cost of equity question??

How does the cost of equity change with lowered interest rates on the debt in the cap structure (assume all else is equal; ie not a floating rate that changes due to an decrease in the risk free rate (as this would clearly affect the CAPM formula)). BIWS claims that lowered interest rate don't affect cost of equity, but if increasing tax rates push down cost of equity (levered beta formula that gets plugged into CAPM) due to the reduced impact of the debt, then why couldn't you say the same thing about lowering the interest rates directly. Thanks

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Comments (8)

  • Analyst 1 in IB-M&A
Jun 29, 2020 - 12:24pm

A change in the risk free rate would alter the cost of equity. Thinking about the cost of equity, it's derived from the company's ability to outperform the risk free rate based on the leverage of the company, sensitivity to market changes, and other idiosyncratic factors. If you look at the formula, increases and decreases of interest rates affect the result.

CAPM= risk free rate + levered beta*(market risk return - risk free rate)

If rates were to increase, CAPM would decrease, and vice versa.

Jun 29, 2020 - 1:38pm

What do you mean? If you increase interest rates, you are decreasing WACC? How is that possible?

Array

  • Analyst 1 in IB-M&A
Jun 29, 2020 - 2:31pm

Try for yourself and plug some numbers in:

Scenario 1: Rfr= 2, Beta= 1.5, Mr= 6

CAPM= 2+ 1.5*(6-2) = 8

Scenario 2 (rate increase): Rfr= 2.5, Beta= 1.5, Mr= 6

CAPM= 2.5+ 1.5*(6-2.5) = 7.75

If all else remains the same, CAPM decreases if rates increase. However, this isn't always the case. Market returns are susceptible to change when there are increases or decreases in rates. I just calculated this based on all other assumptions remaining constant.

Jun 29, 2020 - 2:56pm

I see what you got there. Now change the Beta. Use 1.0 or a Beta

Array

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Jun 29, 2020 - 1:56pm

i think u mean capm would increase as well, but my point wasn't about risk free rates-as that relationship is clear with capm. my point is say you have a fixed rate note at 5% and with a constant risk free rate it hypothetically gets swapped for say 6%. what happens to cost of equity then? biws says it would stay the same but i dont understand that if a decreasing tax rate does essentially the same thing by raising the effective cost of debt which in turn increases the cost of equity (seen with levered beta formula)

Jun 30, 2020 - 5:29am

Interest rate is the absolute value while tax rate is the relative value. If I understand your point, your argument is that a higher / lower interest rate is akin to a higher / lower tax shield from a kE perspective, but it's not. You're getting a relative % of a value in the form of tax shield. That % is dependent on an absolute value. If your interest rate goes up or down, you're still getting that same % nonetheless, hence why increasing or decreasing a rate is irrelevant to the cost of equity formula. If you increase or decrease tax rates, that has a direct impact into your beta due to the tax shield changing

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