When Analysis 1: Valuation of the Assets

When a firm grows, it needs capital, and that capital can come from debt or equity. Debt has two important advantages. First, interest paid on Debt is tax deductible to the corporation. This effectively reduces the debt’s effective cost. Second, debt holders get a fixed return so stockholders do not have to share their profits if the business is extremely successful. Debt has disadvantages as well, the higher the debt ratio, the riskier the company, hence higher the cost of debt as well as equity. If the company suffers financial hardships and the operating income is not sufficient to cover interest charges, its stockholders will have to make up for the shortfall and if they cannot, bankruptcy will result. Debt can be an obstacle that blocks a company from seeing better times even if they are a couple of quarters away.

Capital structure policy is a trade-off between risk and return:
Using debt raises the risk borne by stock holders
Using more debt generally leads to a higher expected rate on equity.

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There are four primary factors influence capital structure decisions:
Business risk, or the riskiness inherent in the firm’s operations, if it uses no debt. The greater the firm’s business risk, the lower its optimal debt ratio.

The firm’s tax position. A major reason for using debt is that interest is tax deductible, which lowers the effective cost of debt. However if most of a firm’s income is already sheltered from taxes by depreciation tax shields, by interest on currently outstanding debt, or by tax loss carry forwards, its tax rate will already be low, so additional debt will not be as advantageous as it would be to a firm with a higher effective tax rate.

Financial flexibility or the ability to raise capital on reasonable terms under adverse conditions. Corporate treasurers know that a steady supply of capital is necessary for stable operations, which is vital for long-run success. They also know that when money is tight in the economy, or when a firm is experiencing operating difficulties, suppliers of capital prefer to provide funds to companies with strong balance sheets. Therefore, both the potential future need for funds and the consequences of a funds shortage influence the target capital structure- the greater the probable future need for capital, and the worse the consequences of a capital shortage, the stronger the balance sheet should be.

Managerial conservatism or aggressiveness. Some managers are more aggressive than others; hence some firms are more inclined to use debt in an effort to boost profits. This factor does not affect the true optimal or value maximizing capital structure but it does influence the manager in determining target capital structure.

Analysis 1: Valuation of the Assets
0% Debt25% Debt50% Debt
100% Equity75% Equity50% Equity
Book Value of Debt025005000
Book Value of Equity1000075005000
Market Value of Debt (D)025005000
Market Value of Equity (E)1000083506700
Pre-tax Cost of Debt (RD)
After-tax Cost of Debt (1-Tc)*RD0.0330.0330.033
Market Value Weights of:
Debt WD = D / (D + E)00.23040.4274
Equity (WE) = E / (D + E)10.76960.5726
Un-Levered Beta (B U)
Levered Beta B L = BU*(1+(1-Tc) (D/E))0.80.95811.1940
Risk-free Rate (Rrf)
Market Premium (MRP)
Cost of Equity RE = Rrf + bL * MRP0.0980.10750.1216
Weighted Average Cost of CapitalWACC = (1-Tc)WDRD+WERE0.0980.09030.08376
(Taxes (@34%))-504.90-504.90-504.90
(Capital Expenses)-500.00-500.00-500.00
Change in Net Working Capital0.000.000.00
Free Cash Flow (FCF)980.10980.10980.10
Value of Assets (FCF/WACC)10001.0110851.1111701.19
The value of Assets is given by the Free Cash Flows divided by the weighted average cost of capital and changes with the financing side effects of the capital structure. The Cash flows are unaffected by the Capital structure changes, however the WACC decreases as the weight of debt increases. This leads to a greater value of assets (at 50% debt, it is $11701.19 which is greater than that at 0% debt). The capital structure that maximizes stock price is also the one that minimizes the WACC. Another observation of the above table shows that increasing Debt increases Beta (a measure of risk, this is consistent with the Hamada’s equation BL= BU (1+(1-TC) (D/E))
Analysis 2: Valuation of the Debt & Equity
0% Debt25% Debt50% Debt
100% Equity75% Equity50% Equity
Cash Flow to Creditors:
Interest (Int)0.00125.00250.00
Pre-tax Cost of Debt (Rd)
Value of Debt (Int/Rd)0.002500.005000.00
Cash Flow to Shareholders:
Interest (Int)-0.00-125.00-250.00
Pretax profit1485.001360.001235.00
Taxes (@34%)-504.90-462.40-419.90
Net Income980.10897.60815.10
Capital Expenses-500.00-500.00-500.00
Change in Net Working Capital0.000.000.00
Debt Amortization0.000.000.00
Residual Cash Flow (RCF)980.10897.60815.10
Cost of Equity (From Analysis 1: RE)0.0980.10750.1216
Value of Equity (RCF/RE)10001.018351.116701.19
Value of Equity + Value of Debt10001.0110851.1111701.19
As the two sides of the balance sheet should match-up, the Values of Assets from Analysis 1 would be equal to the sum of the Value of Equity and Debt from the above Analysis 2. When the firm levers up the value of its debt component rises and the value of its equity component shrinks. But, the overall value of the firm goes up (the pie increases).

