Relationship Between Capital Structure and Cost of Capital
Various hypotheses have been proposed by various writers to explain the relationship between capital structure, cost of capital and business value. There are four prominent theories that give opposing viewpoints on the relation between financial leverage and the valuation of common shares. In terms of the importance of capital structure decisions to business valuation, these theories differ.
Table of Content
The four theories are:
Net Income Approach
According to the Net Income (NI) approach, the considerations of capital structure are related to the value of the firm. On an increase in the financial leverage, there will be a decline in the weighted average cost of capital (WACC), while the value of the firm and the share market price will resultantly increase.
On the other hand, on a decline in the financial leverage, there will be an increase in the weighted average cost of capital (WACC), while the value of the firm and the share market price will resultantly decrease. In other words, the NI approach holds that as debt increases, the overall cost of capital of the firm declines.
The NI approach is given in Figure:
Figure shows that under NI approach, cost of equity (Ke ) and cost of debt (Kd) are constant. As debt is replaced for equity in the capital structure, being less expensive, it causes the weighted average cost of capital (Ko ) to decline, so that it ultimately approaches the cost of debt with 100 percent debt ratio.
Here, the value of the firm can be described as follows:
Value of Firm (V) = S + D
Where,
S = Market Value of Equity
D = Market Value of Debt
Market Value of Equity (S) = NI Ke
Where,
NI = Earnings Available for Equity Shareholders
Ke = Equity Capitalisation Rate
Overall cost of capital = EBIT Value of the firm
The value of the firm will be maximum at a point where the firm’s overall cost of capital is minimum. Thus, the NI approach suggests maximum possible debt financing with a view of minimising the overall cost of capital. The value of the firm can be increased by decreasing the overall cost of capital through increasing the degree of financial leverage.
The overall cost of capital can also be computed as:
Overall cost of capital= ———
Where,
Ke = Cost of equity
Kd = Cost of debt
Let us understand the NI approach with the help of a few illustrations:
Illustration 3: A company has an investment of ₹4,00,000 and a net operating income of ₹1,00,000. It is considering two scenarios: (1) no debt and (2) equal levels of debt and equity of ₹2,00,000 each. The company finds out that the cost of equity is 12% and the cost of debt is 8%. Prove that the NI approach holds true in this case.
Solution:
| Particulars | Scenario (1) | Scenario (2) |
|---|---|---|
| Equity capital | 4,00,000 | 2,00,000 |
| Debt capital | 0 | 2,00,000 |
| Cost of Equity | 12% | 12% |
| Cost of Debt | 8% | 8% |
| Net operating income | 1,00,000 | 1,00,000 |
| Interest on Debt | 0 | 16,000 |
| Equity earnings | 1,00,000 | 84,000 |
| Market value of equity | = 1,00,000 ÷ 0.12 = 8,33,333 | =84,000 ÷ 0.12 = 7,00,000 |
| Market value of debt | 0 | 2,00,000 |
| Total Value of firm | 8,33,333 | 9,00,000 |
Average cost of capital
Scenario (1) = 8% × (0/8,33,333) + 12% × (8,33,333/8,33,333) = 12%
Scenario (2) = 8% × (2,00,000/9,00,000) + 12% × (7,00,000/9,00,000) = 11.103%
From the above computations, it can be seen that:
- As the cost of capital declines, the value of the firm would go up as it is dependent upon the return expected and the cost of capital. Inverse relationship exists between the value of the firm and cost of capital for any given level of return.
- This means that as we increase the level of debt in the company, the value of the firm would go up even further. This would mean that the companies would like to employ as much debt as possible.
Illustration 4: From the following information pertaining to RTZ Ltd., you are required to compute the market value of equity, value of the firm and overall cost of capital.
RTZ Ltd.’s EBIT (Earnings Before Interest and Tax) = ₹2,50,000
Equity capitalisation rate is 16%
The company has ₹10 lakhs debentures carrying a coupon rate of 10%.
Solution:
The statement showing the total value of the firm is as follows:
| Particulars | Amount (₹) |
|---|---|
| EBIT | 2,50,000 |
| Less: Interest on debentures (10% of 10,00,000) | (1,00,000) |
| Earnings available for equity holders, i.e., Net Income | 1,50,000 |
| Equity capitalisation rate | 16% |
| Market value of equity (S) = 1,50,000 ÷ 16% | 9,37,500 |
| Market value of debt (D) | 10,00,000 |
| Total value of the firm (S+D) | 19,37,500 |
| Overall cost of capital = 2,50,000 ÷ 19,37,500 | 12.90% |
Net Operating Income Approach
Net Operating Income (NOI) is referred to as Earnings Before Interest and Tax (EBIT). According to the propositions of the NOI approach, the capital structure decisions are completely irrelevant. This theory states that since the overall cost of capital is a function independent of the degree of financial leverage; therefore, changes in the financial leverage shall not result in changes in the total value of the firm and the market price of ordinary shares.
