Lecture 12: Retention Policies

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Presentation transcript:

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

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

3.3.1 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

The finite example Let us assume that With that we get

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

Proof Quite straightforward: and use Theorem 3.4.

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

The finite example We assume With that we get

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.

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

Finite Example Let us assume With that we get

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»

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

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

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.