WACC Based on Book Value

WACC Based on Book Value

Values฀for฀the฀percentage฀returns฀for฀each฀source฀can฀be฀determined฀from฀their฀book฀or฀market฀values.฀ The฀following฀example฀illustrates฀the฀calculation฀of฀the฀WACC฀based฀on฀book฀value.

Example 9.1:฀ The฀Turnbull฀Corporation’s฀capital฀structure฀is฀composed฀of฀40฀percent฀debt,฀5฀percent฀pre- ferred฀stock,฀and฀55฀percent฀common฀equity.฀ABC฀needs฀to฀raise฀$1฀million฀to฀buy฀a฀small฀office฀building.

The฀effective฀or฀after-tax฀rate฀of฀interest฀ABC฀pays฀on฀its฀long-term฀debt฀is฀8฀percent,฀and฀its฀preferred฀ stockholders฀receive฀a฀rate฀of฀return฀of฀10฀percent.฀Alternate฀investments฀that฀are฀available฀to฀shareholders฀with฀ equal฀risks฀have฀rates฀of฀return฀of฀13฀percent.฀What฀would฀be฀ABC’s฀cost฀of฀capital฀if฀it฀wishes฀to฀retain฀the฀same฀ relative฀amounts฀of฀debt,฀preferred฀stock,฀and฀common฀stock฀in฀its฀capital฀structure?

Solution:฀ Figure฀9-3฀is฀a฀spreadsheet฀solution.฀Key฀cell฀entries฀are฀shown฀at฀the฀bottom฀of฀the฀spreadsheet.

The values entered in Cells B4:B6 are the relative amounts in the firm’s capital structure that the firm wishes฀to฀maintain.฀The฀total฀amount฀of฀capital฀to฀be฀raised฀is฀entered฀as฀data฀in฀Cell฀C7.฀The฀amounts฀to฀be฀ raised฀from฀each฀source฀are฀calculated฀by฀entering฀=B4*$C$7฀in฀Cell฀C4฀and฀copying฀it฀to฀Cells฀C5:C6.

The฀rates฀of฀interest฀to฀be฀paid฀are฀entered฀as฀data฀in฀Cells฀D4:D6.฀The฀after-tax฀costs฀for฀the฀various฀sources฀ are฀calculated฀by฀entering฀=C4*D4฀in฀Cells฀E4฀and฀copying฀the฀entry฀to฀Cells฀E5:E6.฀The฀total฀after-tax฀cost฀ for฀all฀sources฀is฀calculated฀in฀Cell฀E7฀by฀the฀entry฀=SUM(E4:E6).

The฀value฀10.6฀percent฀for฀the฀WACC฀is฀calculated฀in฀Cell฀D7฀by฀the฀entry฀=E7/C7.฀The฀investment฀ must฀earn฀a฀rate฀of฀return฀of฀at฀least฀10.6฀percent฀in฀order฀to฀provide฀each฀source฀of฀funds฀with฀its฀required฀ rate of return. If the investment earns less than 10.6 percent, the common stockholders will receive less than 13฀percent.฀On฀the฀other฀hand,฀if฀the฀investment฀earns฀more฀than฀10.6฀percent,฀the฀sum฀available฀to฀common฀ equity฀(i.e.,฀dividends฀on฀common฀stock฀plus฀retained฀earnings)฀will฀be฀more฀than฀13฀percent.฀In฀other฀words,฀ the฀WACC฀of฀10.6฀percent฀is฀the฀minimum฀acceptable฀rate฀of฀return฀that฀satisfies฀the฀requirements฀of฀three฀ fund sources.

(Continued)

Cost of Capital ❧ 297

Figure฀9-3

Weighted Average Cost of Capital Based on Book Value

1 Example 9.1: TURNBULL CORP., COST OF CAPITAL BASED ON BOOK VALUE

2 Cost of Financing

Amount to be

Required Rate to

After-Tax Cost 4 Debt (i.e, Borrowing)

3 Source of Funds

Capital Structure

Obtained

Pay

36,000 5 Preferred Stock

5,000 6 Common Stock

9 Book-Value WACC

Key cell entries:

C4: =B4*$C$7, copy to C4:C5 E4: =C4*D4, copy to E5:E6 E7: =SUM(E4:E6) D7: =E7/C7

The฀same฀result฀is฀obtained฀if฀the฀weighted฀average฀cost฀of฀capital฀is฀calculated฀by฀the฀following฀equa-

tion:

(9.1) where the ws are the weights or relative amounts of each source of capital and the ks are the rates of return for

WACC = w debt debt k + w preferred preferred k + w commo n n common k ฀

each source of capital. Thus, using the values for Example 9.1, WACC = (. 0 45 0 08 × .)(. + 0 05 0 10 × .)(. + 0 50 0 13 × .) = . 0 1106 10 6 =.%

If฀the฀required฀rate฀for฀common฀stock฀equity฀is฀raised฀to฀16฀percent฀to฀compensate฀for฀increased฀risk,฀the฀ minimum฀acceptable฀rate฀of฀return฀for฀the฀investment฀is฀calculated฀as

WACC = (. 0 45 0 08 × .)(. + 0 05 0 10 × .)(. + 0 50 0 16 × .) = . 0 1121 12 1 =.%

Example 9.2:฀ Given฀ an฀ 8฀ percent฀ cost฀ of฀ borrowing฀ and฀ a฀ return฀ of฀ 10฀ percent฀ on฀ preferred฀ stock,฀ as฀ in฀ Example฀9.1,฀what฀would฀be฀the฀return฀on฀common฀stock฀for฀a฀WACC฀of฀10฀percent?

