Recently, David Corporation has paid $3 dividend for each of the outstanding shares. The dividend is...

Recently, David Corporation has paid $3 dividend for each of the outstanding shares. The dividend is expected to be increased at 2% for the next three years, after which the dividend would be increased by 5% per year forever. If the required return of the share is at 10%, what is the value of a share currently?

Expert Solution

Given,
Dividend paid	$3
Growth rate for next 3 years	2%
After 3 years growth rate (perpetuity)	5%
Required return	10%

Calculation of value during abnormal stage

Year	Calculation of dividend	Dividends ($)	Discount factor @10%	PV of dividends ($)
1	3*102%	3.06	0.909090909	2.781818182
2	3.06*102%	3.1212	0.826446281	2.579504132
3	3.1212*102%	3.183624	0.751314801	2.391903832
			Total	7.753226146

Calculation of value during constant stage

As per Gordon model,
*P3= (D3(1+g))/(Re-g)**
3.183624*(1+0.05)/(0.1-0.05)
$66.856104

PV today= $66.856104/(1.1)^3
$50.229980466

Value of share today= $(7.753226146+50.229980466)
$57.9832066

Value of shares currently= $57.98 (rounded off to two decimal places)

Explaination: The value of stock today is equal to present value of all future cashflows expected from the stock discounted at the required rate of return. In the abnormal stage, the dividend was expected to grow @ 2% per year so we need to prepare the table to calculate the present value for the first 3 years. In the constant stage, as the dividend rate was fixed @5% perpetuity so we have applied the Gordon formula. But the value so derived is at t=3 so we have pulled back to get the worth today. After both calculations, the value derived in both the stages is added to get the final value of stock today.

jeff jeffy answered 1 year ago

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