# RISK FREE DEBT ASSUMPTION IN COST OF CAPITAL

Why it is so important to have an assumption that debt is risk free and the interest rate on debt is the risk free rate?

I keep noting that many corporate valuation textbooks and papers have such explicit assumption.

This assumption is also part of MM Theory.

If debt is risk free that Kd = Rf, which in many cases, analysts will use government bonds as a reference. Why is not using corporate bonds since we are valuing firm (public or private)?

Will this assumption be used because we want to use Book Value of Debt instead of Market Value of Debt? If the Debt is not risk free, what is the impact to WACC or firm valuation?

Kd is only assumed at risk free is a lot confusing.

Kd should be Risk Free + Business Risk Premium

Ke = Risk Free + Business Risk Premium + Financial Risk Premium

Then how come we assume away Kd = Risk Free only?

Risk free debt is very common assumption though I don’t know why is so important to stress this.

See Hamada (1972) paper. He has this assumption as well, risk free here means default free..if this is what it means, then government bond or AAA corporate bonds will be the representative of Default free debt.

Hamada model assumes that tax shield is riskless ( is default risk free or riskless the same?) and thus each period’s tax deduction arising from interest payment shud be discounted back to date 0 at the risk free rate. This implies beta of debt tax shield in the Hamada model is zero.

I resolved this risk free rate assumption for debt.

Risk free here means default risk free, but still includes business risk premium.

Why is default risk free assumption crucial?

It is because we are going to use EXPECTEd rate of return to discount EXPECTED cash flows.

To be EXPECTED rate of return, then it should be default risk free, otherwise it becomes PROMISED rate of return.

For example, a bank wants to lend  \$100 with expected rate of return of 10%, then the actual interest rate the bank will charge the borrower will depend its default probability. The higher the prob % then the higher the promised interest rate it will be charging.

Ignacio Velez-Pareja (Columbia)’s comments

In fact, Kd = Rf + Debt Risk Premium. You can see that in the DB from World Bank. It was a surprise for me because in our model (the xls model I sent you) I said that Kd was estimated as in CAPM: Rf + DRP (debt risk premium). I know that we have been using the wording Kd as risk free, but that is not exact. ANY debt has a risk, but it is lower that the implied risk in Ke

Posted in COST OF CAPITAL.

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