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 0.84 . There is also a (1−0.84) probability of paying back only $952. Current market conditions indicate a 5.8% risk-free rate of return and a 7.6% market risk 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

The fair CAPM market price for the municipal bond is calculated by first determining the expected cash flows based on the probabilities of full and partial repayment. It is then discounted by the expected return, which is derived using the CAPM formula given the risk-free rate, the bond's beta, and the market risk premium. The approximate fair CAPM market price for the bond is $911.94.

Step-by-step explanation:

To calculate the fair CAPM market price for the municipal bond, we need to consider both the expected return in the case of full repayment and the expected return in the case of partial repayment, given the probabilities of each event. The CAPM formula given is:

Expected Return = Risk-free Rate + (Beta × Market Risk Premium)

In this case:

• Risk-free Rate = 5.8%
• Beta = 0.3
• Market Risk Premium = 7.6%

So the expected return using CAPM would be:

5.8% + (0.3 × 7.6%) = 7.08%

The expected cash flows are then:

• 0.84 probability of receiving $1000
• 0.16 probability of receiving $952

This gives us an expected value of the cash flows:

(0.84 × $1000) + (0.16 × $952) = $976.32

Now we discount the expected cash flows by the expected return:

Fair price = Expected Cash Flows / (1 + Expected Return)

Fair price = $976.32 / (1 + 0.0708) = $911.94

The fair CAPM market price of the bond, given the risk of default and current market conditions, can be approximated to $911.94.