Questions: An investor has 1,350 to invest, and his financial analyst recommends two types of juric bonds. The A bonds have a 9% annual yield with a default rate of 7%. The B bonds have a 6% annual yield with a default rate of 3%. (If the bond defaults, the 1,350 is lost) Which of the two bonds is better? Why? Should he select either bond? Why or why not? Which of the two bonds is better? Why? A. The A bonds are better because its expected value is lower than the B bonds. B. The B bonds are better because its expected value is greater than the A bonds. C. The B bonds are better because its expected value is lower than the A bonds. D. The A bonds are better because its expected value is greater than the B bonds.

An investor has 1,350 to invest, and his financial analyst recommends two types of juric bonds. The A bonds have a 9% annual yield with a default rate of 7%. The B bonds have a 6% annual yield with a default rate of 3%. (If the bond defaults, the 1,350 is lost) Which of the two bonds is better? Why? Should he select either bond? Why or why not?

Which of the two bonds is better? Why?
A. The A bonds are better because its expected value is lower than the B bonds.
B. The B bonds are better because its expected value is greater than the A bonds.
C. The B bonds are better because its expected value is lower than the A bonds.
D. The A bonds are better because its expected value is greater than the B bonds.

Transcript text: An investor has $\$ 1,350$ to invest, and his financial analyst recommends two types of juric bonds. The A bonds have a $9 \%$ annual yield with a default rate of $7 \%$. The B bonds have a $6 \%$ annual yield with a defautt rate of $3 \%$. (If the bond defaults, the $\$ 1,350$ is lost) Which of the two bonds is better? Why? Should he select either bond? Why or why not? Which of the two bonds is better? Why? A. The A bonds are better because its expected value is lower than the B bonds. B. The B bonds are better because its expected value is greater than the A bonds. C. The B bonds are better because its expected value is lower than the A bonds. D. The $A$ bonds are better because its expected value is greater than the $B$ bonds.

Solution

Solution Steps

Step 1: Calculate Expected Value for Bond A

The expected value for Bond A can be calculated using the formula:

\[ \text{Expected Value}_A = (1 - \text{default rate}_A) \times (investment \times (1 + \text{yield}_A)) - (\text{default rate}_A \times investment) \]

Substituting the values:

\[ \text{Expected Value}_A = (1 - 0.07) \times (1350 \times (1 + 0.09)) - (0.07 \times 1350) = 1273.995 \]

Step 2: Calculate Expected Value for Bond B

The expected value for Bond B is calculated similarly:

\[ \text{Expected Value}_B = (1 - \text{default rate}_B) \times (investment \times (1 + \text{yield}_B)) - (\text{default rate}_B \times investment) \]

Substituting the values:

\[ \text{Expected Value}_B = (1 - 0.03) \times (1350 \times (1 + 0.06)) - (0.03 \times 1350) = 1347.57 \]

Step 3: Compare Expected Values

Now we compare the expected values of both bonds:

\[ \text{Expected Value}_A = 1273.995 \quad \text{and} \quad \text{Expected Value}_B = 1347.57 \]

Since $ 1273.995 < 1347.57 $, Bond B has a higher expected value.