Solution:฀ Figure฀9-4฀is฀a฀spreadsheet฀solution฀obtained฀with฀Excel’s฀Goal฀Seek฀tool.฀The฀spreadsheet฀setup฀is฀ the฀same฀as฀in฀Example฀9.3.฀Begin฀by฀saving฀the฀spreadsheet฀of฀฀Figure฀9-3฀and฀copying฀it฀to฀a฀new฀worksheet.฀ Then,฀use฀Excel’s฀Goal฀Seek฀tool฀with฀the฀settings฀shown฀in฀฀Figure฀9-5.฀฀Figure฀9-5฀shows฀that฀Cell฀D5฀is฀to฀ be฀changed฀to฀whatever฀value฀is฀needed฀to฀achieve฀a฀value฀of฀10฀percent฀for฀the฀WACC฀in฀Cell฀D6.฀The฀result฀ in฀Figure฀9-4฀shows฀that฀the฀return฀on฀common฀stock฀would฀be฀11.8฀percent.

(Continued)

298 ❧ Corporate Financial Analysis with Microsoft Excel ®

Figure฀9-4

Return on Common Stock for a WACC of 10%

1 Example 9.2: ABC CORPORATION, COST OF CAPITAL BASED ON BOOK VALUE

Amount to be

Required Rate to

2 Source of Funds

After-Tax Cost 3 Debt (i.e., Borrowing)

Capital Structure

Obtained

Pay

36,000 4 Preferred Stock

5,000 5 Common Stock

100,000 7 Goal Seek Settings: Target cell is D6, to be set equal to 10%.

8 Changing cell is D5.

Return on Common Stock

for a WACC of 10.0%

Figure฀9-5

“Goal Seek” Dialog Box with Settings for Example 9.2

Excel฀provides฀another฀tool฀called฀Solver฀that฀can฀be฀used฀to฀solve฀Example฀9.2.฀It฀is฀shown฀in฀Figure฀9-6฀ with฀the฀settings฀to฀solve฀Example฀9.2.฀The฀result฀with฀Solver฀is฀the฀same฀as฀with฀Goal฀Seek฀for฀this฀problem.

Figure฀9-6

“Solver Parameters” Dialog Box with Settings for Example 9.2

(Continued)

Cost of Capital ❧ 299

The฀same฀result฀is฀obtained฀inserting฀known฀values฀in฀equation฀9.1,฀rearranging฀to฀the฀following฀form,฀and฀ solving:

k common =

Should฀You฀Choose฀Goal฀Seek฀or฀Solver? The฀Goal฀Seek฀and฀Solver฀tools฀can฀be฀used฀interchangeably฀to฀solve฀many฀problems฀that฀involve฀setting฀a฀target฀

cell฀equal฀to฀a฀specified฀value฀by฀changing฀the฀value฀of฀one฀other฀cell.฀The฀advantage฀of฀Goal฀Seek฀is฀that฀it฀is฀ simpler to explain and use. Solver, however, is a much more powerful and versatile tool. We will demonstrate some of Solver’s uses in later chapters.

Both tools use an iterative procedure of successive approximations. The first iteration of Goal Seek uses a trial value for the changing cell to calculate the value of the target cell. The calculated value of the target cell is compared฀with฀its฀targeted฀value.฀If฀the฀difference฀is฀greater฀than฀a฀specified฀amount฀(i.e.,฀the฀default฀precision),฀ Goal Seek adjusts the trial value and makes a new calculation of the target cell. A second comparison and adjust- ment are made, and this is repeated until the calculated and targeted values of the target cell agree within the specified฀amount.฀In฀most฀cases,฀the฀result฀with฀Goal฀Seek฀is฀sufficiently฀precise฀for฀the฀purpose฀of฀a฀problem.

The฀default฀level฀for฀Solver฀is฀tighter฀than฀for฀Goal฀Seek.฀Solver’s฀results฀can฀therefore฀be฀more฀accurate฀for฀ problems฀that฀are฀more฀complex฀than฀Example฀9.2.฀In฀addition,฀Solver฀can฀find฀the฀conditions฀for฀maximizing฀ or฀minimizing฀the฀value฀of฀a฀target฀cell฀as฀well฀as฀setting฀it฀to฀a฀specified฀value.฀Solver฀also฀makes฀it฀possible฀to฀ have more than one changing cell and to add constraints that limit the values that the changing cells can take. These฀features฀of฀Solver฀will฀be฀demonstrated฀in฀later฀chapters.

