Question

You own 100 shares of stock of unlevered Gamma Company which has 1000 shares outstanding. Gamma plans to pay $2,200 dividend at the end of the current year (i.e. one year from today) and a liquidating dividend of $4,840 at the end of 2 years from today. The required return on Gamma’s stock is 10 percent. Ignoring taxes, and transaction costs.

a. What is the value of your shares of stock? Show calculations to support your answer.

b. Suppose shareholders want Gamma to increase its $2,200 dividend payout at the end of the current year to $4,000 and Gamma increases the dividend by issuing at the end of the current year new stock worth the amount needed to increase the dividend. Will the value of your shares change under this scenario? Show calculations to support your answer.

c. Suppose instead of increasing the dividend payout to $4,000 at the end of the current year, the capital raised by new stock is invested by Gamma for a year with an expected return of 21%. What will be the change in the current value of your shares under this scenario? Support your answer with calculations, not just words.

Answer 1

GIVEN THAT :-

According to the question we have that

100 shares of stock of unlevered Gamma Company which has 1000 shares outstanding.

Gamma plans to pay $2,200 dividend at the end of the current year

liquidating dividend of $4,840 at the end of 2 years from today

TO FIND:-a) . What is the value of your shares of stock? Show calculations to support your answer.

Value of stock is sum of present value of all future dividends.

So,

PV of dividend at end of current year is $2000

Calculation: PV of dividend

= $2200/(1+10%)^1

= $2000

PV of liquidation dividend at 10% required return is $4000.

Calculation: PV of liquidation dividend = 4840/(1+10%)^2

= $4000

Total present value of all the dividend is we havw a formulae

PV of dividend at end of current year+PV of liquidation dividend at 10% required return

==> $2000+$4000 = $6000

Oustanding Shares = 1000

Now, Value of share of each stock = Total PV of dividend/Outstanding shares

Value of share of stock = $6000/1000 = $6

Therefore the value of share of stock is $6.

As we own 100 shares so the value of our shares of stock will be 100*$6 = $600.

TO FIND :-b)Suppose shareholders want Gamma to increase its $2,200 dividend payout at the end of the current year to $4,000 and Gamma increases the dividend by issuing at the end of the current year new stock worth the amount needed to increase the dividend. Will the value of your shares change under this scenario?

company will issue 1800/6 = 300 shares.

New outstanding shares is 1000+300 = 1300 shares.

PV of dividend paid at end of current year is $4000/(1+10%)^1 = $3636.4

PV of liquidation dividend is same as before i.e. $4000

So Total present value of dividend is $3636.4+$4000 = $7636.4

Value of share is total present value of dividend/outstanding shares = $7636.4/1300 = $5.874.

Thus we can see the value of our stock has fallen. Earlier is was $6 per share but now it is $5.874. Now total va;ue of our share is $5.874*100 = $587.4

TO FIND :-c)what will be the change in the current value of your shares under this scenario?

Now the $1800 raised by issuance of new shares is invested for a year with expected return of 21%.

So the future value of this investment will be 1800*(1+21)^1 = $2178.

As the new shares were issued at the end of current year so this future value is at time period of 2 years from now, 1 year when the shares are issued and 1 year for which the raised amount was invested.

So the present value of this invested amount will be $2178/(1+10%)^2 = $1800

PV of the dividend to be paid at end of current year is $2000. (calculated earlier)

Pv of luidation dividend $4000 ( caluclated earlier)

Total PV of all dividend is $1800+2000+4000 = $8000.

Outstanding shares are 1000 as no new shares were issued so value of shares of stock now is $8000/1000 = $8.

The value of our shares is 100*$8 = $800.

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