Component Costs

Component Costs

The previous discussion has assumed that the component costs of capital are given. This is not the real-life case. We discuss in this section how to calculate the costs of the components, which change from day-to- day.฀In฀fact,฀the฀component฀costs฀change฀continuously฀as฀the฀equity฀markets฀change.

Cost฀of฀Debt

The pre-tax฀cost฀of฀debt฀is฀the฀rate฀of฀return฀on฀the฀bonds฀issued฀to฀raise฀capital.฀It฀appears฀as฀the฀value฀k d in฀the฀following฀equation฀for฀the฀value฀of฀a฀bond:

where V B ฀ =฀ the฀value฀of฀a฀bond฀issued฀in฀return฀for฀borrowing N฀ =฀ the฀life฀of฀the฀bond Pmt฀ =฀ the฀periodic฀bond฀payment FV฀ =฀ the฀future฀value฀of฀the฀bond฀($1,000)

Equation฀9.2฀cannot฀be฀rewritten฀as฀an฀explicit฀function฀for฀k d .฀It฀can฀only฀be฀solved฀by฀an฀iterative฀ technique฀that฀uses฀known฀values฀for฀V D , Pmt, N, and FV and assumes different values for k d until the cal-

culated฀value฀of฀the฀right฀side฀of฀equation฀9.2฀equals฀the฀known฀value฀of฀the฀bond฀on฀the฀left.฀Fortunately,฀ this฀task฀can฀be฀either฀performed฀by฀using฀Excel’s฀Solver฀tool฀or฀avoided฀by฀using฀Excel’s฀RATE฀function.฀ The฀syntax฀for฀Excel’s฀RATE฀function฀is

RATE(number of periods, periodic payment, present value, future value, type, guess)

Adjustment for Income Tax

The฀payments฀to฀interest฀on฀a฀corporation’s฀debts฀are฀tax-deductible฀expenses.฀Therefore,฀the฀after-tax interest

304 ❧ Corporate Financial Analysis with Microsoft Excel ®

pre-tax฀value฀by฀1฀minus฀the฀tax฀rate.฀Thus,฀if฀the฀pre-tax฀cost฀of฀debt฀is฀$80฀on฀a฀$1000฀bond฀and฀the฀tax฀rate฀is฀ 40฀percent,฀the฀dollar฀after-tax฀cost฀of฀debt฀would฀be฀only฀$48฀(computed฀as฀$80X(1-0.40))฀and฀the฀percentage฀ after-tax฀cost฀of฀debt฀would฀be฀4.8฀percent฀(computed฀as฀$48/$1000).฀(Note฀that฀there฀is฀no฀tax฀adjustment฀for฀ preferred฀or฀common฀equity฀because฀dividends฀are฀not฀tax-deductible฀expenses฀for฀the฀company.)

Under฀present฀tax฀law,฀the฀costs฀related฀to฀the฀issuance฀of฀debt฀or฀equity฀securities฀are฀not฀tax฀deduct- ible.฀As฀such,฀the฀before-tax฀and฀after-tax฀costs฀of฀equity฀(preferred฀and฀common)฀securities฀are฀the฀same.฀ If฀some฀of฀the฀flotation฀costs฀were฀to฀become฀tax฀deductible,฀then฀the฀after-tax฀costs฀of฀equity฀would฀be฀ less฀than฀the฀before-tax฀costs.

Example 9.5:฀ The฀ chief฀ financial฀ officer฀ of฀ the฀ Monarch฀ Investment฀ Corporation฀ is฀ interested฀ in฀ buying฀ bonds฀as฀an฀investment฀of฀surplus฀cash.฀Some฀bonds฀that฀are฀available฀provide฀semiannual฀payments฀with฀an฀ annual coupon rate of 8 percent. Their redemption value is $1000, and they reach maturity in 15 years. The bonds฀are฀available฀at฀a฀price฀of฀$560.฀What฀would฀be฀Monarch’s฀after-tax฀rate฀of฀return฀on฀the฀bonds฀if฀they฀ were฀purchased฀at฀the฀current฀offering฀price?฀You฀may฀assume฀that฀Monarch’s฀tax฀rate฀is฀40฀percent.

Solution: Figure 9-11 is a spreadsheet showing two methods for determining the rate. The upper method uses฀the฀RATE฀function,฀and฀the฀lower฀method฀uses฀the฀formula฀given฀by฀the฀right฀side฀of฀equation฀9.2฀and฀ Solver. Solver changes the trial value entered in Cell B16 to the correct value to give the desired after-tax rate of฀return.฀Both฀methods฀give฀a฀pre-tax฀rate฀of฀return฀of฀7.86฀percent,฀which฀is฀converted฀to฀an฀after-tax฀rate฀of฀ return฀of฀4.71฀percent.

