Let's solve step-by-step: ### Given Data - Face value of bond (\(FV\)) = **$1,000** - Coupon rate = **9%** - Annual coupon payment (\(C\)) = 9% of $1,000 = **$90** - Years to maturity (\(N\)) = **9** - Current price (\(P\)) = **$955** We are to find the **Yield to Maturity (YTM)**. --- ## Step 1: YTM Formula (Approximation) The YTM can be approximated using the following formula: \[ YTM \approx \frac{C + \frac{F - P}{N}}{\frac{F + P}{2}} \] Where: - \(C\) = Annual coupon payment = $90 - \(F\) = Face value = $1,000 - \(P\) = Price = $955 - \(N\) = Years to maturity = 9 --- ## Step 2: Plug in the Values First, calculate the numerator: \[ C + \frac{F - P}{N} = 90 + \frac{1,000 - 955}{9} = 90 + \frac{45}{9} = 90 + 5 = 95 \] Calculate the denominator: \[ \frac{F + P}{2} = \frac{1,000 + 955}{2} = \frac{1,955}{2} = 977.50 \] Plug into the formula: \[ YTM \approx \frac{95}{977.50} = 0.0972 \] Convert to percentage: \[ YTM \approx 9.72\% \] --- ## Step 3: Final Answer **The yield to maturity on the Saleemi bonds is \(\boxed{9.72\%}\).** --- ## Step 4: Should you purchase the bond? - The YTM on this bond is **9.72%** - The YTM on a comparable-risk bond is **11%** **Since the comparable bond yields more (11% > 9.72%), you should not purchase the Saleemi bond, as you can get a higher return elsewhere for the same risk.** --- ## **Summary Table** | | Saleemi Bond | Comparable Bond | |--------------------|:-----------:|:--------------:| | Yield to Maturity | 9.72% | 11% | **You should not purchase the Saleemi bond.** --- ### **Final Answers** **a. The yield to maturity on the Saleemi bonds is 9.72%.**

Let's analyze how to determine that the yield to maturity (YTM) on a comparable-risk bond is 11%, and how to interpret this information. --- ### Understanding the Context - **Saleemi Bond**: - Price: $955 - Face Value: $1,000 - Coupon Rate: 9% (annual coupon = $90) - Maturity: 9 years - Calculated YTM: approximately **9.72%** (from previous calculation) - **Comparable-Risk Bond**: - Yield: **11%** --- ### How do we know the comparable-risk bond has an 11% YTM? 1. **Market Information or Given Data**: - Usually, in such problems, the yield on a comparable-risk bond is provided as a market benchmark or is derived from market data. - The problem states: *"if the yield to maturity on a comparable-risk bond is 11%,"* which indicates that this is a given or known market rate for bonds with similar risk and maturity. 2. **Implication of the Comparable Risk**: - Since the bonds are of comparable risk, investors would require an **11%** return on similar bonds. - This is based on market conditions, risk premium, and interest rate environment. 3. **Comparison of Yields**: - Our calculated YTM for the Saleemi bond is **9.72%**, which is **less than** the 11% yield on the comparable-risk bond. --- ### Why is this important? - **Investment Decision**: - If you can buy a similar-risk bond offering **11%**, but Saleemi's bond offers only **9.72%**, the Saleemi bond provides **less return** for the same risk. - Investors would prefer the **higher-yielding** bond unless the Saleemi bond has other advantages (e.g., higher safety, tax benefits, etc.). --- ### **Summary** - The **11% yield** on the comparable-risk bond is typically given or derived from market data. - It reflects the **current market expectation** for returns on bonds with similar credit risk and maturity. - Since the Saleemi bond's YTM (9.72%) is **less than** the market comparable (11%), the Saleemi bond **may be less attractive** unless other factors justify its purchase. --- **Final note**: In practice, the 11% yield is often obtained from **market quotes**, **interest rate comparisons**, or **yield curves** for similar bonds. Here, it’s given as a benchmark to compare against the calculated YTM. --- **In short:** **The 11% yield on a comparable-risk bond is provided as market information or benchmark data, indicating the return investors require for similar risk.**