Question

Suppose a company raised $3,000,000 to fund its expansion. It expects the sustainable growth to be 3% a year. It sold 100 20-year corporate bonds with a $10,000 par value and a 4% coupon rate at the market price of $10,200. The flotation cost is 2% of par value. The corporate income tax rate is 25%. It issued 100,000 new preferred shares at $10.30/share. It promises a $0.60/share annual dividend. The flotation cost is $0.30/share. The company also issued 20,000 new common shares at $51/share. The flotation cost is $1/share. Its next dividend is $2.5/share. Before-tax cost of capital from bond =   % After-tax cost of capital from bond (rd) =   % Cost of capital from preferred stock (rp) =   % Cost of capital from common stock (rn) =   % The weighted average cost of capital is (ra) =   %.

Answer 1

Before-tax cost of bonds (assuming annual coupons):

Current market price of the bond= Present value of all its future coupons+PV of Face value to be recd. At maturity

ie.Price/PV= (Coupon amt.*(1-(1+r)^-n)/r)+(FV/(1+r)^n)

where,

PV= Price-Flotation cost,ie. 10200-(2%*10000)= 10000

Coupon amt.= periodic $ interest amt.= 10000*4%= $ 400

r= the yield /market interest rate/cost to be found out ??

n= no.of coupon periods still pending to maturity,ie. 20

So,plugging in the known values in the above formula,

10000= (400*(1-(1+r)^-20)/r)+(10000/(1+r)^20)

Solving for r, we get the before- tax r as

4%

The corporate income tax rate is 25%.

So, the after-tax cost (rd)=

Before-tax cost*(1-Tax rate)

ie. 4%*(1-25%)=

3%

Cost of preferred stock(r p)

$ Dividend/(net proceeds of issue)

ie. $ Dividend/(Price-Flotation cost)

ie. 0.60/(10.30-0.30)

6%

Cost of Common stock

As per Constant dividend growth model,

r n=(Next dividend/(Market price-Flotation cost))+growth rate

ie.(2.5/(51-1))+3%=

8%

WACC=(Wt.d*rd)+(Wt.p*rp)+(Wt.n*rn)
Type of capital	Market Value		Wt. to total	Cost	Wt.*cost
Bonds	100*10200=	1020000	33.22%	3%	1.00%
Preferred shares	100000*10.30=	1030000	33.55%	6%	2.01%
Common stock	20000*51=	1020000	33.22%	8%	2.66%
Total		3070000	100.00%		5.67%
WACC =(33.22%*3%)+(33.55%*6%)+(33.22%*8%)=
5.67%

ANSWERS:

Before-tax cost of capital from bond = 4  %

After-tax cost of capital from bond (rd) = 3 %

Cost of capital from preferred stock (rp) = 6  %

Cost of capital from common stock (rn) = 8 %

The weighted average cost of capital is (ra) = 5.67 %.