Therefore, any division between debt capital and equity capital is not relevant. According to the NOI approach, any increase in the usage of the debt capital is offset by an increase in the capitalisation rate of equity. The debt capital is somewhat cheaper because equity shareholders expect greater compensation. This is because equity investors are exposed to greater risk owing to the existence of fixed charge securities in the firm’s capital structure.
The capital cost and financial leverage under the NOI approach is shown in Figure:
Figure shows that the firm’s overall capitalisation rate, represented by Ko, and the cost of debt, represented by Kd, are constant. Moreover, the cost of equity represented by Ke increases with an increase in the degree of financial leverage.
Let us understand the NOI approach with the help of an illustration.
Illustration 5: Alpine Limited and Boston Limited are similar except for their capital structures. Alpine Limited has 50 percent of debt and 50 percent of equity, whereas Boston Limited has 20 per cent of debt and 80 per cent of equity in terms of market value measures. The borrowing rate for both the entities is 8 percent in a zero-tax environment, and the capital markets are assumed to be perfect.
If Mr. Ram owns 2 per cent shares in Alpine Limited, then what is his return when the company’s net operating income is given to be ₹7,20,000 and the overall capitalisation rate of the company is 18 per cent? Also, what is the implied required rate of return on equity? Similarly, Boston Limited has the same net operating income as that of Alpine Limited. What would be the implied required equity return of Boston Limited? Why does it differ from that of Alpine Limited?
Solution:
Value of the Alpine Limited = 7,20,000
0.18 o
NOI
K = = ₹40,00,000
| Return on Shares on Alpine Limited | Amount (₹) |
|---|---|
| Value of the company | 40,00,000 |
| Market value of debt (50%) | 20,00,000 |
| Market value of shares (50%) | 20,00,000 |
| Net operating income | 7,20,000 |
| Interest on debt (8% × ₹20,00,000) | 1,60,000 |
| Earnings available to shareholders | 5,60,000 |
| Return on 2% shares (2% × ₹5,60,000) | 11,200 |
| Implied required rate of return on equity | = 5,60,000 ÷ 20,00,000 = 28% |
| Return on Shares on Boston Limited | Amount (₹) |
|---|---|
| Value of the company | 40,00,000 |
| Market value of debt (20%) | 8,00,000 |
| Market value of shares (80%) | 32,00,000 |
| Net operating income | 7,20,000 |
| Interest on debt (8% × ₹8,00,000) | 64,000 |
| Earnings available to shareholders | 6,56,000 |
| Implied required rate of return on equity | = 6,56,000 ÷ 32,00,000 = 20.50% |
The implied required rate of return on equity of Boston Limited is lower than the Alpine Limited because Boston Limited uses less debt in its capital structure. When we use the NOI approach, the equity capitalisation is a linear function of the debt-equity ratio; and the decrease in required return on equity is offset by the practice of not employing much funds in the debt capital. Conversely, the cost of equity represented by Ke increases with increase in the degree of financial leverage.
Traditional Approach
The traditional approach states that the cost of capital is dependent upon the capital structure of a firm. This approach also entails that there exists an optimal capital structure which minimises the firm’s cost of capital. According to the NOI approach, the capital structure decisions are completely irrelevant. Although the MM approach supports the NOI approach, it provides a behavioural justification. The traditional approach strikes to create a balance between these two theories.
According to the traditional approach, the value of the firm increases with a simultaneous increase in the financial leverage up to a certain point. However, beyond such point, the increase in the debt component will increase the firm’s overall cost of capital and thus the value of the firm shall decrease. This is so because when the financial leverage increases beyond a certain acceptable limit, the risk of debt investors can also increase and resultantly the cost of debt also starts increasing.
Therefore, the increasing cost of equity due to increased financial risk factor and simultaneously increasing cost of debt lead to an overall increase in the firm’s cost of capital. The traditional approach holds that the firm must try to reach the optimal capital structure through a judicious mix of both debt and equity in its capital structure. At the point of the optimal capital structure, the firm’s overall cost of capital shall be minimum and the total value of the firm shall be maximum.
