Aaron\'s Rentals has 45,000 shares of common stock outstanding at a market price

Question

Aaron's Rentals has 45,000 shares of common stock outstanding at a market price of $27 a share. The common stock just paid a $1.10 annual dividend and has a growth rate of 3.2 percent. There are 10,000 shares of 5.5 percent preferred stock outstanding at a market price of $48 a share. The preferred stock has a par value of $100. The outstanding bonds mature in 11 years, have a total face value of $800,000, a face value per bond of $1,000, and a market price of $987.60 each. The bonds pay 7.5 percent interest, semiannually. The tax rate is 35 percent. What is the firm's weighted average cost of capital? a. 7.42 percent b. 7.61 percent c. 8.97 percent d. 9.42 percent e. 10.38 percent To whoever answers this can you please write down the calculator inputs please? I'd like to be able to do these on my own and giving me the answer alone doesn't help me. Thank you.

Explanation / Answer

The common stock just paid a D0=$1.10 annual dividend and has a growth rate of g= 3.2 percent. Mkt price P0=$27 So COst of equity Ks = D0*(1+g)/P0 + g = 1.10*(1+3.2%)/27 + 3.2% = 7.40% Total Eqity Cap = 45000*$27 = $1,215,000 Total Debt = 0.9876*800,000 = $790,080 Total Pref Cap = 10000*$48 = $480,000 SO Total Capital = $2,485,080 SO We = 1215000/ $2,485,080 = 0.49 Wd = 790080/2485080 = 0.32 & Wp = 0.19 Bond : Coupon 7.5% Semiannual. SO PMT = 7.5%*1000/2 = 37.50 nper = 11Yrs*2 period/Yr = 22, PV=987.60 & FV =1000 SO CurrentYield = 2*Rate(nper,pmt,pv,fv) =2*Rate(22,37.50,-987.60,1000) = 7.67% ie Kd = 7.67% Return on Pref Share = Kp = 5.5/48 = 11.46% WACC (Ka)= Wd*(Kd)*(1-t)+(Wp)*(Kp) +(We)*(Ke) where Wd= The proportion of the financing taken on by debt=32% Wp= The proportion of the financing taken provided by preferred stock=19% We= The proportion of the financing provided by equity=49% Kp= 11.46% Kd=7.67% Ke (Using CAPM) = 7.40% And WACC (Ka) = Wd*(Kd)*(1-t)+(Wp)*(Kp) +(We)*(Ke) ie wacc = 32%*7.67%*(1-35%) + 19%*11.46% + 49%*7.4% =7.42% ...Ans (a)

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