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Nachman Industries just paid a dividend of D0 = \$1.32. 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? why

A.

\$41.59

B.

\$42.65

C.

\$43.75

D.

\$44.87

E.

\$45.99
We have current Div D0=\$1.32 Stock has SUpernatural growth in Y1 as g1 = 30% & in Y2 as g2=10% & then normal growth from Y3 onwards as g=5%. Reqd return Ks= 9% So we have D1=(1 g1)*Do = (1 30%)*1.32 = \$1.72 D2 = (1 g2)*D1 = (1 10%)*\$1.72 = \$1.89 When Normal growth from Y3, D3=(1 g)*D2 = (1 5%)*\$1.89 = \$1.98 For the price of stock, we have the following three steps: 1. Find the PV of the dividends during the period of (Y1 & y2) nonconstant growth(gn). 2. Find the price of the stock at the end of the nonconstant growth period (P2), at which point it has become a constant growth (g) stock, and discount this price back to the present. 3. Add these two components to find the intrinsic value of the stock, P0. STep 1. Ks=9%, D0=\$1.32, D1= \$1.72, D2=\$1.89 & D3…

s = \$1.98 So PV of Div for 2 yrs = D0 D1/(1 Ks)^1 D2/(1 Ks)^2 = 1.32 1.72/(1 9%)^1 1.89/(1 9%)^2 = 4.49 Step2 : After 2 yrs, the stock becomes a constant growth stock with g =5%, its price at end of Year 2 is given by P2 = D3/(Ks-g) ie P2 = D2(1 g)/(Ks-g) = 1.89*(1 5%)/(9%-5%) = 49.61 PV of P2 = P2/(1 ks)^2 = 49.61/(1 9%)^2 = 41.76 Step 3: So value of Stock P0 = PV of Dividend of 2 yrs PV of Stock price at end of Year 2 = 4.49 41.76 = 46.25 So P0 = \$46.25 Note : When we do rounding off, some rounding error do creep in.

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