Question

A zero-coupon bond with a market-beta of 0.2 promises to pay $1,000 in the first year. However, it may default and pay nothing with probability 0.1%. If the risk-free rate is 5.3%, the equity premium is 6.5%, and the CAPM is correct, what would be the bond price today?________________ Carry out calculations to at least 4 decimal places. Enter percentages as whole numbers. Example: 3.03% should be entered as 3.03. Do not include commas or dollar signs in numerical answers.

Answer 1

Find the expected return on the bond using the Capital asset pricing
model.
Calculate the payoff from the bond using the probability given.
Using the payoff and the expected return you can calculate the price of the
bond.
The probability that the bond pays zero is .1%.
The probability that the bond pays 1000 is 99.9%.
Expected payoff = .999*1000 + .001*0
Expected payoff = 999
Under the Capital Asset pricing model
Rs = Rf + Beta*(Rm-Rf)
Rs is the expected return on the security
where Rf is the risk free rate that is .053, Rm - Rf = difference between the expected return on the market
portfolio and the riskfree rate. (Rm-Rf) = .065
Beta = .2
Rs = .053 + (.2*.065)
Rs = .066
The expected return on the bond is .066.
Set up the cash flow for the bond and find the price.
Price of bond = present value of future cash flows.
Present Value = Future value/ ((1+r)^t)
where r is the interest rate that is 6.6% and t is the time period
Year	1
Cash flow	999
Present value	937.15
The price of the bond is 937.15.