A zero-coupon bond matures in one year and has a market-beta of 0.2. It has a 30% probability of defaulting, in which case investors will receive only 80% of the promised cash
Flow. The relevant risk-free rate is 4% and the risk premium is 6%. What is the maximum
Price at which this bond should sell (per $100 of par value)?
A)$89.35
B)$94.00
C)$66.54
D)This cannot be determined with the information provided.

Question

Quizplus · Accepted Answer

To calculate the maximum price at which this bond should sell, we first need to determine the expected cash flow, taking into account the probability of default. If the bond does not default, the investor receives $100 at maturity. If it defaults, the investor receives 80% of $100, which is $80. The expected cash flow (ECF) can be calculated as follows:$$ ECF = (1 - 0.3) \times 100 + 0.3 \times 80 = 0.7 \times 100 + 0.24 \times 100 = 94 $$Next, we need to discount this expected cash flow back to present value using the appropriate discount rate. The bond has a market-beta of 0.2, so its expected return can be calculated using the Capital Asset Pricing Model (CAPM):$$ Expected\ Return = Risk\ Free\ Rate + Beta \times Market\ Risk\ Premium $$$$ Expected\ Return = 4\% + 0.2 \times 6\% = 4\% + 1.2\% = 5.2\% $$The present value (PV) of the expected cash flow is then:$$ PV = \frac{ECF}{(1 + Expected\ Return)} = \frac{94}{1 + 0.052} = \frac{94}{1.052} \approx 89.35 $$Therefore, the maximum price at which this bond should sell is approximately $89.35 per $100 of par value.

A Zero-Coupon Bond Matures in One Year and Has a Market-Beta