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According to this site, the present value of tax shield of constant and perpetual debt is:

corporate tax rate × interest payment ÷ expectd return on debt

I understand the part about "corporate tax rate × interest payment". But why is expectd return on debt be divided here? (I think that it is also not from summing geometric sequence.)

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  • $\begingroup$ In general you find the value of a perpetuity by dividing the annual payment by the interest rate: $PV=\frac{C}{i}$ (so called Consol Formula). Here for $i$ they are using "expected return on debt". $\endgroup$ – noob2 Oct 14 '20 at 14:52
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    $\begingroup$ Thank you. I find answer here: quant.stackexchange.com/questions/22294/… $\endgroup$ – Aqqqq Oct 14 '20 at 14:55
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Interest payment is determined by the bond (either fixed or variable), expected return varies according to market movements. It is effectively the discount factor.

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