That there are no transactions costs or taxes, so that the value of the firm is unaffected by its capital structure (in other words, Moaning-Miller Proposition 1 is assumed to be valid) that there is a known anachronistic risk- tree rate of interest. That there are homogeneous expectations about the stochastic process that describes the value of the firm’s assets, Algebraically we eave the sum of The Value tot the firm V plus a put option P equal to the sum of shareholder’s equity S plus Bondholder’s equity B rearranged to: we can see in that equation that the value of the trim consists of the difference of default-free debt and a put option, following the risky corporate debt is the same thing.
The exercise price of the put is the value of debt D and the maturity of the put T is equal to the maturity of the risky debt. Poor the shareholder’s equity follows: Stakeholders Positions Shareholders’ Position: Call Option, S 10 V-D Bondholders’ Position: Default-free bond, B ID ID I -(D-V) 10 Minus a put option, P Value Of the firm at maturity I V V The table shows stakeholders’ payoffs in the case that the value Of the firm is lower or equal to the value of debt and the case that it is higher. We are interested in the connection between the CAMP measure of risk ; and the option pricing model. First, we want to know how the CAMP and the MOM are linked to each other.
The definition of Morton says: E(RI)- the instantaneous expected rate of return on asset l, Pi- the instantaneous systematic risk of the Tit asset , E(arm)- the expected instantaneous rate of return on market portfolio, art- the masochistic instantaneous rate of return on the risk-free asset, The partial derivate tooth equerry value S with respect to the value of the asset is: for NO-? the cumulative normal probability of the unit normal variant ODL and finally: we know that that result confirms all other theories of finance. The beta of equity of the Veered firm Inverness monotonically with leverage. The systematic risk of equity falls When the market value of the firm increased also when the debt increases the value of the equity option increases and the systematic risk decreases when the risk-free rate Of return increases. He variance of the value of the firm’s asset increases, the systematic risk of equity decreases.
And last, the the systematic risk Of equity declines as the maturity date Of the debt becomes longer and longer. If we substitute ;s in the definition for KS of the CAMP we obtain: to devolve the WAC from that equation, we multiply the cost of debt, by the percentage of debt in the capital structure, then add this result to the cost of equity, multiplied by the cost the percentage of equity in the capital structure. We maintain: and later this is exactly the same result as the M-M definition of the cost of equity capital n a world without taxes. We assume, that the CAMP, M-M and MOM are all consistent with each other, THE MATURITY STRUCTURE OF DEBT The optimal structure of capital depends also on the maturity structure of debt.
And there is also the question on how to separate between short and long-term debt. Should the firm use Varian or faced debt rate is another question. Morris suggested that short-term debt or variable debt reduce the risk for shareholders and increase equity value of the covariance between net operating income and expected future interest rates is positive, because he assumes that unexpected hanged in interest rates are a priced factor in the arbitrage pricing model and there is no direct connection to bankruptcy costs or to interest tax shield. The argument of cross hedging is useful venue it allows a greater gain from leverage and reduces the risk of bankruptcy.
Myers and Barnes, Hagen and Senses argue that if the shareholder’s claim is similar to a call option interest to handle riskier, because their call option value is higher. If a firm with long-term debt undertakes positive net value projects, shareholders are not able to get the full benefits, because a value goes to the debt holders. Short-term firms avoid this problem, because the debt is due before the firm can invest. Brick and Rapid provide a tax-based explanation. Suppose the term structure of interest rates is not flat and there is a income in the meaning of miller. A long-term maturity is optimal, because coupons on long-term bonds are higher at the moment and the benefit of tax is accelerated, but is valid for positive gain of leverage. But none of them has been tested before.
THE EFFECT OF OTHER FINANCIAL INSTRUMENTS ON THE COST OF CAPITAL Fame and Jensen tried to explain why firms are willing to have two separated rots of financial claims. They confirm that it makes sense to have a relatively low-risk component ( i. E. Debt capital) and a relatively high-risk residual claim (i. E. Equity capital), because that ” reduces contracting costs (i. E. the costs that would be incurred to antidemocratic fulfillment)” and fit lowers the cost of risk-bearing *Vices” shareholder and bondholders do not have to watch each other, it is sufficient if the bondholders watch the shareholders. That example reduces total costs of contracting. Another Pont is that a firm keeps the capital structure simple by using debt and equity.
WARRANTS warrant is a security given by the firm in return cash, therefore it is very similar to an American call option. The problem Of warrants has been studied by Emanuel Schwartz, Schwartz, gala and Schneider, and contraindications. The simplest approach to the problem is assumed to baa a one-period-model. The firm is 100% financed and its investment policy is not depending on the financing decisions. Gala and Schneider show, that for the assumptions of proceeds from issuing warrants are immediately distributed as dividends , and the warrants are assumed to be exercises as a block, the returns on a warrant are depending with hose of a call option in the same firm without warrants.
The price of share is defined by: X-the exercise price of warrant the ratio of warrants to share outstanding n- the current number of shares outstanding V-? the value of the fair-en’s assets (without warrants) at the end of the time period End-of-period Payoffs Warrant on the firm with warrants, W 10 1 Call on the firm without variants, C I O S-X I Nix is the cash receives and is the total number of shares sustaining. The warrants are exercised when their value is greater than the exercise price if: this condition is equal to S>X. The returns on the warrant and the call are perfectly correlated, they will have exactly the same systematic risk and therefore the same required rate Of return. Return is the cost of capital before the tax for warrants and is determined easily for a company that is focused on a new warrant. With that approach we have the problem that a warrant is not forced to be exercised in one block. Emanuel demonstrated that if all warrants are held by one single profit-based monopolist, the warrants would be excised frequently.
Constantine has solved the warrant valuation problem for competitive warrant holders and showed that the arrant privet is given a competitive equilibrium, lower or the same value it would have been exercised in one block. CONVERTIBLE BONDS convertible bond allows the hearer to change it for another share of stock at any time. A convertible bond is EULA to a portfolio of two securities: straight debt with the same coupon rate and maturity as convertible bond, and a warrant written on the value tot the firm. The coupon rate is normally lower than the comparable straight debt or convertible bonds. Brigham received responses from financial officers that 22 firms issued convertible debt and 68% percent of them had used invertible debt, because they thought that their stock price would rise higher than the existing market.
The other 37% said that thy wanted a straight debt, but they couldn’t be sold at a reasonable rate of interest, But convertible bonds are no cheap debt, because they are riskier and their true cost of capital is higher than the straight cost of debt. Brenna and Schwartz and Engineers have analyzed valuation of convertible bonds, assumed that the whole outstanding issue will be converted as a block. Constantine has extended that theory to know the value of convertible debt of conversion does not happen at one time. The derivations show that the market value Of convertible debt C.V. is equal to the market value Of straight debt B and a warrant W is: and the before cost of capital is: if the convertible bond is issued as WAC.