There are a few different ways to estimate cost of capital (and considerable debate among economists about which ways are best), but since we're given some rates of return and a beta, it looks like they want us to use the Capital Asset Pricing Model (CAPM).
Under CAPM, we estimate the cost of retained earnings k using the market beta B, the market rate of return r, and the risk-free rate of return r0:
k = r_0 + B (r - r0)
We're given all that (we'll use six-month T-bills as "risk free"; this isn't quite true but it's pretty close), so we can just plug them in:
k = 0.0388 + 1.23(0.0950 - 0.0388)
k = 0.107926
Since our previous returns were given in hundredths of a percent, we'll do the same: k = 10.79%
Thus, our cost of retained earnings is estimated at 10.79%, which would be fairly typical for a large corporation.
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