Question

A company has 4,900,331 shares of common stock outstanding. The current share price is $73, and the book value per share is $4.85. This company also has two bond issues outstanding. The first bond issue has a face value of $60,094,653, has a 0.05 coupon, matures in 10 years and sells for 83 percent of par. The second issue has a face value of $63,040,210, has a 0.06 coupon, matures in 20 years, and sells for 92 percent of par.

The most recent dividend was $2.81 and the dividend growth rate is 0.06. 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 0.28.

What is the company's WACC? Enter the answer with 4 decimals (e.g. 0.2345)

Answer 1

Solution:
	WACC is     0.0892     or in percentage 8.92%
Working Notes:
Notes:	To get WACC , we have to get market value of Stock & Debt , using given data, weight of each component in capital structure based on their market value. And at last we will compute cost of capital for each component of capital structure, then inserted in given below formula to get WACC.
	WACC = (E/V x Ke) + (D/V x After tax Kd)
	Common stock = 4,900,331 shares
	Bond 1 = Face value of $60,094,653
	Bond 2 = Face value of $63,040,210
	Current share price = $73
	Bond 1 is selling at 83% of par
	Bond 2 is selling at 92% 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) = 4,900,331 x $73
	Total Market value of common stock (E) = $357724163
	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 = $60,094,653 x 83%
	Total Market value of Bond 1 = 49878561.99
	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 = $63,040,210 x 92%
	Total Market value of Bond 2 = $57996993.20
	Total debt market value(D) =Bond 1 +Bond 2 market value
	Total debt market value(D) =49878561.99   + $57996993.20
	Total debt market value(D) =$107875555.19
	the firm’s market value company capital structure (V) = E + D = $357724163 + $107875555.19
	the firm’s market value company capital structure (V) = E + D = $465599718.19
	Debt (Bond) weight in capital structure = D/V = Mkt. Value of Bond / Total Mkt. Value of Company
	Debt (Bond) weight in capital structure = $107875555.19 /$465599718.19
	Debt (Bond) weight in capital structure = 0.231691625
	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 =$357724163 /$465599718.19
	Common stock weight in capital structure = E/V =0.768308375
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 = $73 per share
	g= growth rate= 0.06 = 6%
	D0= recent Dividend=$2.81 per share
	P0 = D1 / (Ke - g)
	P0 = D0(1+g)/(Ke -g)
	73= 2.81 x (1.06)/(Ke-0.06)
	Cost of equity Ke = ((2.81 x 1.06) /73) + 0.06
	Cost of equity Ke = 0.04080274 + 0.06
	Cost of equity Ke = 10.080274%
cost of debt pre tax (kd)
	Total debt market value(D) =$107875555.19
	Total debt market value(D) =Bond 1 +Bond 2 market value
	Total debt market value(D) =49878561.99   + $57996993.20
	weight of bond 1 in total debt d1= mkt. Value of Bond 1/total debt = $49878561.99 / $107875555.19
	weight of bond 1 in total debt d1=0.462371312
	weight of bond 2 in total debt d2= mkt. Value of Bond 2/total debt =$57996993.20 / $107875555.19
	weight of bond 2 in total debt d2=0.537628688
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 = 10 x 2 =nper = N = 20
	Face value of bond = FV= $60094653
	Price of the bond = PV = -$49878561.99         [60,094,653 x 83% = $49878561.99]
	Semi-annual Coupon amount = PMT = coupon rate x face value/2 = 5% x $60094653 /2= $1502366.325
	For calculation YTM by excel
	type above data in below format
	=RATE(N,pmt,PV,FV)
	=RATE(20,1502366.325,-49878561.99,60094653)
	3.7200817%
	=3.7200817%
	The YTM calculated is semi annual
	YTM annual = Semi annual YTM x 2
	YTM annual = 3.7200817% x 2
	YTM annual bond 1 = 7.440163400 %
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 = 20 x 2 =nper = N = 40
	Face value of bond = FV= $63040210
	Price of the bond = PV = -$57996993.20         [63040210 x 92% = $57996993.20]
	Semi-annual Coupon amount = PMT = coupon rate x face value/2 = 6% x $63040210 /2= $1891206.30
	For calculation YTM by excel
	type above data in below format
	=RATE(N,pmt,PV,FV)
	=RATE(40,1891206.30,-57996993.20,63040210)
	3.36692262%
	=3.36692262%
	The YTM calculated is semi annual
	YTM annual = Semi annual YTM x 2
	YTM annual = 3.36692262% x 2
	YTM annual bond 2 = 6.733845240%
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=0.462371312
	weight of bond 2 in total debt d2=0.537628688
	YTM annual bond 1 = 7.440163400 %
	YTM annual bond 2 = 6.733845240%
	Cost of debt (Kd) = (weight of bond 1 x YTM of bond1) + (weight of bond 2 x YTM of bond2)
	Cost of debt (Kd) = (0.462371312 x 7.440163400 %) + (0.537628688 x 6.733845240%)
	Cost of debt (Kd) = 0.070604265
	Cost of debt (Kd) = 7.0604265%
	After Tax cost of debt (kd)= Kd x (1 - tax rate) = 7.0604265% x (1-0.28)
	After Tax cost of debt (kd)=5.083507080%
WACC
	WACC = (E/V x Ke) + (D/V x After tax Kd)
	= (0.768308375 x 10.080274% +0.231691625 x 5.083507080%)
	0.08922564953
	=0.0892
	=8.92%
	WACC is     0.0892     or in percentage 8.92%
Where
	Debt (Bond) weight in capital structure = 0.231691625
	Common stock weight in capital structure = E/V =0.768308375
	Cost of equity Ke = 10.080274%
	After Tax cost of debt (kd)=5.083507080%
Please feel free to ask if anything about above solution in comment section of the question.