A zero-coupon bond has a beta of 0.15 and promises to pay $5,000 next year with a probability of 96%, $1,000 with a probability of 2%, and there is a 2% probability of total default. One-year Treasury securities are yielding 4%, and the expected return on the market is 10%.
-Refer to the information above. What is the time premium for this bond investment?

Question

Quizplus · Accepted Answer

First, we need to calculate the expected return on the zero-coupon bond:
Expected return = (0.96 x $5,000 + 0.02 x $1,000) / $5,000 = 0.962

Next, we need to calculate the risk premium of the bond:
Risk premium = Beta x (Expected market return - Risk-free rate)
= 0.15 x (10% - 4%) = 0.9%

Finally, we can calculate the time premium:
Time premium = Expected return - Risk-free rate - Risk premium
= 0.962 - 4% - 0.9% = 4.06%, which is closest to B) 4.0%. The expected return on the zero-coupon bond can be calculated as follows: 
(0.96 x 5,000 + 0.02 x 1,000) / 1,000 = 4.88 
The beta is given as 0.15, which means the risk is relatively low. 
Using the CAPM, the expected return on the zero-coupon bond can be calculated as: 
4% + 0.15 x (10% - 4%) = 5.6% 
The time premium is the difference between the expected return and the risk-free rate, so: 
5.6% - 4% = 1.6% 
Therefore, the correct answer is B) 4.0%.

A Zero-Coupon Bond Has a Beta of 0