Figure฀9-11

Cost of Debt Borrowing

1 Example 9.5: RATE OF RETURN 2 Solution with RATE Function

3 Current Price of Bond

4 Coupon Rate

5 Redemption Value

6 Maturity, years

7 Frequency, payments/year

8 Before-Tax Rate of Return

9 Tax Rate

10 After-Tax Rate of Return

11 Key Cell Entries

12 B8: =RATE(B6*B7,B4*B5/B7,–B3,B5) 13 B10: =B8*(1–B9)

14 Alternate Solution with Formula 8.2 and Solver

15 Value

16 Before-Tax Rate of Return

17 After-Tax Rate of Return

18 Key Cell Entries

19 B15: =(B4*B5/2)*(1–1/((1+B16)^(B6*B7)))/B16 20 +B5/((1+B16)^(B6*B7)) 21 B16: Enter a trial value, which will be changed by Solver. 22 B17: =B16*(1–B9)

23 Solver Settings

24 Target Cell is B15, to be set equal to $560.

Cost of Capital ❧ 305

Cost฀of฀Preferred฀Equity The value of a share of preferred stock, V p ,฀is฀given฀by฀the฀equation

where D฀=฀the฀dollar฀dividend฀per฀share฀and and

k P ฀=฀the฀rate฀of฀return฀on฀the฀preferred฀stock Equation฀9.3฀can฀be฀rearranged฀to฀the฀following฀form฀for฀calculating฀the฀rate฀of฀return฀from฀known฀

values for V P and D:

Cost฀of฀Common฀Equity A฀company’s฀cost฀of฀common฀equity฀can฀be฀determined฀by฀either฀the฀dividend฀discount฀model฀or฀the฀

CAPM.

The Dividend Discount Model for Common Equity

This฀model฀uses฀the฀following฀equation฀to฀discount฀a฀stream฀of฀dividends฀(D) from common stock with a constant฀rate฀of฀growth฀(g)฀and฀rate฀of฀return฀(k CS )฀to฀the฀stock’s฀present฀value฀(V CS ):฀฀

(9.5) Rearrangement฀of฀equation฀9.5฀gives฀the฀rate฀of฀return฀for฀shareholders฀of฀common฀stock฀in฀terms฀

V CS =

k CS − g k CS − g ฀

of฀current฀market฀price฀of฀the฀stock,฀its฀current฀dividends,฀and฀its฀rate฀of฀growth;฀thus

In฀other฀words,฀the฀required฀rate฀of฀return฀on฀common฀stock฀equals฀the฀sum฀of฀the฀dividend฀yield฀plus฀ the rate of growth of the dividends.

Example 9.6:฀ The฀ common฀ stock฀ of฀ the฀ Argus฀ Corporation฀ sells฀ for฀ $50/share฀ and฀ provides฀ quarterly฀ divi- dends฀of฀$1.00.฀It฀is฀anticipated฀that฀the฀stock’s฀dividends฀will฀increase฀by฀an฀average฀of฀10฀percent฀per฀year฀for฀ the฀next฀five฀years.฀What฀is฀the฀stock’s฀value฀in฀terms฀of฀a฀rate฀of฀return?

Solution:฀ Substituting฀values฀into฀equation฀9.6฀gives

CS =

306 ❧ Corporate Financial Analysis with Microsoft Excel ®

The CAPM Model for Common Equity

The฀CAPM฀model฀uses฀the฀following฀equation฀to฀give฀the฀expected฀rate฀of฀return฀for฀a฀security฀(E(R i ))฀in฀ terms฀of฀the฀risk-free฀rate฀of฀interest฀(R f ),฀the฀market฀risk฀premium฀((R m –R f )),฀and฀the฀risk฀of฀the฀security฀

relative฀to฀a฀market฀portfolio฀( b i ):

ER () i = R f + β i ( R m − R f ) ฀

Example 9.7:฀ Use฀ the฀ CAPM฀ model฀ to฀ calculate฀ the฀ expected฀ rate฀ of฀ return฀ for฀ the฀ security฀ described฀ in฀ Example 9.5. You may assume that the risk-free rate of return is 4 percent, the return on a market portfolio is 12.5฀percent,฀and฀the฀beta฀value฀of฀the฀security฀is฀1.10.

Solution:฀ Inserting฀values฀into฀equation฀9.7฀gives

ER () i = . 0 04 1 10 0 125 0 04 + .(. − .) = . 0 04 0 0935 0 13335 13 35 + . = . =.%