Chapter 09. Ch09 P18 Build a Model

INPUTS USED IN THE MODEL

P0 $50.00

Net Ppf $30.00

Dpf $3.30

D0 $2.10

g 7%

B-T rd 10%

Skye's beta 0.83

Market risk premium, RPM 6.0%

Risk free rate, rRF 6.5%

Target capital structure from debt 45%

Target capital structure from preferred stock 5%

Target capital structure from common stock 50%

Tax rate 35%

Flotation cost for common 10%

a. Calculate the cost of each capital component, that is, the after-tax cost of debt, the cost of preferred stock (including flotation costs), and the cost of equity (ignoring flotation costs). Use both the DCF method and the CAPM method to find the cost of equity.

Cost of debt:

B-T rd × (1 – T) = A-T rd

10%*(1-35%) 6.5%

Cost of preferred stock (including flotation costs):

Dpf / Net Ppf = rpf

= 3.30 / 30 11%

12.22% answer of cost of preferred stock

(including flotation stock)

rPf=Dpf/Pps(1-F)

Cost of common equity, DCF (ignoring flotation costs):

D1 / P0 + g = rs

D1=Do(1+g)=2.10(1+0.07)=2.247

=(2.247/50) + 0.07 11.49

Cost of common equity, CAPM:

rRF + b × RPM = rs

=6.5% + (0.83 * 6%) = 11.48%

IMPORTANT NOTE: HERE THE CAPM AND THE DCF METHODS PRODUCE APPROXIMATELY THE SAME COST OF EQUITY. THAT OCCURRED BECAUSE WE USED A BETA IN THE PROBLEM THAT FORCED THE SAME RESULT. ORDINARILY, THE TWO METHODS WILL PRODUCE SOMEWHAT DIFFERENT RESULTS.

b. Calculate the cost of new stock using the DCF model.

D0 × (1 + g) / P0 × (1 – F) + g = re

=[2.10 * (1 + 0.07) / {50 (1-0.1)} ] + 0.07 11.99%

c. What is the cost of new common stock based on the CAPM? (Hint: Find the difference between re and rs as determined by the DCF method and add that differential to the CAPM value for rs.)

rs + Differential = re

11.48 + 0.51% = 11.99%

Again, we would not normally find that the CAPM and DCF methods yield identical results.

d. Assuming that Gao will not issue new equity and will continue to use the same capital structure, what is the company's WACC?

wd 45.0%

wpf 5.0%

ws 50.0%

100.0%

wd × A-T rd + wpf × rpf + ws × rs = WACC

= (45.0% * 6.5%) + (5.0% * 11%) + (50.0% * 11.48%) = 9.215%

e. Suppose Gao is evaluating three projects with the following characteristics:

(1) Each project has a cost of $1 million. They will all be financed using the target mix of long-term debt, preferred

stock, and common equity. The cost of the common equity for each project should be based on the beta estimated for

the project. All equity will come from reinvested earnings.

(2) Equity invested in Project A would have a beta of 0.5 and an expected return of 9.0%.

(3) Equity invested in Project B would have a beta of 1.0 and an expected return of 10.0%.

(4) Equity invested in Project C would have a beta of 2.0 and an expected return of 11.0%.

Situation Rm B Equation= Rf + (Rm – Rf)B

Required Return Return of Invested $1 Million

1 9.0% 0.5 = 6.5% + {( 9.0% - 6.50% ) * 0.5} 7.75% $775002 10.0% 1.0 = 6.5% + {( 10.0% - 6.5% ) * 1.0} 10.0% $100003 11.0% 2.0 = 6.5% + {( 11.0% - 6.5% ) * 2.0} 15.5% $155000

Chapter 9. Tool Kit for The Cost of Capital

The cost of capital is a vital element in the capital budgeting process.  For a project to be accepted, it must provide a return that exceeds its cost of capital, which is used as a hurdle rate.  The cost of capital also serves three other purposes: (1) It is used to help determine the EVA, (2) managers use the cost of capital when deciding between buying and leasing, and (3) the cost of capital is used in the regulation of electric, gas, and telephone companies.

