Chapter 17, Problem 1Q

a)

Summary Introduction

To determine: The definition of MM proposition 1 without taxes and with corporate taxes.

Explanation of Solution

The relationship between leverage and firm value is specified in MM Proposition I. Proposition I without taxes is $\text{V=}\frac{\text{EBIT}}{{\text{r}}_{\text{s}}\text{U}}$. As both earnings before interest and taxes and rsU are fixed, there is also consistent firm value, and meaningless is the capital structure. With taxes on corporates, Proposition I becomes $\text{V}={\text{V}}_{\text{u}}+\text{TD}$. Therefore, with leverage firm value rises, and the optimum capital structure is essentially whole debt.

b)

Summary Introduction

To determine: The definition of MM proposition II without taxes and with corporate taxes.

Explanation of Solution

The connection between leverage and equity costs is stated in MM Proposition II. Sans taxes, Proposition II is ${\text{r}}_{s\text{L}}={\text{r}}_{\text{sU}}+\left({\text{r}}_{\text{sU}}-{\text{r}}_{\text{d}}\right)\left(\frac{\text{D}}{\text{S}}\right)$. Therefore rs rises as the leverage rises in an accurate method. This rise is just enough to set off the enhanced application of lower-cost debt. When levying corporate taxes, Proposition II becomes ${\text{r}}_{\text{sL}}={\text{r}}_{\text{sU}}+\left({\text{r}}_{\text{sU}}-{\text{r}}_{\text{d}}\right)\left(1-\text{T}\right)\left(\frac{\text{D}}{\text{S}}\right)$ Here, the rise in equity costs is lower than the zero-tax case, and the growing application of lower-cost debt creates the company's capital cost to fall, and again, the optimal capital structure is virtual all the debt.

c)

Summary Introduction

To determine: The definition of miller model.

Explanation of Solution

The MM method brings in individual taxes. The impact of individual taxes is, in essence, to decrease the benefit of financing corporate debt.

d)

Summary Introduction

To determine: The definition of adjusted present value (APV) model.

Explanation of Solution

The balanced present-value demonstrates rebates anticipated free cash streams and interest-tax shields at the unlevered value taken a toll to reach an operational esteem. To induce the esteem of the complete company (both obligation and value) you add within the esteem of non-operating resources. Subtract the esteem of the obligation to urge the value esteem. This show is especially accommodating when the acquirer alters the capital structure of the company after the exchange since it values the intrigued charge shields and the firm's unlevered esteem separately.

e)

Summary Introduction

To determine: The definition of value of debt tax shield.

Explanation of Solution

The value of the shield of debt tax is the present value of the interest payments tax savings. In the tax model MM. this is just $\text{Interest}\times \frac{\text{Tax rate}}{\text{Discount rate}}=\frac{\text{iDT}}{\text{r}}$, and since i = r in the MM model, this is just TD. If a company is expanding and the discount rate is not r, then the value of this increasing tax shield is $\frac{{\text{rdTD}}_g}{\left(1+\text{rTS}\right)}$ where rd is the debt interest rate and rTS is the tax shield discount rate. The tax savings in the APV model are discounted at the unleveraged equity cost.

f)

Summary Introduction

To determine: The definition of equity as an option.

Explanation of Solution

In the event that a company has an extraordinary obligation, it can select to default in case the company isn't worth more than the obligation standard value. This choice to renege in the event that the firm's value is little is comparative to the choice not to work out a call option when the stock cost is low. If the administration (and so the stockholders) make the obligation installment, they will be able to keep the business. It permits value like a choice on the total firm's basic value, with a strike cost comparable to the debt's standard value. If D is the par value of the debt growing in one year and S is the value of the whole business  then the payout to the stockholder when the debt matures is: $\text{Payout}=\text{max}\left(\text{S}-D,0\right)$ This is the same payoff as with a strike, or exercise, price of D on S call option.