sascha owns stock in lewis corp and she bought a $5,000 corporate bond. she received $52.50 in quarterly…

sascha owns stock in lewis corp and she bought a $5,000 corporate bond. she received $52.50 in quarterly interest from the bond. sascha also owns stock in lewis corp which is worth $46 per share, and it pays a $2 annual dividend.\n\npart a\nwhich is higher, the yield on the stock or the annual interest rate on the bond? show your work and explain how you determined your solution.\n\npart b\nif the bond matures in seven years, how much will lewis corp have paid sascha in total?\n\npart c\nif sascha owns 1,500 shares of lewis corp, how much would she receive in annual dividends?\n\npart d\nif lewis corporation later offers corporate bonds at an annual interest rate that is one percent higher than half the rate of the bond sascha bought, create an equation that models the quarterly interest earned, q, for any given bond face value, v.

sascha owns stock in lewis corp and she bought a $5,000 corporate bond. she received $52.50 in quarterly interest from the bond. sascha also owns stock in lewis corp which is worth $46 per share, and it pays a $2 annual dividend.\n\npart a\nwhich is higher, the yield on the stock or the annual interest rate on the bond? show your work and explain how you determined your solution.\n\npart b\nif the bond matures in seven years, how much will lewis corp have paid sascha in total?\n\npart c\nif sascha owns 1,500 shares of lewis corp, how much would she receive in annual dividends?\n\npart d\nif lewis corporation later offers corporate bonds at an annual interest rate that is one percent higher than half the rate of the bond sascha bought, create an equation that models the quarterly interest earned, q, for any given bond face value, v.

Answer

Explanation:

Step1: Calculate stock - yield

The formula for stock - yield is $\text{Yield}=\frac{\text{Annual Dividend}}{\text{Stock Price}}$. Given that the annual dividend per share is $$2$ and the stock price per share is $$46$. So, $\text{Yield}=\frac{2}{46}\approx 0.0435 = 4.35%$.

Step2: Calculate bond - annual interest rate

The quarterly interest on the $$5000$ bond is $$52.50$. The annual interest $I = 52.50\times4=$210$. The formula for the annual interest rate $r$ of a bond is $r=\frac{I}{P}$, where $P$ is the principal amount. Here, $P = 5000$, so $r=\frac{210}{5000}=0.042 = 4.2%$. Since $4.35%>4.2%$, the yield on the stock is higher.

Step3: Calculate total payment for bond in 7 years (Part B)

The annual interest payment is $$210$. In 7 years, the total interest payment is $210\times7=$1470$. At maturity, the company also returns the principal of $$5000$. So the total amount paid by Lewis Corp is $1470 + 5000=$6470$.

Step4: Calculate annual dividends for 1500 shares (Part C)

If the annual dividend per share is $$2$ and Sascha owns 1500 shares, then the total annual dividend is $2\times1500=$3000$.

Step5: Calculate new bond - quarterly interest formula (Part D)

The original bond's annual interest rate is $4.2%$. Half of this rate is $0.042\div2 = 0.021$. One percent higher than this is $0.021+0.01=0.031$. The quarterly interest rate $i$ for the new bond is $0.031\div4 = 0.00775$. The formula for quarterly interest $q$ in terms of face - value $v$ is $q = 0.00775v$.

Answer:

Part A: The yield on the stock is higher. Part B: $$6470$ Part C: $$3000$ Part D: $q = 0.00775v$