1. Lecture 12: Retention Policies
Discounted Cash Flow, Section 3.3
© 2004, Lutz Kruschwitz and Andreas Löffler

2. Retention policies We analyse four different retention policies:
– autonomous retention
– retention based on cash flows,
– retention based on dividends,
– retention based on market values.

3. 3.3.1 Autonomous retention
Definition: A firm follows autonomous retention if At is deterministic
Valuation: The following equation holds
If, in particular, retention is constant and the firm lives on for ever, then

4. The finite example
Let us assume that
With that we get

5. 3.3.2 Retainment based on cash flows
Definition: Retention is based on cash flows if the firm
retains a deterministic percentage of cash flows
Valuation: The following equation holds

6. Proof
Quite straightforward:
and use Theorem 3.4.

7. Infinite lifetime
If the firm lives for ever and a is constant, we get

8. The finite example
We assume
With that we get

9. 3.3.3 Definition
Retention is based on dividends if until n«T the dividend is
determined. We furthermore assume that the investment policy
is given and that the free cash flows suffice to pay this dividend.
Hence, the retention has to be
Because of the maximum function without any further
assumptions a valuation equation has to take options into
account. If we assume that the retention stays positive or
then a closed form solution will be possible.

10. Valuation equation Valuation: The valuation equation then reads
We consider generalization for n as being useless
(then the formula might violate the transversality condition).

11. Finite Example
Let us assume
With that we get

12. 3.3.4 Retention based on market values
Managers now retain a fixed proportion of levered firm
value. The more valuable the firm, the more managers
retain. We assume that the factor
is deterministic.
«Growth financed by constant intensity»

13. Valuation equation Valuation: Valuation equation reads where
This equation is very similar to the Miles-Ezzell formula.

14. Finite example We assume a retention-value ratio of
Then the following results for the cost of equity:
With that we get the value of the levered firm as

15. Summary
We considered four different retention policies and their impact on valuation of the levered firm:
– autonomous retention
– retention based on cash flows,
– retention based on dividends,
– retention based on market values.