Question

There are two bonds on sale the investors can choose from: Bond A: 4-year, 10% coupon rate, $1,000 face value. Bond B: 30-year, 8% coupon rate, $1,000 face value. Investors may have access to different information or interpret the information differently which would cause them to arrive at different conclusions regarding the evaluation of assets. Assume that investor I sees both bonds as risky investments and asks a promised yield of 12% from each. Investor II does not see them as risky investments. Assume further that the market rate (alternative investment rate) for both investors is 10%. a) (10 points) What would be the maximum price each investor would be willing to pay for each bond today? b) (10 points) Assume that 20% of the investors of type I and 80% of them are of type II. The market price of each bond today is obtained by: 20%* max Price of Investor I + 80% * Max Price of Investor II (Note that this is a pretty good proxy for how the market price would be arrived at in real world) Then, which investor would buy which bond, if any? c) (20 points) Assume one year passes and the first coupons are just distributed. Assume that all uncertainty regarding these bonds have been resolved and it is public information now that the bond issuers will be able to pay all coupons and the face values at the required times. What is the annual return of each investor?

Answer 1

a) For investor 1:

For investor 2: (He/she will be happy with 10% since he/she does not consider this risky)

b) Market price of bond 1 = (0.2*939.3)+(0.8*1000) = 987.85

Only second type of investors will buy this bond. First type wont pay more than 939.3

Market price for second bond = (0.2*677.79)+(0.8*811.46) = 784.726

Only second type of investors will buy this bond.

c) From b prices of the bonds in the beginning were as following:

Bond 1: 987.85

Bond 2: 784.726

After one year prices will be calculated with yield as 10%. Hence new prices will be:

The risk averse investor wouldn't have bought any of the bonds in first year and therefore this return is for the second investor who bought the bond