Question

A group of investors decides to invest $500,000 in the stocks of three companies.

• Company D sells for $60 a share and has an expected growth of 16% per year
• Company E sells for $80 a share and has an expected growth of 12% per year
• Company F sells for $30 a share and has an expected growth of 9% per year.

The group plans to buy twice as many shares of company F as of company E. If the group’s goal is 14.52% growth per year. How many shares of each stock should the investors buy?

Answer 1

Company	No.of shares	$ /share	Growth rate /yr.
E	x	80	1.12
F	2x	30	1.09
D		60	1.16

Amt. to be invested = 500000

Equating the money values of individual stock's growth & the overall growth ,

with data from the above table,

(1.12*(80*x))+(1.09*(30*2x))+(1.16*(500000-140x))=1.1452*500000

& solving for x, we get,

x=no.of shares of Company E= 1000

so, no.of shares of Company F= 1000*2=2000

& no.of shares of Company D=(500000-(1000*80)-(2000*30))/60= 6000

So, the

ANSWER is;

Shares of each stock the investors should buy is:

Company
D	6000
E	1000
F	2000

VERIFICATION:
Company	No.of shares	$ /share	Initial value	Growth rate /yr.	Value at end of 1 yr.
1	2	3	4=2*3	5	6=4*5
E	1000	80	80000	1.12	89600
F	2000	30	60000	1.09	65400
D	6000	60	360000	1.16	417600
			500000		572600
Overall growth (572600-500000)					72600
Overall growth rate= 72600/500000					14.52%