A zero-coupon bond has a beta of 0.1 and promises to pay $1,000 next year with a probability of 98%. If the bond defaults, it will pay nothing. One-year Treasury securities are yielding 5%, and the equity premium is 7%.
-Refer to the information above. What is the promised rate of return on this bond? Round your answer to the nearest tenth of a percent.
A)7.9%
B)2.0%
C)5.7%
D)5.2%

Question

Quizplus · Accepted Answer

The promised rate of return on the bond can be calculated using the expected payment and the current price. The expected payment is $1,000 * 98% = $980. To find the current price (P), we use the formula for the expected return (E[R]) given by the Capital Asset Pricing Model (CAPM): E[R] = risk-free rate + beta * (market return - risk-free rate). Here, the risk-free rate is 5%, the market return can be assumed to be the risk-free rate plus the equity premium, so 5% + 7% = 12%, and beta is 0.1. Thus, E[R] = 5% + 0.1 * (12% - 5%) = 5% + 0.1 * 7% = 5% + 0.7% = 5.7%. However, this is not the promised rate of return; it's the expected return based on CAPM, which doesn't directly apply here.To find the promised rate of return, we consider the promised payment of $1,000 (since we're looking for the promised, not expected, return). The bond will pay $1,000 next year with a 98% probability, but we're interested in the promised return, not the expected return. The promised return is calculated based on the full payment of $1,000, not the expected payment of $980. If we buy the bond today, we need to know how much we pay to get $1,000 next year.Given the information, we don't directly calculate the current price from the given data, but we can infer the promised rate of return from the expected payment and the probabilities. The promised rate of return is essentially the interest rate that would make the present value of the promised payment equal to the current price. Since the question doesn't provide the current price directly but asks for the promised rate of return, we look for the rate that would apply to the full $1,000 payment, not just the expected value.The correct calculation involves finding the yield to maturity on the bond, which is not directly calculable with the provided information without assuming the current price of the bond. However, the question seems to aim at understanding the concept rather than the calculation. Given the misunderstanding in the explanation, the correct approach to find the promised rate of return would involve calculating the yield that equates the present value of the promised payment to the bond's current price, which requires knowing or assuming the bond's current price.Without the current price or more direct information, we cannot accurately calculate the promised rate of return. The explanation mistakenly mixed the concepts of expected return using CAPM and the promised return based on the bond's payment structure. The correct answer should reflect the yield that equates the bond's price to its future payment, considering the bond's risk and market conditions, but the provided information is insufficient for a precise calculation. The intended answer seems to be based on an understanding of the bond's characteristics and market conditions, suggesting a higher return due to the bond's risk profile compared to the risk-free rate, but the exact calculation cannot be completed as intended.

A Zero-Coupon Bond Has a Beta of 0