Sustainable Growth

EXERCISE 01

The payout ratio is 50.00% and the return on new investment is 10.00%. New investment is financed through retained earnings.

A.Calculate sustainable dividend growth.

A.

g=(1-\mathrm{payout})ROE

g=(1-0.5)(0.1)

5.00%

Sustainable Growth

EXERCISE 02

The payout ratio is 37.50% and the return on new investment is 12.00%. New investment is financed through retained earnings.

A.Calculate sustainable dividend growth.

A.

g=(1-\mathrm{payout})ROE

g=(1-0.375)(0.12)

7.50%

Sustainable Growth

EXERCISE 03

A.For a firm financing new investment solely with retained earnings, how do payout and ROE affect dividend growth?

A.

g=(1-\mathrm{payout})ROE

In the constant-policy model, growth falls as payout rises and increases as ROE on new investment rises, holding the other input fixed. This is a growth identity, not proof that retaining more earnings creates value.

Sustainable Growth

EXERCISE 04

An analyst values the stock at €75. Expected EPS is €6 and the next dividend is €4. The risk-free rate is 2.5%, market risk premium 7% and beta 1.2. Market price is €80.

A.Infer the analyst’s growth rate and ROE.
B.Compare analyst and market PVGO.

A.

r_E=2.5\%+1.2(7\%)=10.9\%

g=0.109-4/75=5.5667\%,\quad ROE=\frac{g}{1-4/6}=16.7\%

B.

P_{no\ growth}=6/0.109\approx55.045872

PVGO_{analyst}=75-6/0.109\approx19.95

PVGO_{market}=80-6/0.109\approx24.95

Analyst PVGO = €19.95; market PVGO = €24.95.