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 Financial Mathematics Old FM Forum

#1
11-13-2017, 05:18 PM
 Futon Member SOA Join Date: Jul 2016 Studying for FM Posts: 128
Stock question

A common stock will pay 2 per share in dividends at the end of the current year. You are given that the earnings of the corporation increase 7% per year indefinitely, the number of shares increases 4% per year indefinitely, and that the corporation plans to continue to pay the same percentage of its earnings in dividends.

The price of the stock 10 years from the beginning of the current year will be X. At that time, the annual effective interest rate is assumed to be 10%.

Calculate X using the dividend discount model.
(A) 36.32
(B) 36.91
(C) 37.35
(D) 37.97
(E) 38.55

I'm not sure what I'm supposed to do here. I'm armed with P=D/(i-k).
#2
11-13-2017, 09:40 PM
 Academic Actuary Member Join Date: Sep 2009 Posts: 8,056

Quote:
 Originally Posted by Futon A common stock will pay 2 per share in dividends at the end of the current year. You are given that the earnings of the corporation increase 7% per year indefinitely, the number of shares increases 4% per year indefinitely, and that the corporation plans to continue to pay the same percentage of its earnings in dividends. The price of the stock 10 years from the beginning of the current year will be X. At that time, the annual effective interest rate is assumed to be 10%. Calculate X using the dividend discount model. (A) 36.32 (B) 36.91 (C) 37.35 (D) 37.97 (E) 38.55 I'm not sure what I'm supposed to do here. I'm armed with P=D/(i-k).
You need to forecast the dividend per share at time 11. The k is the growth rate in dividends per share.
#3
11-15-2017, 01:19 PM
 Futon Member SOA Join Date: Jul 2016 Studying for FM Posts: 128

Quote:
 Originally Posted by Academic Actuary You need to forecast the dividend per share at time 11. The k is the growth rate in dividends per share.
Thanks.

How do I figure out what the dividend is when I'm just given the price? Is it 2=D/(.1-.07)? And what is the relationship between time and the stock price/dividend?
#4
11-15-2017, 10:05 PM
 Academic Actuary Member Join Date: Sep 2009 Posts: 8,056

The assumption of the model is a constant payout ratio so the stock price, earnings per share and the dividend all grow at the same rate. So the dividend yield dividend/stock price is a constant.