The Harrison Company’s bonds currently sell for $\$1,275$ . They pay a $\$120$ annual coupon, have a $20$ -year maturity, and a par value of $\$1,000$ , but they can be called in $5$ years at $\$1,120$ . If the yield curve remained flat, which rate would investors expect to earn? Group of answer choices

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Q. The Harrison Company’s bonds currently sell for

\$1,275

. They pay a

\$120

annual coupon, have a

20

-year maturity, and a par value of

\$1,000

, but they can be called in

5

years at

\$1,120

. If the yield curve remained flat, which rate would investors expect to earn? Group of answer choices

Calculate Annual Income: To find the expected rate of return, also known as the yield to call (YTC), we need to consider the annual coupon payments, the call price, the current bond price, and the time until the call date.
Calculate Total Gain: First, let's calculate the annual interest income the investor would receive from the coupon payments. $\newline$ Annual coupon payment = $\$120$
Determine Total Cost: Next, we need to calculate the total amount the investor will gain if the bonds are called in $5$ years. This includes the call price plus the total coupon payments until the call date. $\newline$ Total gain from call = Call price + (Annual coupon payment $\times$ Number of years until call) $\newline$ Total gain from call = $\$1,120 + (\$120 \times 5)$ $\newline$ Total gain from call = $\$1,120 + \$600$ $\newline$ Total gain from call = $\$1,720$
Calculate Net Profit: Now, we need to determine the total cost of purchasing the bond at the current price. $\newline$ Total cost = Current bond price = $\$1,275$
Find Yield to Call: The net profit if the bond is called in $5$ years is the total gain from the call minus the total cost. $\newline$ Net profit = Total gain from call - Total cost $\newline$ Net profit = $\$1,720 - \$1,275$ $\newline$ Net profit = $\$445$
Express as Percentage: To find the yield to call, we divide the net profit by the total cost and then divide by the number of years until the call to annualize it. $\newline$ Yield to call (annualized) = $(\text{Net profit} / \text{Total cost}) / \text{Number of years until call}$ $\newline$ Yield to call (annualized) = $(\$(445) / \$(1,275)) / 5$ $\newline$ Yield to call (annualized) = $0$ . $34901960784$ / $5$ $\newline$ Yield to call (annualized) = $0$ . $06980392157$
Express as Percentage: To find the yield to call, we divide the net profit by the total cost and then divide by the number of years until the call to annualize it. $\newline$ Yield to call (annualized) = $(\text{Net profit} / \text{Total cost}) / \text{Number of years until call}$ $\newline$ Yield to call (annualized) = $(\$(445) / \$(1,275)) / 5$ $\newline$ Yield to call (annualized) = $0$ . $34901960784$ / $5$ $\newline$ Yield to call (annualized) = $0$ . $06980392157$ Finally, to express the yield to call as a percentage, we multiply by $100$ . $\newline$ Yield to call (percentage) = \text{Yield to call (annualized)} \times $100$ $\newline$ Yield to call (percentage) = $0$ . $06980392157$ \times $100$ $\newline$ Yield to call (percentage) = $6$ . $980392157$ \%