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 fair market value of this bond investment?

Question

Quizplus · Accepted Answer

To calculate the fair market value of the bond investment, we need to calculate the expected cash flow and discount it back to the present value using the required rate of return. 
The expected cash flow is calculated as follows:

Expected cash flow = (0.96 x $5,000) + (0.02 x $1,000) 
= $4,880

The probability of total default is not taken into account because in case of default, the bondholder will not receive any cash flows.

The required rate of return is calculated as the risk-free rate plus beta multiplied by market risk premium:

Required rate of return = 4% + 0.15 x (10% - 4%) 
= 5.6%

Using the present value formula:

Present value = expected cash flow / (1 + required rate of return) 
= $4,880 / (1 + 5.6%) 
= $4,594.85

Therefore, the fair market value of the bond investment is $4,594.85, which is closest to option B. First, we need to calculate the expected payment from the bond:

Expected payment = ($5,000 x 0.96) + ($1,000 x 0.02) = $4,880

Next, we need to calculate the expected return on the bond:

Expected return = ($4,880 / Fair market value) - 1

Using the one-year Treasury rate of 4% as the risk-free rate, we can use the Capital Asset Pricing Model to estimate the expected return on the market:

10% = 4% + Beta x (expected market return - 4%)

Solving for the expected market return, we get:

Expected market return = (10% - 4%) / 0.15 + 4% = 13.33%

Finally, we can use the expected payment and expected return to calculate the fair market value of the bond:

Fair market value = $4,880 / (1 + 0.1333) = $4,594.85

Therefore, the best choice is B.

A Zero-Coupon Bond Has a Beta of 0