Question

Assume that the tax rate on capital gains is 15%, while the tx rate on dividend income is 20 %. An investor is comparing two options for the stock of ABC firm: I) receive $100 of dividend income now,  II) get unrealized capital gains of $100 now which are left to grow with the firm for five years. The expected rate of return on the stock of ABC firm is 8%. The investor will invest his after-tax dividend income in ABC stock for five years. How much higher after-tax income the investor will get in five years under the capital gains option II than under the dividend income option I (i.e., difference of option II income over option I income)?

	1.	$15.37
	2.	$12.977
	3.	$7.08
	4.	$5.798

Answer 1

Option-1
Receive dividend and then invest in the stock of ABC firm
Dividend	$ 100.00
Dividend tax	20%
Dividend after dividend tax	$   80.00
This is invested in stock @ 8% for 5 years
Amount invested	$   80.00
Return	8%
Time in years	5
Amount accumulated=	Investment * (1+ Interest rate)^Time
Amount accumulated=	80*(1+8%)^5
Amount accumulated=	$ 117.55
Capital gain on this stock=	117.55-80.00
Capital gain on this stock=	$   37.55
Capital gain tax=	15%
Capital gain tax=	37.55*15%
Capital gain tax=	$     5.63
Amount net received net of tax=	117.55-5.63
Amount net received net of tax=	$ 111.91
Option-2
Do not receive dividend and invest in the stock of ABC firm
Profit	$ 100.00
This is invested in stock @ 8% for 5 years
Amount invested	$ 100.00
Return	8%
Time in years	5
Amount accumulated=	Investment * (1+ Interest rate)^Time
Amount accumulated=	100*(1+8%)^5
Amount accumulated=	$ 146.93
This whole amount will be considered as a capital gain.
Capital gain on this stock=	$ 146.93
Capital gain tax=	15%
Capital gain tax=	146.93*15%
Capital gain tax=	$   22.04
Amount net received net of tax=	146.93-22.04
Amount net received net of tax=	$ 124.89
The amount received more than option 1=	124.89-111.91
The amount received more than option 1=	$   12.98
hence option 2 is correct.