The Marginal Wacc Curve

The Marginal Wacc Curve

The฀supply฀of฀available฀new฀capital฀is฀not฀without฀limit.฀Therefore,฀as฀firms฀raise฀more฀and฀more฀new฀ money, the incremental cost of additional amounts increases. In addition, total flotation costs may increase as more capital is raised. This section interprets these increases in terms of a marginal WACC curve, which is simply a chart on which the cost of capital is plotted as the ordinate against the amount of capital฀to฀be฀raised.฀The฀following฀example฀illustrates฀the฀construction฀of฀a฀marginal฀WACC฀curve.

Example 9.9:฀ Assume฀that฀the฀Holdberg฀Corporation’s฀(see฀previous฀example)฀after-tax฀cost฀of฀raising฀capital฀ varies as follows for the amounts raised from the various sources:

Source of Capital

Amount Sold or Borrowed

Marginal After-Tax Cost

Debt฀Borrowing

Up฀to฀$200,000

More฀than฀$400,000

Preferred฀Stock

Up฀to฀$50,000

More฀than฀$100,000

Common฀Stock

Up฀to฀$250,000

More฀than฀$1,000,000

Prepare a chart that shows how the weighted average cost of capital varies with the amount of capital raised, from฀zero฀to฀$2฀million.฀If฀Holdberg฀must฀borrow฀$1฀million,฀what฀will฀its฀WACC฀be?฀If฀Holdberg฀must฀borrow฀

Cost of Capital ❧ 309

Solution: Figure 9-13 is a spreadsheet solution. Figure฀9-13

Marginal WACC Curve

Example 9.9: MARGINAL WEIGHTED AVERAGE COST OF CAPITAL CURVE FOR HOLDBERG 1 CORPORATION BASED ON MARKET VALUE WITH FLOTATION COSTS ADDED 2 Source

% of total

Level

After-Tax cost

Up to $200,000

5 More than $400,000

Up to $50,000

8 More than $100,000

Up to $250,000

12 More than $1,000,000

13 Total Capital

Cost of Debt

Cost of Preferred

Cost of Equity

32 MARGINAL WACC CURVE FOR HOLDBERG CORPORATION

41 13% 42 GE COST OF CAPIT

44 VERA 45 46 12% 47 48 11.24% 49 WEIGHTED A 50 11% 51 $0 52 53

56 TOTAL CAPITAL RAISED

310 ❧ Corporate Financial Analysis with Microsoft Excel ®

To transfer the percentages of total market value that were calculated in Cells E3:E5 of Example 9.8, make the following entries in Figure 9-13:

Cell

Entry

B3 =‘Figure฀9-12’!E3 B6 =‘Figure฀9-12’!E4 B9 =‘Figure฀9-12’!E5

To฀make฀these฀entries฀on฀Figure฀9-13,฀click฀on฀Cell฀B3฀on฀Figure฀9-13,฀enter฀=,฀click฀on฀the฀Sheet฀tab฀for฀ Figure฀9-12,฀click฀on฀Cell฀E3฀on฀Figure฀9-12,฀and฀press฀Enter.฀Repeat฀to฀transfer฀values฀for฀Cells฀B6฀and฀B9฀of฀ Figure 9-13 from Cells E4 and E5 of Figure 9-12.

The฀data฀values฀for฀the฀amounts฀sold฀or฀borrowed฀are฀entered฀in฀Cells฀C3:C12.฀For฀example,฀enter฀200000฀ in Cell C3, enter 400000 in Cell C4, etc. Custom format the cells to hide the data values and display the text shown in Figure 9-13. For example, the custom formats for the entries in Cells C9:C12 are as follows:

Cell

Custom Format

C9 “Up฀to฀“$#,###

“More฀than฀“$#,###

In place of the “$#,### parts of the custom formats, Excel inserts the data values entered in the cells. The฀break-even฀points—the฀amount฀of฀capital฀raised฀that฀causes฀after-tax฀cost฀to฀shift฀to฀the฀next฀higher฀ percentage—are฀calculated฀by฀entering฀=C3/B$3฀in฀Cell฀E3฀and฀copying฀the฀entry฀to฀E4:E5,฀by฀entering฀=C6/ B$6฀in฀Cell฀E6฀and฀copying฀the฀entry฀to฀E7:E8,฀and฀by฀entering฀=C9/B$9฀in฀Cell฀E9฀and฀copying฀the฀entry฀

to E10:E12. The฀ table฀ of฀ values฀ in฀ Rows฀ 13฀ to฀ 27฀ is฀ used฀ to฀ create฀ the฀ marginal฀ WACC฀ chart฀ at฀ the฀ bottom฀ of฀ Figure฀9-13.฀The฀table฀begins฀with฀the฀total฀capital฀equal฀to฀zero฀Cell฀A14.฀At฀this฀point฀the฀after-tax฀costs฀for฀the฀ three฀sources฀are฀at฀their฀minimum฀values฀(Cells฀B14:D14),฀and฀the฀value฀of฀WACC฀(Cell฀E14)฀is฀calculated฀ by฀the฀entry฀=$B$3*B14+$B$6*C14+$B$9*D14.