From the analysis on the previous page, the cost of equity of a levered firm is more than that of the un-levered firm. This is in accordance to the Modigliani and Miller (MM) proposition II; the cost of equity rises with leverage (Debt to Equity ratio), because the risk to equity rises with leverage.

Analysis 3: Understanding Changes in Cash Flows
0% Debt25% Debt50% Debt
100% Equity75% Equity50% Equity
Pure Business Cash Flows:
Taxes (@34%)504.90504.90504.90
Capital Expenses-500.00-500.00-500.00
Change in Net Working Capital0.000.000.00
Free Cash Flow980.10980.10980.10
Unlevered Beta (bU)
Risk-Free Rate (Rrf)
Market Premium (MRP)
Cost of Un-Levered Equity (RE)0.0980.0980.098
Unlevered WACC Using WD = 0 ;WE = 1 in WACC = (1-Tc)WDRD+WERE 0.0980.0980.098
Value of Pure Business Flows: (FCF/Unlevered WACC)10000.0010000.0010000.00
Financing Cash Flows:
Interest (From Analysis 2: Int)0-125.00-250.00
Tax Reduction (Int * TC)042.5085.00
Pre-Tax Cost of Debt (RD)
Value of financing effect: Considering Perpetual Debt(Tax Reduction/Pre-tax Cost of Debt)0.00850.001700.00
Total Value (Sum of Pure Business Flows and Financing effects)10000.0010850.0011700.00

Following the Adjusted Present Value (APV) approach to calculate the value of the firm, Present Value of the Un-Levered firm (NPV) is summed up with the Present Value of the financing side effects (NPVF). From the above analysis, we observe that the NPV calculated with the un-levered cost of capital does not change with the leverage. Only the value financing side effects, which is discounted at the cost of debt, changes with the leverage.

In the above case, the debt tax shield on the debt interest payment is the only side effect of financing. This is discounted at the cost of debt, accounting for the increase in the total value of the firm. This is in accordance with the Modigliani and Miller (MM) proposition I; the value of the levered firm is the value of the all-equity firm plus the present value of the tax shield. In this case it is assumed that there are no other financing side effects and that the debt is perpetual in nature.

Analysis 4: Value to Shareholders
If we assume, that the firm leverages its capital structure and pays out the capital raised by debt to the shareholders without investing in the operations, the share value (value to shareholders) can be determined as shown in the below table.

