3887

D5 = D4 * (1 + g) = 2.3887 * (1 + 8.4%) = 2.5894

D6 = D5 * (1 + g) = 2.5894 * (1 + 2.9%) = 2.6645

Now, we can calculate the terminal value of the P&G share as well as the value of share today (2009).

V5 = 60.5557

Now, applying the final equation to calculate value of share today (2009) is:

V0 (Value in 2009) = $51.49