A money manager is holding the following portfolio:

            Stock     Amount Invested	Beta
              1	       $300,000		0.6
              2	        300,000		1.0
              3	        500,000		1.4
              4	        500,000		1.8

The risk-free rate is 6 percent and the portfolio's required rate of
return is 12.5 percent. The manager would like to sell all of her
holdings of Stock 1 and use the proceeds to purchase more shares of
Stock 4. What would be the portfolio's required rate of return
following this change?

Answer is simple:

The beta of the portfolio is the weighted average of individual betas,
which is changing after the sale of stock 1 and the purchase of stock
4.
The CAPM formula describes the required rate of return: rj=rf+ß(rm-rf)
with rj being the required rate, rf being the risk-free rate and rm
being the market rate.
Firstly, solve portfolio a for the market rate.
Secondly, since rm and rf do not change, solve portfolio b for the
adjusted required rate.

Portfolio a (original)		
Stock	Invested	Beta	Weight	Portfolio's beta
1	300000	0,60	0,1875	0,1125
2	300000	1,00	0,1875	0,1875
3	500000	1,40	0,3125	0,4375
4	500000	1,80	0,3125	0,5625
 	1600000	 	 	1,3
				
CAPM  Rj=Rf + Beta (Rm-Rf)		
 	Rj	Rf	Beta	Rm
Portfolio a	12,50%	6%	1,3	11%
				
				
Portfolio b (changed)		
Stock	Invested	Beta	Weight	Portfolio's beta
1	0	0,60	0	0
2	300000	1,00	0,1875	0,1875
3	500000	1,40	0,3125	0,4375
4	800000	1,80	0,5	0,9
 	1600000	 	 	1,525
				
CAPM  Rj=Rf + Beta (Rm-Rf)		
	Rj	Rf	Beta	Rm
Portfolio b	13,63%	6%	1,525	11%

Literature: Keown/Martin/Petty/Scott, Financial Management, 11th ed., pages 205ff
regards FinanceProf