The฀values฀in฀Cells฀A15:A28฀are฀the฀break-points฀in฀Cells฀E3:E12฀sorted฀by฀increasing฀values.฀The฀final฀ value฀in฀Cell฀A29฀is฀set฀at฀a฀value฀greater฀than฀the฀last฀break-point.฀The฀value฀should฀be฀at฀least฀as฀large฀as฀the฀ last฀value฀on฀the฀chart฀to฀be฀plotted.

The costs for raising capital from each of the sources are discontinuous rather than continuous. They change฀from฀one฀value฀to฀a฀higher฀value฀as฀the฀amount฀of฀capital฀raised฀passes฀through฀each฀break-point.฀Up฀ to฀a฀break-point,฀they฀have฀one฀value.฀As฀a฀break-point฀is฀reached฀and฀exceeded฀(theoretically,฀by฀one฀penny),฀ they฀take฀on฀a฀higher฀value.฀Therefore,฀there฀are฀two฀values฀for฀the฀WACC฀at฀each฀break-point:฀one฀for฀capital฀ raised฀up฀to฀and฀including฀the฀break-point฀and฀another฀for฀capital฀raised฀that฀exceeds฀the฀break-point.฀The฀ WACC฀then฀continues฀unchanged฀until฀the฀next฀break-point฀is฀reached.

The฀first฀break-point฀is฀$340,556฀(Cell฀E9),฀at฀which฀the฀after-tax฀cost฀of฀common฀equity฀changes฀from฀ 12.50฀percent฀(Cell฀D9)฀to฀14.00฀percent฀(Cell฀D10).฀Copy฀the฀value฀in฀Cell฀E9฀to฀Cells฀A15:A16฀by฀entering฀ =E$9฀in฀Cell฀A15฀and฀copying฀the฀entry฀to฀Cell฀A16.฀Repeat฀this฀step฀to฀enter฀each฀successively฀higher฀break- point฀in฀Cells฀E3:E12฀twice฀in฀Cells฀A17:A28.฀In฀Cell฀A29,฀enter฀an฀arbitrary฀value฀larger฀than฀the฀highest฀ break-point฀for฀which฀values฀of฀WACC฀might฀be฀of฀interest.

(Continued)

Cost of Capital ❧ 311

To transfer the percentages for the after-tax costs, enter the following set of three IF statements in Cells B14,฀C14,฀and฀D14฀and฀copy฀them฀to฀the฀ranges฀B15:B28,฀C15:C28,฀and฀D15:D28,฀respectively:

Cell฀B14 =IF(A15*$B$3<=$C$3,$D$3,IF(A15*$B$3<=$C$4,$D$4,$D$5))฀ Cell฀C14

=IF(A15*$B$6<=$C$6,$D$6,IF(A15*$B$6<=$C$7,$D$7,$D$8)) Cell฀D14:฀

IF(A15*$B$9<=$C$9,$D$9,IF(A15*$B$9<=$C$10,$D$10,IF(A15*$B$9<=$C$11,$D$11,$D$12)))

Note in these entries that the row for values in the A column (e.g., Cell A15) is the row immediately below

the row in which the entry is made.฀(If฀you฀find฀it฀difficult฀to฀understand฀the฀logic฀of฀the฀IF฀statements,฀try฀ verbalizing฀them;฀try฀translating฀the฀expressions฀into฀words,฀using฀the฀meanings฀of฀the฀cells฀and฀terms฀in฀place฀ of฀the฀column฀and฀row฀identities.)

In฀Cell฀B29,฀enter฀=D5;฀in฀Cell฀C29,฀enter฀=D8;฀and฀in฀Cell฀D29,฀enter฀D12. To฀compute฀the฀WACCs,฀enter฀=$B$3*B14+$B$6*C14+$B$9*D14฀in฀Cell฀E14฀and฀copy฀the฀entry฀to฀

the฀Range฀E15:E29. To฀create฀the฀chart฀shown฀at฀the฀bottom฀of฀Figure฀9-13,฀select฀the฀Ranges฀A14:A29฀and฀E14:E29฀and฀plot฀ with฀a฀scatter฀type฀chart.฀Be฀sure฀to฀delete฀the฀check฀in฀the฀“Smoothed฀line”฀box฀on฀the฀“Patterns”฀tab฀of฀the฀ “Format฀Data฀Series”฀dialog฀box,฀as฀shown฀in฀฀Figure฀9-14.

If฀Holdberg฀must฀borrow฀$1฀million,฀its฀WACC฀will฀be฀13.95฀percent.฀If฀Holdberg฀must฀borrow฀$2฀million,฀ its฀WACC฀will฀be฀14.58฀percent.

Figure฀9-14

Settings on “Patterns Tab” of the “Format Data Series” Dialog Box

Note that the box for smoothed line is not checked. This results in

a series of straight-line segments between the points, as in Figure 9.10, rather than a wavy curve.

312 ❧ Corporate Financial Analysis with Microsoft Excel ®