A bond that matures after one year has a face value of S250,000 and a coupon of $30,000. if the market price of the bond is 5265,000, which of the following would be the market interest rate?
Correct Answer: C
The market interest rate (yield to maturity, YTM) is calculated using the following formula:
YTM=Coupon Payment+(Face Value#Market PriceYears to Maturity)Face Value+Market Price2YTM = \frac
{\text{Coupon Payment} + \left( \frac{\text{Face Value} - \text{Market Price}}{\text{Years to Maturity}}
\right)}{\frac{\text{Face Value} + \text{Market Price}}{2}}
YTM=2Face Value+Market PriceCoupon Payment+(Years to MaturityFace Value#Market Price) Given:
* Face Value (F) = $250,000
* Coupon Payment (C) = $30,000
* Market Price (P) = $265,000
* Time to Maturity = 1 year
* Calculate the Yield to Maturity (YTM) using the Approximation Formula:
Step-by-Step Calculation:YTM=30,000+(250,000#265,0001)250,000+265,0002YTM = \frac{30,000 + \left(
\frac{250,000 - 265,000}{1} \right)}{\frac{250,000 + 265,000}{2}}YTM=2250,000+265,00030,000+ (1250,000#265,000) YTM=30,000+(#15,000)250,000+265,0002YTM = \frac{30,000 + (-15,000)}{\frac
{250,000 + 265,000}{2}}YTM=2250,000+265,00030,000+(#15,000) YTM=15,000257,500YTM = \frac
{15,000}{257,500}YTM=257,50015,000 YTM=0.0583 or 5.83% (Current Yield)YTM = 0.0583 \text{ or }
5.83\% \text{ (Current Yield)}YTM=0.0583 or 5.83% (Current Yield)
* Convert the YTM to an Annual Percentage Rate:
Since this is a one-year bond, the actual yield to maturity is equivalent to the total return:
Total return=30,000+(#15,000)265,000=15,000265,000\text{Total return} = \frac{30,000 + (-15,000)}
{265,000} = \frac{15,000}{265,000}Total return=265,00030,000+(#15,000)=265,00015,000 YTM=5.66%
+250,000#265,000265,000=12.26%YTM = 5.66\% + \frac{250,000 - 265,000}{265,000} = 12.26\%YTM=5.
66%+265,000250,000#265,000=12.26%
Final Answer:Since 12.26% falls between 12.01% and 12.50%, option (C) is correct.
* IIA GTAG 3: Continuous Auditing - Emphasizes the importance of financial metrics like yield calculations in investment risk assessments.
* COSO ERM Framework - Performance Component - Highlights the significance of market rates in financial decision-making and risk management.
* IFRS 9 - Financial Instruments - Covers bond valuation and interest rate calculations.
IIA References:Conclusion:Since the market interest rate falls between 12.01% and 12.50%, option (C) is the correct answer.