corporate finance 7

7/25/2019 Corporate Finance 7

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7. THE COST OF CAPITALpart II

Chapter 5



When a firm borrows money at a stated rate of interest froma bank, determining the real cost rate of the debt is

relatively straightforward.

Because the interest paid on bank loans is a tax-deductibleexpense, the firm’s cost rate is less than the required rateof interest of the suppliers of debt capital.

The explanation is the same as in the case of bond credits.

2. Cost of Bank Loans



● Under the incidence of the taxes, the interests are deductiblefrom the taxable profit and the real load undertaken by the

company is smaller, that is if the debtor company is profitable,the interest that it will deliver each year to its lender will allowrealizing tax shield .

In this case:

The after-tax % cost of debt (real rate of cost) = nominal

interest rate * (1 – T)

T – Corporate income tax rate

● Observation: If the debtor company is not profitable, the realcost rate equals the nominal interest rate paid to the bank,

because in this case there are no tax savings.




●




Preferred stock represents a special type of ownership interest in thefirm. Preferred shareholders must receive their stated dividends prior

to the distribution of any earnings to common stockholders.Calculating the cost of preferred stock:

The cost of preferred stock is found by dividing the annual preferredstock dividend by the net proceeds from the sale of the preferred

stock.

The net proceeds represent the amount of money to be received net ofany flotation costs required to issue and sell the stock. For example,if a preferred stock is sold for $100 per share but $3 per share

flotation costs are incurred, the net proceeds from the sale are $97.

3. Cost of Preferred Stock




EXAMPLE:

The Zero Company is contemplating issuance of a 9 percent preferred

stock expected to sell for its $85 per share par value. The cost of issuingand selling the stock is expected to be $3 per share. The firm would liketo determine the cost of the stock.



Application

▪ The first step in finding this cost is to calculate the dollaramount of preferred dividends, since the dividend is

stated as a percentage of the stock’s $85 par value.▪ The annual dollar dividend is: $85 * 9% = $7,65.

▪ The net proceeds = $85 - $3 = $82 per share.

▪ So, the cost of the preferred stock is: $7,65 / $82 =9,33%.

Ex. The Beta Company issues 100 preferred shares of stock ata par value $90. The cost of issuing and selling the stock isexpected to be $4 per share. The annual rate of the preferred

dividend is 10%. The firm would like to determine the cost ofthe stock.




● Preferred stock is more expensive than debt because:

(1) preferred stockholders accept more risk than debtholders who have a claim senior to that of preferredstockholders and

(2) the cost of debt (interest) is tax deductible.



4. Cost of Common Stock

● The cost of common stock is not as easy to calculate asthe cost of debt or the cost of preferred stock.

● The difficulty arises from the definition of the cost, which isbased on the premise that the value of a share of stock in

a firm is determined by the present value of all future

dividends expected to be paid on the stock over an infinite

period of time.● The rate at which these expected dividends are

discounted to determine their present value represents

the cost of common stock .




Not all earnings are paid out as dividends, but it isexpected that earnings that are retained and reinvested will

boost future dividends. At infinity, a liquidating, or finaldividend is expected, which actually represents thedistribution of the firm’s assets.

Two techniques for measuring the cost of common stockequity capital are available.

A. One is the constant growth valuation method;

B. The other relies on the capital asset pricing model

(CAPM).




A. The constant growth valuation model

To value any security, we must determine the expected cashflows an investor will receive from owning it.

One-year investor

There are two potential sources of cash flows from owning astock.

First, the firm might pay out cash to its shareholders in the

form of a dividend.Second, the investor might generate cash by choosing to sell

the shares at some future date.

The total amount received in dividends and from selling thestock will depend on the investor’s investment horizon.



4. Cost of Common StockA. The constant growth valuation model

● When an investor buys a stock, he will pay the currentmarket price for a share, P

0 . While he continues to hold

the stock, he will be entitled to any dividends the stockpays.

● Let Div 1 be the total dividends paid per share of the

stock during the year. At the end of the year, the investor

will sell his share at the new market price P 1. Assumingfor simplicity that all dividends are paid at the end of theyear, we have the following timeline for this investment:





The future dividend payment and the stock price in thetimeline above are not known with certainty; rather, these

values are based on the investor’s expectations at the timethe stock is purchased.

Given these expectations, the investor will be willing topay a price today up to the point that this transaction has a

zero NPV – that is, up to the point at which the currentprice equals the present value of the expected futuredividend and sale price. Because these cash flows arerisky, we cannot discount them using the risk-free interestrate.





Instead, we must discount them based on the equity cost of

capital, r E , for the stock, which is the expected rate of return of

other investments available in the market with equivalent risk tothe firm’s shares. Doing so leads to the following equation for thestock price:

(1)

If the current market price were less than this amount, it wouldbe a positive NPV investment. We would therefore expectinvestors to rush in and buy it, driving up the stock’s price. If thestock price exceeded this amount, selling it would have apositive NPV and the stock price would quickly fall.





● Dividend Yields, Capital Gains, and Total Returns. We canreinterpret the equation (1) if we multiply by (1 + r

E), divide by

P0, and subtract 1 from both sides:

The first term on the right side of the equation is the stock’s dividend yield,which is the expected annual dividend of the stock divided by its current price.The dividend yield is the percentage return the investor expects to earn fromthe dividend paid by the stock.





The second term on the right side of the equation reflects thecapital gain the investor will earn on the stock, which is the

difference between the expected sale price and purchase pricefor the stock, P

1 – P

0 . We divide the capital gain by the current

stock price to express the capital gain as a percentage return,called the capital gain rate.

The sum of the dividend yield and the capital gain rate is calledthe total return of the stock.

The total return is the expected return that the investor will earn

for a one-year investment in the stock.





Thus, Eq. 2 states that the stock’s total return should equal the

equity cost of capital. In other words, the expected total return of

the stock should equal the expected return of the investmentsavailable in the market with equivalent risk.

This result is what we expected: the firm must pay itsshareholders a return commensurate with the return they canearn elsewhere while taking the same risk. If the stock offered ahigher return than other securities with the same risk, investorswould sell those other investments and buy the stock instead.



4. Cost of Common StockA. The constant growth valuation model

A multiyear investor

Eq. 1 depends upon the expected stock price in one year, P 1. But

suppose we planned to hold the stock for two years. Then wewould receive dividends in both year 1 and year 2 before sellingthe stock, as shown in the following timeline:

Setting the stock price equal to the present value of the future cash flows in thiscase implies:





● A multiyear investor

We suppose the investor sells the stock to another one-year

investor with the same beliefs. The new investor willexpect to receive the dividend and the stock price at theend of year 2, so he will be willing to pay

Substituting this expression for P 1 into Eq. 1, we get the same result as

in Eq. 3:





● We can continue this process for any number ofyears by replacing the final stock price with the value

that the new holder of the stock would be willing topay. Doing so leads to the general dividend-

discount model for the stock price, where thehorizon N is arbitrary:





● For the special case in which the firm eventually pays dividendsand is never acquired, it is possible to hold the shares forever .

Consequently, we can let N go to infinity in Eq. 4 and write it asfollows:

That is, the price of the stock is equal to the present value of the expectedfuture dividends it will pay .



Exercise

● An investor bought a share of stock for 4.5 lei in January 2008.The share of stock offered dividends in amount of 0.25 lei in

2008, 0.28lei in 2009, 0.25lei in 2010 and 0.3 lei in 2011. InNovember 2011 he sold the share for 4.6 lei.What was the real profitability from holding the share during thisperiod?

corporate finance 7

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