Petroleo Brasileiro (PBR) has just issued 1M one year bonds. Each bond hasa face value of1,000 Reais. Owners of the bonds are entitled to receive $R 1000 back at the end of the yearalong with 80 of interest. The bonds were sold for par which means each bond was sold for$R 1,000 or a price which is equal to face value.
a) What is the coupon rate on the bond? What is the promised rate on the bond?
b) The current one year risk free rate is 5% and the market price of risk is 8.5. If the return on the bond is uncorrelated with the return on the market, what is theexpectedreturn on the bond? Hint: If the return on the bond is uncorrelated with the market, what does this imply about the β of the bond?
c) Petroleo Brasileiro bonds are risky in the sense they could default. If the market isassuming that investors will receive only 750 for each bond they own if the bondsdefault, what does the market think is the probability that the bonds will default.
Hint: - how is the probability of default related to the expected return on the bonds?