DCF Example (infinite case, personal income tax) by Kruschwitz/Löffler

In this notebook we only consider examples where the stochastic structure of the cash flows is not used.

Parameters of the Model

We are dealing here with an (unlevered) company,which will bear infinitely many years of payments to its owners.They,however,cannot be predicted with certainty. We know that the firm will live infinitevily  and the free cash flow after tax will have constant expectation.

(Subscript[C, 1]) = 100;  τ = 0.5;  (Subscript[r, f]) = 0.1; (Subscript[k, u]) = 0.2;

Valuation concept: the unlevered company

To value the firm we need to know the cost of capitel of the (unlevered) firm. These cost of capital are expected returns of holding the firm's share for one period. This allows us to value the unlevered company.

Notice that we will use a slightly different notation for the cost of capital than in the DCF-book. For more details see DCF, chapter 3.1.

(Subscript[V, u]) = Sum[((Subscript[C, 1])/(((1 + (Subscript[k, u])))^t)),  {t,  1, ∞}]

Autonomous retainment

With autonomous retention, the retetntion is deterministic.

Notice that due to some limitations of Mathematica we will use a slightly different notation for the cost of capital than in the DCF-book. For more details see DCF, chapter 3.3.1.

A = 10;  (Subscript[V, l]) = (Subscript[V, u]) + A

Retention based on cash flows

A firm is following an earnings retention policy based on cash flows if the retention is a determinate multiple of the free cash flow of the unlevered firm.

α = 0.5;  
    (Subscript[V, l]) = (1 + ((τ (Subscript[r, f]) (1 - τ))/(1 + (Subscript[r, f]) (1 - τ))) α) 
          (Subscript[V, u]) + (((1 + 
                    (Subscript[r, f])) (1 - τ))/(1 + (Subscript[r, f]) (1 - τ))) (Subscript[C, 1])

Retention based on market values

The firm is following a retention policy based on market values if the relation of retention and value of the firm.

l = 0.1; 
    k = (1 + 
              (Subscript[k, u])) (1 - (((1 + 
                          (Subscript[r, f])) (1 - τ))/(1 + (Subscript[r, f]) (1 - τ))) l) - 1

(Subscript[V, l]) = ((Subscript[C, 1])/(k + (1 - τ) l))