Question

A $1,000 municipal bond is in danger of default, and you are a bond-holder trying to sell the asset at a fair price. The municipality is facing uncertainty in the face of decreasing tax revenues, but is expected to repay the bond in its entirety with probability 0.71. There is also a (1-0.71) probability of paying back only $950. Current market conditions indicate a 6% risk-free rate of return and a 5.7% equity premium, and the bond has a beta of 0.3. What would you conclude is a fair CAPM market price, in dollars, for this bond?

Answer 1

Using the CAPM model, given a risk-free rate of 6%, beta of 0.3, and equity premium of 5.7%, the expected rate of return is 7.71%. Factoring in default risk, the expected recovery is $995, leading to a fair CAPM market price for the municipal bond of approximately $923.52.

Step-by-step explanation:

To determine a fair market price for a $1,000 municipal bond using the Capital Asset Pricing Model (CAPM), we have to consider the expected rate of return based on the bond's risk. The CAPM formula is expressed as:

Expected return = Risk-free rate + (Beta × Market risk premium)

Given a risk-free rate of 6%, a beta of 0.3, and an equity premium of 5.7%, the expected rate of return can be calculated as:

Expected return = 0.06 + (0.3 × 0.057) = 0.06 + 0.0171 = 0.0771 or 7.71%

Now, considering the default risk, the expected recovery on the bond is 0.71 × $1,000 + (1 - 0.71) × $950 = $710 + $285 = $995.

The fair price of the bond can be calculated based on the expected recovery and the required rate of return:

Fair price = Expected recovery / (1 + Expected return) = $995 / (1 + 0.0771) ≈ $923.52

Thus, considering the default risk and the CAPM expected return, a fair CAPM market price for the bond would be approximately $923.52.