Question

Dinklage Corp. has 4 million shares of common stock outstanding. The current share price is $70, and the book value per share is $9. The company also has two bond issues outstanding. The first bond issue has a face value of $75 million, a coupon rate of 7 percent, and sells for 95 percent of par. The second issue has a face value of $60 million, a coupon rate of 6 percent, and sells for 107 percent of par. The first issue matures in 25 years, the second in 8 years.

Suppose the most recent dividend was $4.30 and the dividend growth rate is 4.5 percent. Assume that the overall cost of debt is the weighted average of that implied by the two outstanding debt issues. Both bonds make semiannual payments. The tax rate is 21 percent. What is the company’s WACC? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Answer 1

Solution:
	WACC = 8.97%
Working Notes:
	Common stock = 4 million shares
	Bond 1 = Face value of $75 million
	Bond 2 = Face value of $60 million
	Current share price = $70
	Bond 1 is selling at 95% of par
	Bond 2 is selling at 107% of par
	Total Market value of common stock (E) = No. of Common stock shares x Market price per share
	Total Market value of common stock (E) = 4 million x $70
	Total Market value of common stock (E) = $280 million
	Total Market value of Bond 1 = Total Face value of bond x % of par at which bond is selling in market
	Total Market value of Bond 1 = $75 million x 95%
	Total Market value of Bond 1 = $71.25 million
	Total Market value of Bond 2 = Total Face value of bond x % of par at which bond is selling in market
	Total Market value of Bond 2 = $60 million x 107%
	Total Market value of Bond 2 = $64.20 million
	Total debt market value(D) =Bond 1 +Bond 2 market value
	Total debt market value(D) =$71.25 million + $64.20 million
	Total debt market value(D) =$135.45 million
	the firm’s market value company capital structure (V) = E + D = $280 million + $135.45 million
	the firm’s market value company capital structure (V) = E + D = $415.45 million
	Debt (Bond) weights in capital structure (D/V)= 0.326032013
	Common stock weight in capital structure(E/V) =0.673967987
	Debt (Bond) weight in capital structure = D/V = Mkt. Value of Bond / Total Mkt. Value of Company
	Debt (Bond) weight in capital structure = $135.45/$415.45
	Debt (Bond) weight in capital structure = 0.326032013
	Common stock weight in capital structure = E/V = Mkt. Value of common stock / Total Mkt. Value of Company
	Common stock weight in capital structure = E/V = $280/$415.45
	Common stock weight in capital structure = E/V =0.673967987
Cost of Equity (Ke)
	Using Gordon growth model : P0 = D1 / (Ke - g), where D1 = D0(1+g)
	ke = cost of Equity
	Po=current share price = $70 per share
	g= growth rate= 4.5%
	D0= Current Dividend=$4.30 per share
	P0 = D0(1+g)/(Ke -g)
	70 = 4.30(1.045)/(Ke-0.045)
	10.9192857143%
	Ke=(4.4935/70) + 0.045
	Ke=0.06419285714 + 0.045
	Ke=0.109192857
	Ke=10.9192857%
cost of debt pre tax (kd)
	Total debt market value(D) =$135.45 million
	Total debt= Bond 1 + Bond 2 =$135.45million
	weight of bond 1 in total debt d1= mkt. Value of Bond 1/total debt = $71.25 / $135.45
	weight of bond 1 in total debt d1=0.526024363
	weight of bond 2 in total debt d2= mkt. Value of Bond 2/total debt = $64.20/ $135.45
	weight of bond 2 in total debt d2=0.473975637
Computation of YTM of Bond 1
	As the bond is paying coupon semi annually , its Ytm can be calculated by Excel or financial calculator
	First we get the semi annual YTM
	No. of period = years to maturity x no. of coupon in a year = 25 x 2 =nper = N = 50
	Face value of bond = FV= $1,000
	Price of the bond = PV = -$950         [1000 x 95% = $950]
	Semi-annual Coupon amount = PMT = coupon rate x face value/2 = 7% x $1,000 /2= $35
	For calculation YTM by excel
	type above data in below format
	=RATE(N,pmt,PV,FV)
	=RATE(50,35,-950,1000)
	0.037217663
	=3.721766304%
	The YTM calculated is semi annual
	YTM annual = Semi annual YTM x 2
	YTM annual = 3.721766304% x 2
	YTM annual bond 1 = 7.443532608 %
Computation of YTM of Bond 2
	As the bond is paying coupon semi annually , its Ytm can be calculated by Excel or financial calculator
	First we get the semi annual YTM
	No. of period = years to maturity x no. of coupon in a year = 8 x 2 =nper = N = 16
	Face value of bond = FV= $1,000
	Price of the bond = PV = -$1070         [1000 x 107% = $1070]
	Semi-annual Coupon amount = PMT = coupon rate x face value/2 = 6% x $1,000 /2= $30
	For calculation YTM by excel
	type above data in below format
	=RATE(N,pmt,PV,FV)
	=RATE(16,30,-1070,1000)
	2.465255788%
	=2.465255788%
	The YTM calculated is semi annual
	YTM annual = Semi annual YTM x 2
	YTM annual = 2.465255788% x 2
	YTM annual bond 2 = 4.9305115758 %
Cost of debt (Kd) = (weight of bond 1 x YTM of bond1) + (weight of bond 2 x YTM of bond2)
	weight of bond 1 in total debt d1=0.526024363
	weight of bond 2 in total debt d2=0.473975637
	YTM annual bond 1 = 7.443532608 %
	YTM of bond 2 = 4.9305115758 %
	Cost of debt (Kd) = (weight of bond 1 x YTM of bond1) + (weight of bond 2 x YTM of bond2)
	Cost of debt (Kd) = (0.526024363 x 7.443532608 %) + (0.473975637 x 4.9305115758 %)
	Cost of debt (Kd) = 0.062524219
	Cost of debt (Kd) = 6.2524219%
	After Tax cost of debt (kd)= Kd x (1 - tax rate) = 6.2524219% x (1-0.21)
		=4.93941330%
WACC
	WACC = (E/V x Ke) + (D/V x After tax Kd)
	= (0.673967987 x 10.9192857% + 0.326032013 x 4.93941330%)
	=0.0896966
	=0.0897
	=8.97%
WACC	=8.97%
	Where
	Debt (Bond) weights in capital structure (D/V)= 0.326032013
	Common stock weight in capital structure(E/V) =0.673967987
	Ke=10.9192857%
	Kd (after tax) = 4.93941330%
Please feel free to ask if anything about above solution in comment section of the question.