Math Problem Statement

The Saleemi​ Corporation's ​$1 comma 000 bonds pay 11 percent interest annually and have 14 years until maturity. You can purchase the bond for ​$1 comma 075. a.  What is the yield to maturity on this​ bond? b.  Should you purchase the bond if the yield to maturity on a​ comparable-risk bond is 11 ​percent? Question content area top Part 1 ​(Related to Checkpoint​ 9.2)  ​(Yield to​ maturity)  The Saleemi​ Corporation's ​$1 comma 000 bonds pay 11 percent interest annually and have 14 years until maturity. You can purchase the bond for ​$1 comma 075. a.  What is the yield to maturity on this​ bond? b.  Should you purchase the bond if the yield to maturity on a​ comparable-risk bond is 11 ​percent? Question content area bottom Part 1 a.  The yield to maturity on the Saleemi bonds is

enter your response here​%. ​ (Round to two decimal​ places.)

Solution

Part 1: Yield to Maturity (YTM)

The Yield to Maturity (YTM) is the interest rate that equates the present value of the bond's future cash flows to its current price. The formula to calculate YTM approximately is as follows:

YTMC+FPnF+P2\text{YTM} \approx \frac{C + \frac{F - P}{n}}{\frac{F + P}{2}}

Where:

  • CC = Annual coupon payment = 11% of $1,000 = $110
  • FF = Face value of the bond = $1,000
  • PP = Price of the bond = $1,075
  • nn = Number of years to maturity = 14

We can plug the values into this formula.

YTM110+1,0001,075141,000+1,0752\text{YTM} \approx \frac{110 + \frac{1,000 - 1,075}{14}}{\frac{1,000 + 1,075}{2}}

Let's compute this step-by-step.

Part 2: Bond Purchase Decision

Once we calculate the YTM, we will compare it with the yield on a comparable-risk bond, which is 11%. If the YTM of the Saleemi bond is greater than 11%, it is a good investment; otherwise, it's not.

Let me calculate the YTM for you now.### Part 1: Yield to Maturity (YTM) The yield to maturity (YTM) on the Saleemi bond is approximately 10.09%.

Part 2: Should you purchase the bond?

Since the YTM of the Saleemi bond (10.09%) is less than the yield on a comparable-risk bond (11%), it would not be advisable to purchase this bond, as you could potentially earn a higher return with the comparable bond.


Do you have any questions or want further clarification? Here are some related questions to explore:

  1. How does bond price affect the yield to maturity?
  2. What is the difference between yield to maturity and current yield?
  3. How does time to maturity impact the bond's sensitivity to interest rates?
  4. What other factors should be considered when deciding whether to invest in a bond?
  5. What is the impact of a callable bond on yield to maturity?

Tip: When bond prices increase, the yield to maturity decreases, as the fixed coupon payments represent a smaller return relative to the price you paid.

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Math Problem Analysis

Mathematical Concepts

Finance
Yield to Maturity (YTM)
Bond Valuation
Investment Decision-Making

Formulas

Yield to Maturity (YTM) Formula: YTM ≈ (C + (F - P) / n) / ((F + P) / 2)
Where: C = Annual coupon payment F = Face value of the bond P = Price of the bond n = Number of years to maturity

Theorems

Time Value of Money
Yield to Maturity Theory

Suitable Grade Level

College Level (Finance or Economics)