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I start my disclaimer that i might be wrong..But i must give it a Try...

Now According to the cost of equity formula it is =Rf+B(Risk premium),,,,risk premium is nothing but the difference b/w Rm-Rf.....so the equation becomes Rf+B(Rm-Rf)..here Rm is Expected returns from the stock........

When the Rf increases Ist part of the equation increases the cost of equity whereas if we see the second part of the equation decreases the cost of Equity(If Rm is kept constant)......but As Rf increases the Rm also increases and hence the The Second part of the equation Also increases so the effect of Increases Cost of equity....


I hope i made some sense....


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Q: Why would the cost of equity increase if the risk-free rate increases?
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