Question

Consider a one-year, 10 percent coupon bond with a face value of $1,000 issued by a private corporation. The one-year risk-free rate is 10 percent. The corporation has hit on hard times, and the consensus is that there is a 20 percent probability that it will default on its bonds. If an investor were willing to pay at most $775 for the bond, is that investor risk neutral or risk averse?

Answer 1

Answer:

Suppose we consider the Bond to be risk -free then: after one year the amount to be received by the investor is:

Amount to be received by the investor after one year=Principal Amount on Maturity+Coupon Payment.

Again: Coupon Payment= Coupon Rate*Face Value of the bond .As given in the question: Coupon Rate= 10% and Face Value of the Bond= $1000.Putting these values into the formula for Coupon Payments we get: Coupon Payments= $1000*10% ie. $ 100

Again as given in the question:the principal amount on maturity will be $ 1000(ie. face value).So putting this value and the value of the coupon payment in the formula for Amount to be received by the investor after one year: we get:

Amount to be received by the investor after one year= $1000+$100 ie. $ 1100

Now again as given in the question there is a 20% or.2 chance that the company will default on the payment while there is a 80%(100-20) or 0.8 chance that the company will not default.

So taking the above considerations into effect: the expected payment from this bond will be:

Expected Payment from the bond = Payment without Default * Probability of Default not occurring +Payment with default*Probability of Default occurring

or: Expected Payment from the bond = $1100*0.8+0*0.2 ie. $880.

The value determined as above is one year from now but we need to determine the value today for determination of risk averse or risk neutral nature of an investor so we will determine the present value of the above by using the below formula:

Present Value =Future Value/(1+ Rate of Return)^n where n= time period

Here:Future Value= $880

Rate of Return=Risk Free Rate as given in the question: 10%

n=time period -1 year

Putting these values into the Present Value formula we get:

Present Value= $880/(1+.1)^1 ie. $800

If an investor is risk-neutral then he will be willing to pay $ 800

But in this case the investor is willing to pay only $775 this means that he/she is asking for some compensation for bearing the risks associated with the bond.So the investor is risk averse.