Question

# The last dividend payment of a stock was \$0.80 and this dividend is expected to grow...

The last dividend payment of a stock was \$0.80 and this dividend is expected to grow at 6% per year for three years. After that, the dividend will grow at 3% indefinitely. Using the two-stage dividend growth model, what is the correct formula for B6 if the required rate of return on this stock is 15%?

 A B 1 Last Dividend \$0.80 2 Required Return 15% 3 Growth Rate 1 6% 4 Growth Rate 2 3% 5 Growth Rate 1 Time 3 6 Intrinsic Value 7.42

=B1/(B2-B3)*(1+((1+B3)/(1+B2))^B5)+(B1*(1+B3)^B5*(1+B4)/(B2-B4)/(1+B2)^B5)

=B1*(1+B3)/(B2-B3)*(1-((1+B2)/(1+B3))^B5)+(B1*(1+B4)^B5*(1+B3)/(B2-B3)/(1+B2)^B5)

=B1*(1+B3)/B2-B3*1-(1+B3)/(1+B2)^B5+B1*(1+B3)^B5*(1+B4)/(B2-B4)/(1+B2)^B5

=B1*(1+B3)/(B2-B3)*(1-((1+B3)/(1+B2))^B5)+(B1*(1+B3)^B5*(1+B4)/(B2-B4)/(1+B2)^B5)

=B1*(1-B3)/(B2+B3)*(1+((1-B3)/(1-B2))^B5)-(B1*(1-B3)^B5*(1-B4)/(B2+B4)/(1-B2)^B5)

Given that,

Last dividend paid D0 = \$0.8

required rate of return r = 15%

growth rate for 3 years g1 = 6%

Thereafter growth rate g2 = 3%

So, using 2-stage dividend growth model, intrinsic value is calculated as

P0 = D0*(1+g1)/(1+r) + D0*((1+g1)^2)/(1+r)^2 + D0*((1+g1)^3)/(1+r)^3 + D0*((1+g1)^3)*(1+g2)/((r-g2)*(1+r)^3)

=> P0 = (D0*(1+g)/(1+r))*(1 - ((1+g)/(1+r))^3) + D0*((1+g1)^3)*(1+g2)/((r-g2)*(1+r)^3)

So, Formula in cell B6 =B1*(1+B3)/(B2-B3)*(1-((1+B3)/(1+B2))^B5)+(B1*(1+B3)^B5*(1+B4)/(B2-B4)/(1+B2)^B5)

Hence option D is correct.

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