0% Debt25% Debt50% Debt
100% Equity75% Equity50% Equity
Total Market Value of Equity (VE) (From Analysis 2)10001.018351.116701.19
Cash Paid Out (VF) (From Analysis 2)0.002500.005000.00
Number of Original Shares (NO)100010001000
Total Value per share = (VE + VF)/ NO10.0010.8511.70
From the above analysis it is evident that leverage is good for existing shareholders, the value per share has increased, increasing the wealth of the shareholders. However the higher share price is a result of higher expected returns that resulted from the additional debt risk assumed. The optimal leverage is that which lowers the WACC and achieves maximum share price. A point beyond the optimal leverage would begin to factor the risk component and may not be good for shareholders.
Levering or un-levering the firm is not something that shareholders can do for themselves, it is a decision taken by the managers of a company. Shares of levered companies have a higher expected rate of return and thus have a higher price. However, leverage to a certain extent ensures limitations on managers’ free hand with cash flows, debtors have to be paid on time and this limit reduces the likelihood that managers will reward themselves with perquisites and will over-invest. Thus leverage has some benefits to shareholders in ensuring that management is kept in line by debtors.
Also, a firm that wants to raise capital goes to the debt market only when it is sure that the expected returns from the project are going to be very high, and returns to debtors would be fixed. With leverage the company generates capital without diluting the share prices. On the other hand, if the firm issues new equity it signals that the firm is not really sure of the returns of the projects and would like new investors to share the risk. If the company issued more stock to raise capital, the value of the share price would decline. Shareholders have no control over the capital structure decision-making process, but they do have free will on whether they want to hold any more stock or bonds in the company and can “vote with their feet”.

Value to Society:
Society is better off if firms use some debt in their capital structure. Firms with revenue generating and good projects would be able to acquire (otherwise impossible) capital because of the resource allocation of leverage medium. Institutions with excess capital can invest in firms that increase their wealth, firm’s wealth and provide better products and services to the society as a whole.
Debt unlike equity has to be serviced regularly and interest payments are required to be made on time. This has several benefits in limiting the control that managers have on free cash flow. Managers who own equity in the firm do not resort to shirking their duties, as an increased NPV of the project will yield them high returns personally. Raising debt does not dilute the equity of the managers and keeps them motivated to work harder. Debt limits free cash flows as it demands timely payment of interest. Managers cannot reward themselves with perquisites, as they have to make interest payments and retire debt. This keeps a check on the managers who may want to put their hand in the till and help themselves at the cost of shareholders (and society).

Debt lowers the agency costs arising between management and shareholders. Therefore, the new debt from leveraging can be thought of as a type of control device for shareholders. For companies in high growth areas, debt is not a great avenue to raise capital as competitive pressures and uncertain nature of cash flows can push them into bankruptcy in the presence of debt. However for slow growth companies with strong balance sheets and steady business, debt is the best avenue in the interest of the equity holders.

Analysis 7: Re-capitalization of Koppers Company Inc. (all values in thousands).

Before RecapitalizationAfter Recapitalization
Book Value Balance Sheets
Net Working Capital212,453212,453
Fixed Assets601,446601,446
Total Assets813,899813,899
Long-term Debt172,4091,738,095
Deferred Taxes195,616195,616
Preferred Stock15,00015,000
Common Equity430,874-1,134,812
Total Capital813,899813,899
Market Value Balance Sheets
Net Working Capital212,453212,453
Fixed Assets1,618,0811,618,081
PV debt tax shield (Long-term Debt * Tax Rate)58,619590,952
Total Assets1,889,1532,421,486
Long-term debt172,4091,738,095
Deferred Taxes00
Preferred Stock15,00015,000
Common Equity1,701,744668,391
Total Capital1,889,1532,421,486
Number of Shares28,12828128
Price per Share60.5023.76
Value to Public Shareholders
Cash Received = (Debt After Recap – Debt Before Recap)01,565,686
Value of Shares = (Value of Common Equity)1,701,744668,391
Total Value1,701,7442,234,077
Total per share = (Total Value)/(No. of Shares) 60.5079.43
Before re-capitalization, the weight of debt of the Kopper’s firm is around 9.1% (172,409 / 1,889,153) and the share price is $60.50. Issuing a debt of $1,738,095,000 has changed the capital structure of the firm and the new weight of Debt is 71.8% (1,738,095 / 2,421,486). Though, the share price has decreased to $23.76 after re-capitalization, shareholders have a cash flow of $79.43 due to the dividend of $55.67 (79.43 – 23.76) paid out.
Share Price before Re-capitalization$60.50
New Share Price after Re-capitalization (SP)$23.76
Number of Shares (N)28,128
Value of Dividend Paid Out (D)$1,565,686
Dividend Distributed per share (Div/share = D/N)$55.67
Total Value to Shareholder (SP + Div/Share)$79.43