A company has just paid its first dividend of $4.01. Next year's dividend is forecast to...

A company has just paid its first dividend of $4.01. Next year's dividend is forecast to grow by 10 percent, followed by another 10 per cent growth in year two. From year three onwards dividends are expected to grow by 3.3 percent per annum, indefinitely. Investors require a rate of return of 18 percent p.a. for investments of this type. The current price of the share is (round to nearest cent)

Expert Solution

current price of the share = dividend in year 1/(1+required return) + dividend in year 2/(1+required return)2 + terminal value/(1+required return)2

dividend in year 1 = last dividend paid*(1+dividend growth rate) = $4.01*(1+0.10) = $4.01*1.10 = $4.411‬

dividend in year 2 = dividend in year 1*(1+dividend growth rate) = $4.411*(1+0.10) = $4.411*1.10 = $4.8521‬

dividend in year 3 = dividend in year 2*(1+indefinite dividend growth rate) = $4.8521*(1+0.033) = $4.8521*1.033 = $5.0122193‬

terminal value = dividend in year 3/(required return - indefinite dividend growth rate) = $5.0122193‬/(0.18 - 0.033) = $5.0122193‬/0.147 = $34.096729931972789115646258503401‬

terminal value is calculated at the end of year 2. so it will be discounted for 2 years only.

current price of the share = $4.411/(1+0.18) + $4.8521‬/(1+0.18)2 + $34.096729931972789115646258503401‬/(1+0.18)2

current price of the share = $4.411/1.18 + $4.8521‬/1.182 + $34.096729931972789115646258503401‬/1.182

current price of the share = $4.411/1.18 + $4.8521‬/1.3924‬ + $34.096729931972789115646258503401‬/1.3924

current price of the share = $3.7381355932203389830508474576271‬ + $3.4847026716460787130135018672795‬ + $24.487740542927886466278553938093‬ = $31.71

current price of the share is $31.71.

jeff jeffy answered 2 years ago

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