Modigliani-Miller (M&M) Approach
The NOI approach is definitional and it lacks behavioural conception. It fails to offer operational justification for the irrelevance concept of the firm’s capital structure. The Modigliani-Miller (MM) approach seeks to provide a justification for the constant overall cost of capital and the total value of the firm.
The M&M approach is based on the following assumptions:
- Information is available to all free of cost.
- The same information is available for all present and prospective investors.
- The shares/securities are infinitely divisible.
- The present and prospective investors are free to buy or sell securities.
- There is no transactions cost.
- There are no bankruptcy costs.
- The investors can borrow without restriction on the same terms on which a firm can borrow.
- Dividend pay-out ratio is 100%.
The M&M approach without tax:
This approach is based on the assumptions that investors are rational and there is a perfect capital market having no transactions costs and no taxes. The value of the firm and its overall cost of capital remain unchanged irrespective of any deviations in the capital structure.
This approach holds the following propositions:
- The market value of the firm is equal to the expected NOI divided by the discount rate appropriate to the firm’s risk class.
Value of levered firm (Vg ) Value of unleve u red firm (Vu )
Net Operating Income (NOI) Value of a firm Ko - A firm with the debt capital is likely to have a higher cost of equity as compared to an unlevered firm. The cost of equity in a levered firm is given as follows:
Ke = Ko + (Ko – Kd) Debt Equity - The capital structure (or financial leverage) does not impact the firm’s overall cost of capital. It is only impacted by the business risk.
This theory assumes that the value of the levered firm can neither be greater nor lower than that of an unlevered firm, i.e., the two must be equal. Using debt in the capital structure of a firm neither offers any advantage nor a disadvantage. Thus, the total value of the firm and the overall average cost of capital remains the same, regardless of how the capital structure of a firm is divided (among debt, equity, etc.).
MM Approach With Tax
Due to the imperfections in the capital market, existence of transaction costs and the presence of corporate income taxes, the MM model was amended by incorporating tax. It was stated that the value of the firm shall increase and the overall cost of capital shall decline when corporate taxes exist. It recognises that there are differences in the earnings of equity shareholders and debt-investors in a levered and an unlevered firm. The value of the levered firm shall be higher than the value of theunlevered firm by an amount of debt multiplied by tax rate.
The following formulae are provided under the M&M approach with taxes:
- Value of levered firm (Vg ) = Value of unlevered firm (Vu) + Tax benefits
- Cost of equity in a levered company (Keg) = (Keu – Kd)
Debt Debt Equity
Where,
Keg = Cost of equity in a levered company
Keu = cost of equity in an unlevered company
Kd = Cost of debt
T = Tax rate - WACC in a levered company (Kog) = Keu (1 -tL)
Where,
Keu = Cost of equity in an unlevered company
T= tax rate
L = Debt Debt equity
Illustration: ABC ltd. and DEF ltd. are two companies having same business risk. Following data is available in respect of both companies.
Capital employed = ₹2,00,000
EBIT = ₹30,000
Ke = 12.5%
| Sources | Levered Company (₹) | Unlevered Company (₹) |
|---|---|---|
| Debt (@10%) | 1,00,000 | Nil |
| Equity | 1,00,000 | 2,00,000 |
Investor is holding 15% shares in levered company.
Calculate increase in annual earnings of investor if investor switches his holding from levered to unlevered company.
Solution:
Valuation of firms
| Particulars | Levered Firm (₹) | Unlevered Firm (₹) |
|---|---|---|
| EBIT | 30,000 | 30,000 |
| Less: interest | 10,000 | Nil |
| Earnings available to Equity Shareholder/Ke | 20,000 | 30,000 |
| 12.5% | 12.5% | |
| Value of Equity | 1,60,000 | 2,40,000 |
| Debt | 1,00,000 | Nil |
| Value of Firm | 2,60,000 | 2,40,000 |
The value of a levered company exceeds the value of an unlevered company. As a result, the investor will sell his shares in the leveraged firm and purchase shares in the unlevered company. To maintain the risk level, he will borrow a corresponding amount and invest it in unlevered firm shares.
Investment & Borrowings
| Sell shares in Levered company (1,60,000 × 15%) | 24,000 |
| Borrow money (1,00,000 ×15%) | 15,000 |
| Buy shares in Unlevered company | 39,000 |
Change in Return
| Income from shares in Unlevered company (39,000 × 12.5%) | 4,875 |
| Less: interest on loan (15,000 × 10%) | 1,500 |
| Net Income from unlevered firm | 3,375 |
| Income from Levered firm (24,000 × 12.5%) | 3,000 |
| Incremental Income due to arbitrage | 375 |
