FINANCIAL MANAGMENT

Financial Management



Financial management

The market value of a firm is given by: Equity + Debt = E + D = V. The objective of the managers is the maximization of the firm's value i.e. of its share price (no agency problems). Debt finance is cheaper than equity finance (rd < re), because equity is more risky than debt.

Traditional theory: if a firm substitutes debt for equity, it will reduce its cost of capital so increasing the firm's value:

.

But, when the D/E ratio is considered too high, both equity-holders and debt-holders will start demanding higher returns so that the cost of capital of the firm will rise. Hence, There exists an optimal, cost minimizing value of the D/E ratio.

 

Modigliani- Miller (M-M) proposition 1: The value of a firm is the same regardless of whether it finances itself with debt or equity. The weighted average cost of capital: ra is constant.

 

Assumptions of M-M: perfect and frictionless markets, no transaction costs, no default risk, no taxation, both firms and investors can borrow at the same rd interest rate. 

Ex. Consider two firms: one has no debt while the other is leveraged (i.e. has debts). They are identical in every other respect. In particular they have the same level of operating profits: X. Let A have 1000 shares issued at 1 euro and B have issued 500 (1 euro) shares and 500 euro of debt.

  

 

Firm A

Firm B

Equity       E

1000

500

Debt         D

0

500

 

100 shares of B (1/5EB) give right to receive a return:  

200 shares of A (1/5EA) bought using 100 euro of borrowed money (100=1/5DB) give the same return: . 

The two investments yield the same return (and have the same financial risk) Hence 1/5 of A must have the same value of 1/5 of B: both shares should be equally priced. If not, arbitrageurs will have profitable operations at their disposal.

 

 

 Firm A

 Firm B

Possible equilibrium

Firm A

Possible equilibrium Firm B

Operating profits         X

10.000

10.000

10.000

10.000

Interests                   rdD

¾

3.600

¾

3.600

Profits of shares   X-rdD

10.000

6.400

10.000

6400

Shares market value    E

66.667

40.000

68.000

38.000

Return on equity         re

15%

16%

14,7%

16,8%

Market value of debt   D

¾

30.000

¾

30.000

Market value of firm   V

66.667

70.000

68.000

68.000

Av. cost of capital      ra

15%

14,3%

14,7%

14,7%

Debt ratio                D/E

0%

75%

0%

78,9%

 

Firm B is overvalued with respect to A. An operator owning 1% of B can:

sell his shares of B for a market value of 400;

borrow 300 (i.e. 1% of the debt of B) at rd = 12%

buy 1% of A for a value of 667.

 

He then owns 1% of the unleveraged firm but has a debt equal to 1% of that of B. His risk is unchanged. Before he had an expected return of 64 (=0.16*400). Now he still have a return of 64 (he expects to receive 100 = 0.15*667 but he has to pay 36 as interests). But: before he had invested 400 of his money, now only 367=667-300

Hence it is profitable to sell B (the overvalued shares) and buy A (the undervalued ones). The price of A rises and that of B falls. The table shows a possible position of equilibrium: ra is the same as it should be since, by hypothesis, A and B have the same degree of ...