I do not understand the calculations provided in the solution.

Question:A researcher has determined that a two-factor model is appropriate to determine the return on a stock. The factors are the percentage change in GNP and an interest rate. GNP is expected to grow by 3.6 percent and the interest rate is expected to be 3.1 percent. A stock has a beta of 1.3 on the percentage change in GNP and a beta -.75 on the interest rate. If the expected rate of return on the stock is 12 percent, what is the revised expected return on the stock if GNP grows by 3.2 percent and theinterest rate is 3.4%

Solution Given:

Average beta = {(1.3 *3.6) -.75} /2 = 1.965

Expected Return = 12%

Using the formula :

Expected return = Risk free rate + Beta * Market risk premium

12% = 3.1% +1.965 * Market risk premium

Hence Market risk premium = (12-3.1)/1.965 = 4.52%

Revised Beta = {(1.3 *3.2) -.75} /2 = 1.705

So Revised Expected Return = 3.4% + 1.705*2.40% = 6.81

Please explain how the average beta was calculated. In the solution the beta of GNP (1.3) is multiplied by the expected increase in GNP (3.6%) then they deduct the beta of Interest rates (-.75). Why are they not multiplying the beta on interest rates (-.75) by the expected interest rate of 3.1%? Additionally, they are using the 3.1% interest rate as the Risk Free rate, if this rate was the risk free rate wouldn't it have a beta of 0, instead of -.75? Very confused???