Capital Structure

Abstract

The capital structure of a company is the founding stone for the daily development of its operation, and for an adequate planning of the business. It says in fact how many resources are available, and where they come from.

Appendices

Problems

• 1. Tecom LTD is an all equity firm with a current market value of 750,000,000 €, and will be worth 600,000,000 € or 900,000,000 € in 1 year. The risk-free interest rate is 3 %. Suppose Tecom LTD. issues zero-coupon, 1-year debt with a face value of 850,000 €, and uses the proceeds to pay a special dividend to shareholders. Assuming perfect capital markets, use the binomial model to answer the following:

  • (a) What are the payoffs of the firm’s debt in 1 year?

  • (b) What is the value today of the debt today?

  • (c) What is the yield on the debt?

• 2. Given the company and the number in exercise 1:

  • (d) According to the Modigliani-Miller theory, what is the value of the equity before the dividend is paid?

  • (e) What is the value of equity just after the dividend is paid?

• 3. Media Corp. has planned free cash flow in the coming year of 18,000,000 €, expected to grow at a rate of 2 % per year perpetually, afterwards. Media Corp. has a cost of equity of 16 %, a cost of debt of 7 %, and corporate tax rate of 38 %. The debt to equity ratio is 0.65. What is the value of Flagstaff as an all equity firm?

• 4. Rina Industries is an all-equity firm with 65,000,000 shares outstanding and 180,000,000 € in cash. The firm expects future free cash flows of 68,000,000 € per year. Money can be used to expand the business and increase the expected future free cash flows by 12 %. The cost of capital is 10 %, and capital markets are perfect. An alternative strategy is to use the 200,000,000 € to repurchase shares instead of funding the expansion. If you were advising the board:

  • (a) What course of action would you recommend, expansion or repurchase?

  • (b) Which provides the higher stock price?

• 5. According to Modigliani and Miller, what is the significance of a company’s capital structure? How did they come to this conclusion?

• 6. According to the trade-off theory:

  • (a) What is traded off against what in the trade-off theory?

  • (b) When is optimal capital structure reached? Be precise in your answer.

• 7. For each of the four characteristics below, does the trade-off theory predict that it will lead to more or less debt in optimal capital structure, other things equal?

  • (a) Selling durables that need future maintenance and repair

  • (b) Having very volatile earnings

• 8. Firms can change their capital structures with stock repurchases and with equity offerings.

  • (a) What does the trade-off theory of optimal capital structure predict about the effect on the value of the firm of stock repurchases, will the value go up or down?

  • (b) What does the trade-off theory of optimal capital structure predict about the effect on the value of the firm of equity offerings, will the value go up or down?

• 9. The trade-off theory and the pecking order theory both explain firms’ capital structures as a function of firms’ characteristics. The table below lists a number of empirical proxy variables that are often used to test these theories. Complete the table below by writing “+”, “–”, or “0” in the columns behind each variable, depending on whether the theory predicts it is associated with more (+), or less (−) debt in capital structure, or 0 if the theory does not predict anything regarding this variable.

  Proxy variable	Trade-off theory	Pecking order theory
  Depreciation/total costs
  Return on equity
  Standard deviation of stock returns
  Fixed-to-total assets
  Market-to-book value
  R&D expenses-to-total costs
  Size (total assets)

• 10. Two companies A and B have the same assets that produce the same perpetual cash flow of 10 million €. Both companies have 16,000,000 shares outstanding. Company A has outstanding debt with a value of 18,000,000 € and current price of shares 8 €, for an annual return of 11.5 %. Company B has outstanding debt with a value of 80,000,000 €. All debt is risk free and the risk free interest rate is 5 %. Assume a Modigliani-Miller world without taxes.

  • (a) Calculate the value of the assets of company A. Use an alternative calculation to check your results.

  • (b) Calculate the price and return of the shares of company B. Check your results.

• 11. Arko LTD has generated a considerable amount of cash and it now wants to pay out 15 million € of it to its shareholders. Its balance sheet is depicted below. Arko LTD has 15,000,000 shares outstanding. Assume no taxes and transaction costs.

  Balance sheet of Arko LTD (million €)
  Cash	20	Debt	25
  Other assets	80	Equity	75
  Total	100	Total	100

  • (a) Calculate the value per share after Arko LTD has paid out 7,000,000 € dividends to its shareholders and demonstrate that this does not affect the wealth of the shareholders.

  • (b) Calculate the value per share after Arko LTD has used 7,000,000 € to buy back its shares and demonstrate that this does not affect the wealth of the shareholders.

  • (c) Describe under which circumstances the management of Arko LTD would prefer buying back shares instead of paying cash dividends.

Appendix: Risk Adjusted Return On Capital

The Risk Adjusted Return On Capital (RAROC) is a risk-adjusted performance measurement tool, which has become important in assessing the profitability of business units.

Generally, risk adjustments compare return with capital employed in a way to incorporate an adjustment for the risk involved in the business, therefore taking in account the fact that the metrics is affected by uncertainty. RAROC is the ratio of adjusted income over economic capital

$$ \begin{array}{l} RAROC=\frac{R-C-{E}_L}{E_C}\\ {} =\frac{A_{NI}}{E_C}\end{array} $$

where

• R is the amount of revenues.

• C is the amount of costs.

• E _L is the expected loss.

• E _C is the economic capital.

• A _NI is the adjusted net income.

For a bank issuing a loan, the numerator of RAROC measure for that loan will look like

$$ {A}_{NI}=I-{E}_L-{C}_O $$

where

• I is the financial income.

• C _O is the amount of operating costs.

Assuming τ is the corporate tax rate, a step further consists in multiplying the amount obtained by $\left(1-\tau \right)$, in order to get the post-tax RAROC measure.

A further degree of complication can be added by multiplying the economic capital by a compounding factor obtained from the risk-free rate. The amount obtained is added to the numerator of RAROC equation.

RAROC can be related to CAPM analysis in order to capture the relationship with the hurdle rate. Recall CAPM equation to be

$$ {R}_i={R}_f+{\beta}_i\left({R}_m-{R}_f\right) $$

and

$$ \begin{array}{l}{\beta}_i=\frac{\sigma_{im}}{\sigma_m^2}\\ {} =\frac{\rho_{im}{\sigma}_i{\sigma}_m}{\sigma_m^2}\\ {} =\frac{\rho_{im}{\sigma}_i}{\sigma_m}\end{array} $$

The CAPM equation becomes

$$ {R}_i={R}_f+\frac{\rho_{im}{\sigma}_i}{\sigma_m}\left({R}_m-{R}_f\right) $$

from which

$$ {R}_i-{R}_f=\frac{\rho_{im}{\sigma}_i}{\sigma_m}\left({R}_m-{R}_f\right) $$

and

$$ \frac{R_i-{R}_f}{\rho_{im}{\sigma}_i}=\frac{R_m-{R}_f}{\sigma_m} $$

The equation sets an important equivalence for the asset i in the portfolio. The left hand side is the RAROC of the asset, while the right hand side is the hurdle rate on the asset. The two are equal.