Question

Assume that you have the following information:-

Market Info:- Real interest rate = 2.0%; Expected inflation = 4.0%; Rm = 12.0%; Tax = 30.0%.

Com. Stock info:- Par value = $1.0 ; Market value (price) = ?? ; Beta = 1.60 ; No. of outstanding shares = 1,000,000.0 ; EPS $3.0 ; pay-out ratio = 30.0%;

Growth in EPS & Dividends = 5.0% ;

Preferred Stock info:- Par value = $100.0; Dividend per share = 10.0%; Rp=8.0%; No. of outstanding shares = 100,000.0; Price = ????

Bonds info:- Par value = $1,000.0; Coupon interest = 4.0% ; YTM = 6.0%; Time to maturity = 20 years ; No. of bonds = 100.0; Price = ???

The market values for bonds, pref., & comm. in your example were chosen as $1,050.0; $2.0; $3.0.

1- Calculate the WACC using historical weights in the capital structure.

2 - Calculate the WACC using market weights in the capital structure.

Answer 1

Solution:

1)Calculation of cost of capital

i)Cost of common stock(Re)

Risk free rate=(1+real rate)*(1+inflation rate)-1

=(1+0.02*1+0.04)-1

=6.08%

Re=Risk free rate+Beta(Rm-risk free rate)

=6.08%+1.60(12-6.08)

=15.55% or 15.6%

ii)Before tax Cost of debt=YTM

=6%

After tax cost of debt=6%(1-tax rate)

=6%(1-0.30)

=4.2%

iii)Cost if preferred stock(Rp)=8%

a)Calculation of Historical weight

Book value of common stock=Par value*No. of shares

=$1*1,000,000

=$1000,000

Book value of Preferred Stock=$100*100,000

=$10,000,000

Book value of Bonds=$1000*100

=$100,000

Total book value=$1000,000+$10,000,000+$100,000=$11,100,000

Weight of common stock(We)=Book value of common stock/Total book value

=$1000,000/11,100,000=0.09

Weight of Preferred stock(Wp)=$10,000,000/$11,100,000=0.90

Weight of bond(Wd)=$100,000/$11,100,000=0.01

WACC=Re*We+Rp*Wp+Rd*Wd

=15.6%*0.09+8%*0.90 +4.2%*0.01

=8.64%

WACC using historical weights in the capital structure is 8.64%

b)Caculation of market weight

Market value of common stock=Market price*no. of shares

=$3*1000,000=$3000,000

Market value of preferred stock=$2.0*100,000

=$200,000

Market value of bonds=$1,050*100=$105,000

total market value=$3000,000+$200,000+$105,000=$3305,000

Weight of common stock(We)=$3000,000/$3305,000=0.91

Weight of preferred stock(Wp)=$200,000/$3305,000=0.06

Weight of bond(Wd)=$105,000/$3305,000=0.03

WACC=Re*We+Rp*Wp+Rd*Wd

=15.6%*0.91+8%*0.06+4.2%*.03

=14.76%

WACC using market weights in the capital structure is 14.76%