How to get the answer 1/7 and 6/7,pls work out and explain in details,thanks!

A firm with an asset beta of 0.5 has a quarter of its assets as excess cash ("excess cash" means that this cash is not being used to sustain the operations of the firm and is simply invested in Government bonds). Suppose the firm pays half of its excess cash to shareholders and invests the other half in the market (i.e., in an exchange traded index fund such as the SPDR S&P/ASX 200 Fund). What is the firm's asset beta now? beta_A = V(Cash)/V beta_Cash + V(Non - Cash)/V beta_Non-cash 0.5 = 1/4 times 0 + 3/4 beta_Non-cash beta_Non-cash = 4/3 times 0.5 = 2/3 After the return of the cash, 6/7 of the firm is invested in the Non-cash assets and 1/7 in the market. So the new asset beta is: beta_Asset-post = 6/7 times 2/3 + 1/7 times 1 = 0.71