THE WEIGHTED AVERAGE COST OF CAPITAL  (Section 9.1)

The cost of capital is the weighted average cost of the debt, preferred stock, and common equity that the firm uses to finance its assets, or its WACC. There is an overall, or corporate, WACC which reflects the average riskiness of all the firm's assets.  However, since different assets may have more or less risk than the average, the overall WACC must be adjusted up or down to reflect the riskiness of different proposed capital budgeting projects.

A firm's target capital structure is used for the weights when calculating the WACC. The capital structure decision is discussed in detail in Chapter 15, but consideration is generally given to the actual current book value structure and the

market value structure.  In addition, firms generally conduct "stress tests" to get an idea of their ability to meet debt coverage requirements under different capital structures under different economic conditions.

Basic Data (Millions, except per share data)

Number of common shares outstanding =

325

Price per share of common stock =

$32.00

Number of preferred shares outstanding =

12

Price per share of preferred stock =

$100.00

Figure 9-1.  National Computer Corporation: Book Values, Market Values, and the Target Capital Structure (Millions of Dollars, December 31, 2010)

         

         

                       

Balance Sheets

               Investor-Supplied CapitalTargetCapitalStructure

                   Book      Market

          Percent Book Percent Market Percent

  of Total Value   of Total

 Value   of Total

Assets       Liabilities and Equity  

                       

Cash $   65    Accounts payable $  650 6.5%           

S-T investments

    10    Accruals       399   4.0%            

Receivables  1,800       Spontaneous liabilities $1,049 10.5%           

Inventories   3,100     Notes payable     350   3.5% $  350 3.9% $   350 2.2%      Total C.A. $4,975       Total C.L.   $1,399 14.0%                   Long-term debt   4,200   42.0%   4,200   46.9%   4,200   26.0%    Net fixed assets

 5,020       Total  liabilities $5,599 56.0% $4,550 50.9% $ 4,550 28.2%wd = 30.0%

        Preferred stock  1,200 12.0%  1,200 13.4%  1,200 7.4%wps =

10.0%

        Common stock    650 6.5%    650 7.3%       

        Retained earnings   2,546   25.5%   2,546   28.5%        

           Total common equity $3,196   32.0% $3,196   35.7%   10,400   64.4% ws =   60.0%

Total assets $9,995    Total liabilities and equity $9,995 100.0% $8,946 100.0% $16,150 100.0%  100.0%                       Notes:                      1.  The market value of the notes payable is equal to the book value. Some of NCC’s long-term bonds sell at a discount and some sell at a premium, but their aggregate market value is approximately equal equal to their aggregate book value.

                           

2.  The common stock price is $32 per share. There are 325 million shares outstanding, for a total market cap of $32(325) = $10,400 million.

                  

3.  The preferred stock price is $100 per share. There are 12 million shares          

outstanding, for a total market value of preferred of $100(12) = $1,200 million.           4.  No distinction is made between common equity raised by issuing stock vs. retaining earnings when establishing the target capital structure.

                  

5.  The firm assumes that it will eventually replace most notes payable with long-term bonds and that the costs of notes payable and long-term debt are approximately the same, hence it simply uses a 30% weight for all investor-supplied debt, i.e., for the combined notes payable and long-term debt.

                                    

6.   Accounts payable and accruals are not sources of investor-supplied capital, so we exclude them when calculating the WACC. However, we include the effect of  payables and accruals on free cash flow and on a project's cash flows in a capital budgeting project, so  we do not ignore payables and acrruals.  See Chapter 16 for more discussion of payables.

                           

         

7.  When deciding on a target capital structure, managers consider the firm's current and recent past book and market value structures, as well as those of benchmark firms. They also perform stress test by forecasting financial statements under different assumptions regarding capital structures and different states of the economy. See Chapter 15 for more on setting the target capital structure weights.

                                             

                       

BASIC DEFINITIONS (Section 9.2)

WACC = Weighted average cost of capital= wd rd(1 – T) + wps rps + ws rs

rd  = Cost of debtrps  = Cost of preferred stockrs  = Cost of stock (comon equity)

wd  = Percent of target capital structure financed with debtwps  = Percent of target capital structure financed with preferred stock

ws  =Percent of target capital structure financed with stock (common equity)

T =Tax rate