1. Carby Hardware has an outstanding issue of perpetual preferred stock with an

Question

1. Carby Hardware has an outstanding issue of perpetual preferred stock with an annual dividend of $8.50 per share. If the required return on this preferred stock is 6.5%, at what price should the preferred stock sell?

2. Burke Tires just paid a dividend of D0 = $3.75. Analysts expect the company's dividend to grow by 30% this year, by 10% in Year 2, and at a constant rate of 5% in Year 3 and thereafter. The required return on this low-risk stock is 9.00%. What is the best estimate of the stock's current market value?

Explanation / Answer

1)

preferred stock pays annually till perpetuity,so value of preferred stock is the present value of all this future dividends till perpetuity.Let Annual pay=D=6, required return=r=16%

value of a share of preferred stock=Present value of all future dividends till perpetuity discounted at r

value of a share of preferred stock=D/(1+r) + D/(1+r)2 +.........perpetuity

value of a share of preferred stock=D(1/(1+r) + 1/(1+r)2 +.........perpetuity)

1/(1+r) + 1/(1+r)2 +.........perpetuity is infinite GP with first term=1/(1+r) and common ratio=cr=1/(1+r) ,sum of infinite GP is first term/(1-cr)=(1/(1+r))/(1-1/(1+r) )=(1/(1+r))/((1+r)-1/(1+r) )=(1/(1+r))/(r/(1+r) )=1/r

value of a share of preferred stock=D/r=8.5/.065=130.77

Thus at $130.77  should the preferred stock sell.

2. dividend in year 1=D1=D0*(1+g1)=3.75*1.3=4.875

dividend in year 2=D2=D1*(1+g2)=4.875*1.1=5.3625

dividend in year 3=D3=D2*(1+g3)=5.3625*1.05=5.630625

Terminal value of cash flows after year 2=TV=dividend in year 3/(r-g) where r= 9% and g=5%

Terminal value of cash flows after year 2=TV=5.630625/(.09-.05)=140.765625=Exp. Price of stock at end of year 2.

stock's current market value=D1/(1+r)+(D2+TV)/(1+r)2

stock's current market value=4.875/(1.09)+(5.3625+140.765625)/(1.09)2

stock's current market value=4.875/(1.09)+(146.128125)/(1.09)2 =4.47+122.99=127.46

Thus $127.46 is the best estimate of the stock's current market value.

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