Question

You own 2,530 common shares of a company, which will pay a dividend of $2.05 per share next year and a liquidating dividend of $59.40 per share in two years form today. The require return on the common shares is 8.74%. You want to create a homemade dividend so that you can get an equal dollar amount of total dividends in each of the two years. What will be the amount of homemade dividend in the second year?

A) $70,962

B) $72,829

C) $74,697

D) $76,564

E) $78,431

Answer 1

Solution

Answer-$74697

Here we have dividends being paid in 2 years

Present value of dividends paid in 2 years = Present value of dividend recieved in first year+PV of dividend recieved in second year

Dividend recieved first year=number of shares*dividend per share=2530*2.05=5186.50

Dividend recieved at end of second year=number of shares*dividend per share=2530*59.4=150282

Now the formula for Present value is

Present value=Cashflow/(1+r)^n

where

r=Req rate of return of common stocks=8.74%

n=period in which cashflow occurs

Therefore Present value of dividends recieved in 2 years=5186.50/(1+.0874)^1+150282/(1+.0874)^2

=131864.588

Now calculation for equal annual payments of homemade dividends will be made

The present value of the dividends recieved in 2 years should be equal to present value of 2 equal annuity payments of the homemade dividends

The present value of dividends paid in 2 years=Annual dividend payment of homemade dividend*((1-(1/(1+i)^m))/i)

where

i=rate of retun require=8.74%

m=number of periods=2

131864.588=Annual dividend payment*((1-(1/(1+.0874)^2))/.0874)

Solving we get Annual dividend payment (Home made dividend)=74696.6562

Thus homemade dividend in second year=74697

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