Dada Adefolami

By Dada Adefolami

Debt is an amount owed for funds borrowed. The lender agrees to lend funds to the borrower upon a promise by the borrower to pay interest on the debt, usually with the interest to be paid at regular intervals.

Equity financing often means issuing additional shares of common stock to an investor. With more shares of common stock issued and outstanding, the previous stockholders’ percentage of ownership decreases.

Debt financing means borrowing money and not giving up ownership. Debt financing often comes with strict conditions or covenants in addition to having to pay interest and principal at specified dates. Failure to meet the debt requirements will result in severe consequences. In the U.S. the interest on debt is a deductible expense when computing taxable income. This means that the effective interest cost is less than the stated interest if the company is profitable. Adding too much debt will increase the company’s future cost of borrowing money and it adds risk for the company.

A person or business acquires debt in order to use the funds for operating needs or capital purchases. In a business, debt may also be used as the source of funds for buying back shares in the business or to acquire another organization.

Debt may be secured by an entity’s other assets, which will become the lender’s property if the entity cannot pay back the debt. Alternatively, the debt may be unsecured. Debt may also be guaranteed by a third party, such as an owner or a corporate parent.

When borrow money to purchase valuable asset e.g. a car, a house, or some other, we enter into a forward contract to purchase from the lender, when the loan matures, the asset concerned for the face value of the debt. If the asset has risen in value above the amount we owe at the maturity of the loan, then we keep that surplus value; if not we must make good the difference. This is exactly the position of the owner of a firm who has unlimited liability for the debts of their business. With limited liability, however, the shareholders are not liable for their firm’s debts in the event of default. If, when the loan matures, the values of the assets are greater than the value of the firm’s debts, then the equity shareholders are entitled to the difference. If the value of the assets falls below the value of the firm’s debts, the firm can liquidate the business and walk away. Therefore, the price a firm pays for its shares in the company represents the premium on a call option written by the lenders on the underlying assets of the business 

In practice, of course, complexities arise. Lenders do not collect their premium directly. They might do it by means of a zero coupon bond i.e. the amount they lend is lower than the amount to be repaid, but no interest is charged. More often they do it by charging interest which includes a premium to cover the risk that the business will default and leave them with assets worth less than the value of the loan. However, none of these complexities undermine the logic of the argument that we should value equity as a derivative.

VALUATION VARIABLES
Black, Scholes and Merton taught that the premium on a call or put option is defined by five variables below:
1. the value of the underlying asset
2. its volatility
3. the exercise price
4. the time to settlement
5. the risk free rate of interest. 

Where the assets of a firm are actively traded and easily liquidated then their current market value should be used. For example, in April 2008, let say the assets of XYZ a Nigeria mortgage bank were shown at fair value of N113.2bn. In the case of a bank, the majority of its assets are actively traded and hence the fair value in the balance sheet will represent their economic value. In the case of other companies, value in use will normally be based on the present value of the future cash flows that the firm’s assets are expected to generate over their useful lives.

The volatility of assets is probably the most difficult variable to estimate accurately. One approach implies the asset value and the volatility from the BSM model. Another approach is to project and simulate the expected future cash flows of the business, generating a distribution of present values from which the volatility can be obtained.
The applications of the BSM model to the problem of valuation, the firm was assumed to have issued debt in the form of a single, zero coupon bonds. In practice, firms issue debt of all sorts – some variable term, some fixed interest, some with convertibility. The simplest approach to identifying the effective exercise price is to go through the following steps:

1. Estimate the average term to maturity of the company’s outstanding long-term debt.
2. Estimate the average coupon rate of interest paid on the debt.
3. Using the current yield on the company’s debt this could be the quoted rate on any variable debt in issue or that given for the company’s credit rating), estimate the market value of a notional N100 bond.
4. Estimate the repayment value of an equivalent bond where no interest is paid.

Under IFRS, the company’s debt may be shown at fair value and so steps 2 and 3 are not required.

EXAMPLE 1
A company has N100 of debt in issue carrying 5% interest and with five years to maturity. The company’s current cost of debt capital is 8%.
The market value of the debt is estimated as follows:
 
The repayment value on a zero coupon bond of the same current market value is calculated by finding the unknown future value which, when discounted at 8% over five years, gives a present value of N88.
             FV 
N88 = 1.08
Therefore
FV = N88*1.08 = N129

Thus N129 would be the redemption value of a zero coupon bond of the same value as the debt currently in issue.

Alternative approach is to use the redemption value as quoted in the accounts but use the duration of the debt in place of the term to maturity. This should give comparable results to the method shown above.

BRINGING IT ALL TOGETHER
Let assume that we have achieved good estimates of the input variables – the next task is to bring it all together in the BSM model. The model has a number of assumptions that restrict its application, but for our purposes it demonstrates the problem of corporate valuation quite nicely. To illustrate, a very interesting application of this approach occurred with respect to the value of the previously mentioned, distressed Nigeria bank.In April 2008, the company reported assets and liabilities at fair value of N113.2bn and N110.7bn respectively. The average term to maturity on the bank’s liabilities was approximately 100 trading days. This is not unusual for a bank whose liabilities are in the form of short-term money market borrowing and deposits. At that point, the risk free rate of interest was 3.5%.

The logic of option pricing is that the value of an option rises with the level of risk, and that this is particularly the case when the option is near the money, i.e. when its level of gearing approaches 100%. Taking two test values, of 5% and 10%, for the volatility of the bank’s assets, the BSM model gives the following valuation:

 The share price of the bank in April 2008 was around N9.50 per share based on 495.6m shares in issue. Now let see what happens to the valuation if the asset value falls to N110.7bn. On the balance sheet the value of the firm’s equity should be zero. However, the BSM model gives a quite different result. At a volatility of 5%, the equity is still worth N2.29bn or N4.62 per share – almost exactly its value in October 2008.At this point the information coming from the company suggested that its assets had shrunk in value as the bank’s mortgage book was written down in line with falling house prices and potential defaults. Below we can see how the value of the bank’s equity is predicted to change with changing asset value.