4. Interim Conclusions

The previous considerations have shown that, in our simplified world, financing policy does not matter.

  • The share price is the same (10) under both policies
  • The value of the firm is the same under both policies (5'000).

  

More specifically, we found that under the current situation with no leverage (unlevered firm):

  • Value of debt (D) = 0
  • Value of equity (E) = 5'000
  • Value of unlevered firm (\(V_U\)) = D + E = 0 + 5'000 = 5'000.

 

Under the proposed capital structure, the valuations were as follows (levered firm):

  • Value of debt (D) = 2'500
  • Value of equity (E) = 2'500
  • Value of unlevered firm (\(V_L\)) = D + E = 2'500 + 2'500 = 5'000.

  

Consequently, the value of the firm is unaffected by its financing policy (VU = VL). This is the famous first proposition of Modigliani and Miller.

 

Another way to see the irrelevance of financing decisions in our stylized world is to consider individual investors who do not agree with how the company is financed. As it turns out, they can adjust the financing policy in their own portfolio --- they do not need the firm to do that for them! To see this, consider the following two scenarios:

  • First, let us assume that the firm does NOT adopt the new capital structure and remains fully equity financed. A shareholder does not like this because she believes the unlevered stock is not risky enough.
  • Second, let us assume that the firm does adopt the new capital structure with 50% of debt. A shareholder does not like this because he believes that the levered stock will be too risky.

What can these shareholders do to return to their preferred situations?

  

Case A: Unlevered firm not risky enough for the investor

Suppose an investor owns 50 shares of the unlevered firm at a current price of 10 (total portfolio value of 500). What can she do to earn the same returns as she would earn with the levered firm?

  • The answer is very simple: She can lever her own portfolio! 
  • Specifically, she could borrow an additional 500 from a bank at an interest rate of 10% and use the money to buy 50 additional shares of the unlevered firm. 
  • Each year, she then collects the earnings per shares of her 100 shares and uses parts of the proceeds to pay interest on the loan:
    • In the pessimistic scenario, she collects EPS of 60 (100 × 0.6). The interest expenses are 50 (0.1 × 500) so the investor's net earnings are 10. Given a net investment of 500, this corresponds to a return on equity of 2%.
    • In the optimistic scenario, in contrast, she collects EPS of 180. Net of interest expenses (50), her earnings are 130, which corresponds to a return on equity of 26%.
  • These returns are identical to the ones of the levered firms.
  • Put differently, the investor can use "home-made" leverage to gear the riskiness of her stock. She does not need the firm to do that for her.

 

Case B: Levered firm too risky for the investor

To illustrate this case, suppose an investor currently owns 100 shares of the unlevered firm (total portfolio value of 1'000). After the change in leverage, he thinks the stock is too risky. What can he do to return to the original returns of the unlevered firm?

  • Again, the answer is very simple: He can unlever his own portfolio!
  • Specifically, he could sell 50 of the 100 shares and invest the proceeds in the risk-free asset at a rate of return of 10%.
    • Consequently, after the transaction, the investor will own 50 shares of the levered firm as well as a "bank account" that pays an annual interest of 50.
    • In the pessimistic scenario, the investor will collect dividend payments of 10 (= 50 × 0.2) as well as interest payments of 50. This total return of 60 corresponds to a rate of return of 6% on the total portfolio value of 1'000.
    • In contrast, in the optimistic scenario, the investor will collect dividend payments of  130 (= 50 × 2.6) as well as interest payments of 50. This total return of 180 corresponds to a rate of return of 18% on the total portfolio value of 1'000.
  • Aftern unlevering his portfolio, the investor therefore expects to earn a rate of return between 6% and 18%. 
  • Again, these returns are identical to those of the unlevered firm.
  • Therefore, the investor can use "home-made" leverage also to unlever the riskiness of a stock.

 

Therefore, the conclusion from the beginning of this page remains: In our perfect world, financing is irrelevant. If investors disagree with the firm's financing policy, they can use home-made leverage and adjust their own portfolios.

 

Finally, let us consider the implications of these considerations for the cost of capital of a firm. This is the topic of the following page.