Question

Balance Sheet Data

               Long-Term Debt               80,000,000

               Preferred Stock                20,000,000

               Common Equity                20,000,000

Number of shares of Common                 1,500,000                         Price per share Common             $42

Number of shares of Preferred                     150,000                               Price per share Preferred            $108

Number of 8% Coupon 25-year Bonds          40,000               Price of 8% 25-year Bonds   $1075

Number of 6% Coupon 15-year Bonds          40,200                           Price of 6% 15-year Bonds   $920

Forecasted Dividend on Common (D₁)             $3.30                           Dividend Rate on Preferred            9.5%

Par Value of Preferred                                           $100                                 Current 10-Year Treasury Yld.        4.3%

Standard Deviation of Stock                                   40%                              Correlation Stock vs. Market 0.50

Standard Deviation of Market                                15%                      Market Risk Premium                    5.0%

Risk Premium of our Stock over our 15-yr Bonds          3.9%        Forecasted Constant Growth             3.0%

Tax Rate                                                                       25%                        Flotation costs on Bonds               1.4%

Flotation costs on Preferred                                   2.4%

1. Calculate the appropriate weights to use for the financing sources. (Hint: Assume that the firm feels their current mix of long-term debt is good and would like to raise capital with the same mix of maturities)
2. Calculate the after-tax cost of debt (hint: You can account for the two bonds by taking a weighted average of their cost or by keeping them separate and putting both into the WACC formula at their individual weights). Note that there are flotation costs of 1.4% on bonds.
3. Calculate the cost of preferred. Note that there are flotation costs of 2.4% on preferred stock.
4. Calculate the cost of common (Hint: Use all three methods and take an average). Note that all common equity will come from internally generated equity (retained earnings) which means no new shares will be issued and no flotation costs incurred.
5. Calculate the WACC

Answer 1

1. Calulation of appropriate weights to be used for financing sources :

Source	$	Calculation of Weight	Weight
Common Equity	20,000,000	=20,000,000/120,000,000	.167
Preferred Stock	20,000,000	=20,000,000/120,000,000	.167
Long term Debt	80,000,000	=80,000,000/120,000,000	.66
Total	120,000,000		1.00

               Weight = Source/ Total

2. Calculation of after tax cost of debt:

1. 8% coupon 25 year bond (Assumption: Par Value is $1000)

Number of bonds = 40,000

Price of bond = $1075 each

Interest = 8%

Flotation Cost = 1.4%

Tax rate = 25%

After Tax Cost of debt = Interest         X (1- tax rate)

                                                    Price (1- Flotation Cost)

                                        =[ 80/1075(1-.014)] X (1-.25)

                                       = 5.66%

2. 6% coupon 15 year bond (Assumption: Par Value is $1000)

Number of bonds = 40,200

Price of bond = $920each

Interest = 6%

Flotation Cost = 1.4%

Tax rate = 25%

After Tax Cost of debt = Interest         X (1- tax rate)

                                                        Price (1- Flotation Cost)

                                       = [60/920(1-.014)] X (1-.25)

                                        = 4.96%

Weighted average cost of debt = 4.96 * 40200*920/total debt + 5.66 *40000*1075/Total debt= 5.2%

3. Cost of Preferred Capital

Price per preferred share = $108

Flotation Cost = 2.4%

Par Value of Preferred = $ 100

Dividend Rate = 9.5%

Cost of Preferred Capital (Kp)

= Dividend/ Price (1-Flotation Cost)

= 9.5/108(1-.024)

=9.01%

4. Cost of common stock

1. Cost of Common (ke)= (D1/Po) + g

   Where, D1= Expected dividend = $3.30

                  Po = Price per Common Stock = $42

                   g = constant growth rate = 3%

Ke = (3.30/42) + 3%

      = 0.07857 + .03

   = .10857 or 10.857%

2. Ke= Rf + Beta (Rm-Rf)

Where, Rf = Risk free rate (treasury bill yield) = 4.3%

      Beta= covariance between stock and market return/ variance         of market

Rm- Rf = Market risk premium = 5%

Calculation of Beta

Covariance (stock, market) = Correlation between stock & marker (Rsm) X Standard deviation of stock (Ss) X Standard deviation of market (Sm)

= 0.5 X .40 X .15

= 0.03

Now, Beta = Covariance (stock, market)/Variance of market

                  =   0.03/ (.15)^2

                  = 1.33

Therefore,

Ke= Rf + Beta (Rm-Rf)

     = 4.3% + 1.33 (5%)

    = .1095 or 10.95 %

3. Ke = Bond Yield (Yltd) + Equity Risk Premium

   =   3.9% + 5% (i.e. market risk premiu)

   = 8.9%

**As given in the question Cost of Common (Ke) has to be calculating by taking average of three methods used above,

Therefore Ke =[ (i) +(ii) + (iii)]/3

                       = [10.857% + 10.95% + 8.9%]/3

                     = 10.235%

5. WACC (Weighted average cost of capital)

= After tax cost of debt (Kd) X Debt/(Debt + Common Stock + Preferred Stock) + Cost of Preferred Stock (Kp) X Preferred Stock/ (Debt + Common Stock + Preferred Stock) + Cost of Common (Ke) /( Debt + Common Stock + Preferred Stock)

= Kd X D/(D+E+P) + Kp X P/(D+E+P) + ke X E/(D+E+P)

= 5.2* 2 million/ 12 million + 9.01 *2 million/ 12 million +10.235 * 8 million/12 million