In comparison to Solver, Goal Seek is a limited tool. Solver can do everything Goal Seek can, as well as do more,฀and฀do฀it฀better.฀Once฀you฀understand฀how฀to฀use฀Solver,฀it฀should฀become฀your฀tool฀of฀preference.

Example 9.3:฀ Given฀ the฀ starting฀ conditions฀ of฀ Example฀ 9.1,฀ prepare฀ a฀ table฀ and฀ chart฀ that฀ show฀ how฀ the฀ WACC฀varies฀with฀borrowing฀rates฀from฀6฀to฀8฀percent฀(in฀increments฀of฀0.5%)฀and฀required฀rates฀of฀return฀for฀ common฀stockholders฀from฀10฀to฀16฀percent฀(in฀increments฀of฀2%).

Solution:฀ Figure฀9-7฀provides฀a฀two-variable฀input฀table฀and฀a฀chart฀that฀show฀how฀the฀value฀of฀WACC฀varies฀ with฀different฀combinations฀of฀borrowing฀rates฀and฀rates฀of฀return฀on฀common฀stock.

Figure฀9-7฀can฀be฀created฀as฀an฀addition฀to฀the฀spreadsheet฀of฀Figure฀9-3฀or฀a฀copy฀of฀it.฀Enter฀values฀for฀ the฀required฀rates฀of฀return฀to฀common฀stockholders฀in฀Cells฀B11:E11฀and฀values฀for฀the฀borrowing฀rates฀in฀ Cells฀A12:A16.฀Next,฀enter฀=D7฀in฀Cell฀A11.฀In฀order฀to฀avoid฀confusion,฀hide฀the฀entry฀in฀Cell฀A11฀by฀custom฀ formatting฀Cell฀A11฀as฀;;;.฀(Click฀on฀Cell฀A11,฀select฀Format/Cells/฀Number/Custom฀and฀type฀three฀semicolons฀ in฀the฀format฀box.)

Drag฀the฀mouse฀to฀select฀the฀Range฀A11:E16.฀Click฀on฀Data/Table฀to฀expose฀the฀dialog฀box฀shown฀in฀ Figure฀9-8,฀and฀enter฀D6฀for฀the฀row฀input฀cell฀and฀D4฀for฀the฀column฀input฀cell.฀Click฀on฀the฀OK฀button฀or฀ press฀Enter.฀The฀result฀will฀be฀the฀values฀shown฀in฀Cells฀B12:E16.฀

(Continued)

300 ❧ Corporate Financial Analysis with Microsoft Excel ®

Figure฀9-7

Effects of Borrowing Rate and Rate of Return for Common Stockholders on the Weighted Average Cost of Capital

Example 9.3: VARIATION OF WACC WITH CHANGES IN THE BORROWING RATE AND

1 RATE OF RETURN FOR COMMON STOCKHOLDERS

2 Cost of Financing

Amount to be

Required Rate to

After-Tax Cost 4 Debt (i.e., Borrowing)

3 Source of Funds

Capital Structure

Obtained

Pay

36,000 5 Preferred Stock

5,000 6 Common Stock

EFFECT OF BORROWING RATE AND RATE OF RETURN FOR COMMON STOCKHOLDERS ON

9 THE WEIGHTED AVERAGE COST OF CAPITAL

10 Borrowing Rate Required Rate of Return for Common Stockholders

20 CAPITAL STRUCTURE

5% Preferred Stock

RATES

23 alue)

50% Common Stock

29 30 AL (based on book v 10.5%

37 9.5% 38 GE COST OF CAPIT 39 40 VERA 41 9.0% 42 43 44

45 WEIGHTED A 8.5% 46 47 48

51 RATE OF RETURN FOR COMMON STOCKHOLDERS

(Continued)

Cost of Capital ❧ 301

Figure฀9-8

Dialog Box with Entries for Creating a Two-Variable Input Table

To฀ create฀ the฀ chart฀ shown฀ in฀ Figure฀ 9-7,฀ drag฀ the฀ mouse฀ cursor฀ to฀ select฀ Cells฀ B11:E16.฀ Select฀ the฀ XY-scatter฀type฀chart฀and฀identify฀the฀data฀as฀being฀in฀rows฀rather฀than฀columns,฀as฀shown฀in฀Figure฀9-9.

Figure฀9-9

Step 2 with Series in Rows Selected

Note฀that฀the฀values฀in฀the฀table฀and฀chart฀of฀Figure฀9-7฀are฀valid฀only฀for฀the฀capital฀structure฀and฀rate฀for฀ preferred฀stockholders฀shown฀in฀Cells฀B4:B6฀and฀D5.฀Changing฀the฀values฀in฀these฀cells฀causes฀the฀values฀in฀ the฀table฀and฀chart฀to฀change฀also.฀(Try฀it!)

302 ® ❧ Corporate Financial Analysis with Microsoft Excel