XYZ Corporation Treasury Bill Investment Yield Calculation

Introduction

In this analysis, we will delve into the investment made by XYZ Corporation into 91-day treasury bills. The corporation has allocated $5,000 to this investment, with the bills offering an interest rate of 2.5%. However, a crucial aspect of this investment is the $30 commission charged by the broker. To accurately assess the profitability of this venture, we need to calculate the yield, taking into account both the interest earned and the commission paid. Understanding the yield is paramount for XYZ Corporation as it provides a clear picture of the actual return on investment, which can then be compared with other investment opportunities. This calculation will not only help in evaluating the current investment but also aid in making informed decisions for future financial strategies. The yield calculation is a fundamental aspect of financial analysis, and its precise determination is essential for effective financial planning and decision-making.

The calculation involves several steps, starting with determining the interest earned on the treasury bills. This is a straightforward calculation based on the principal amount and the interest rate. However, the commission fee introduces a complexity that needs to be carefully addressed. The commission reduces the net return on the investment, and therefore, it must be factored into the yield calculation. The yield is essentially the effective rate of return, considering all costs associated with the investment. This is a more accurate measure of profitability compared to the nominal interest rate, which does not account for transaction costs. Therefore, the yield provides a more realistic view of the investment's performance.

Furthermore, the time frame of the investment, which is 91 days, adds another layer of consideration. Since the yield is typically expressed as an annual rate, we need to annualize the return earned over the 91-day period. This involves scaling up the return to reflect a full year. The method of annualization can vary, and it's important to choose a method that accurately reflects the investment's characteristics. In this case, we will use a simple annualization method, which involves multiplying the 91-day return by the ratio of the number of days in a year to the investment period. This approach provides a reasonable estimate of the annual yield, assuming that the investment's performance remains consistent over the year. The final yield figure will provide XYZ Corporation with a clear understanding of the profitability of their treasury bill investment, considering all factors involved.

Calculating Interest Earned

The initial step in determining the yield is to calculate the interest earned on the treasury bills. XYZ Corporation invested $5,000 at an interest rate of 2.5%. To find the interest earned, we multiply the principal amount by the interest rate. This calculation is a fundamental aspect of understanding the return on any investment. It provides a clear picture of the income generated from the invested capital, before considering any costs or fees. In this case, the interest earned represents the gross return on the investment, which will subsequently be adjusted to account for the broker's commission.

The formula for calculating simple interest is: Interest = Principal × Rate × Time. However, since the interest rate given is an annual rate and the investment is for 91 days, we need to adjust the time component accordingly. The time should be expressed as a fraction of a year. Therefore, we divide the number of days of the investment (91) by the total number of days in a year (365). This adjustment is crucial for accurately calculating the interest earned over the specific investment period. Without this adjustment, the interest calculation would be based on a full year, leading to an overestimation of the actual earnings.

Therefore, the calculation becomes: Interest = $5,000 × 0.025 × (91/365). This calculation will give us the amount of interest earned over the 91-day period. The result will be in the same currency as the principal amount, which is dollars in this case. The interest earned represents the income generated by the investment before accounting for any expenses, such as the broker's commission. This figure is a key component in determining the overall yield of the investment. It provides a baseline for assessing the investment's profitability, which will be further refined by considering the impact of the commission fee.

Accounting for the Broker's Commission

The next crucial step in calculating the yield is to account for the broker's commission. XYZ Corporation was charged a $30 commission for this transaction. This commission represents a cost associated with the investment and directly impacts the net return. It's essential to factor this cost into the yield calculation to get an accurate representation of the investment's profitability. The commission reduces the overall earnings from the investment, and therefore, it must be considered when assessing the true return.

To account for the commission, we subtract it from the interest earned. This will give us the net return on the investment before annualization. The net return represents the actual profit made from the investment after deducting all associated costs. This is a more realistic measure of the investment's performance compared to the gross interest earned, which does not consider the expenses. In this case, the commission is a fixed fee, but in other investment scenarios, commissions can be variable and may depend on the transaction size or other factors. Regardless of the nature of the commission, it's crucial to include it in the yield calculation to accurately assess the investment's profitability.

The calculation involves subtracting the $30 commission from the interest earned, which was calculated in the previous step. This subtraction will result in the net amount earned on the investment over the 91-day period, after accounting for the broker's fee. This net return is a critical figure in determining the yield, as it represents the true profit generated by the investment. The next step will involve annualizing this net return to express the yield as an annual percentage, which is a standard way of comparing investment returns across different time periods.

Annualizing the Return to Determine Yield

To determine the annual yield, we need to annualize the net return earned over the 91-day period. Yield is typically expressed as an annual percentage, making it easier to compare returns across different investments with varying time horizons. Annualizing the return involves scaling up the return earned over the investment period to reflect a full year. This provides a standardized measure of investment performance, allowing for meaningful comparisons between different investment opportunities. Without annualization, it would be difficult to accurately compare investments with different durations.

The formula for annualizing the return is: Annual Yield = (Net Return / Principal) × (365 / Investment Period). In this formula, the net return is the interest earned minus the commission, the principal is the initial investment amount, and the investment period is the duration of the investment in days. The ratio of 365 to the investment period is used to scale up the return to a full year. This calculation assumes that the investment's performance remains consistent over the year, which may not always be the case in reality. However, it provides a reasonable estimate of the annual yield for the purpose of comparison.

By plugging in the values for XYZ Corporation's investment, we can calculate the annual yield. The net return is the interest earned minus the $30 commission, the principal is $5,000, and the investment period is 91 days. The calculation will result in a percentage figure, which represents the annual yield on the investment. This yield figure provides a comprehensive measure of the investment's profitability, taking into account both the interest earned and the commission paid. It allows XYZ Corporation to accurately assess the return on their investment and compare it with other potential investment opportunities.

Final Yield Calculation and Conclusion

Now, let's put all the pieces together to calculate the final yield for XYZ Corporation's investment in 91-day treasury bills. We have already calculated the interest earned, accounted for the broker's commission, and established the method for annualizing the return. The final step is to plug in the values into the annual yield formula and arrive at the result. This final calculation will provide XYZ Corporation with a clear and concise understanding of the profitability of their investment.

The annual yield formula, as previously mentioned, is: Annual Yield = (Net Return / Principal) × (365 / Investment Period). We need to substitute the values we have for each component. The net return is the interest earned minus the $30 commission. The principal is the initial investment amount of $5,000, and the investment period is 91 days. By performing this calculation, we will arrive at the annual yield as a percentage.

This final yield figure is a critical metric for XYZ Corporation. It represents the effective rate of return on their investment, considering all costs and the time frame of the investment. This yield can then be compared with other investment options to assess the relative attractiveness of the treasury bills. A higher yield indicates a more profitable investment, while a lower yield may suggest that other opportunities could provide better returns. Therefore, the yield calculation is a fundamental aspect of financial decision-making, allowing organizations like XYZ Corporation to make informed choices about how to allocate their capital effectively. In conclusion, the yield calculation provides a comprehensive assessment of investment profitability, essential for sound financial planning and strategy.

Therefore, the yield can be calculated as follows:

Interest Earned: $5,000 * 0.025 * (91/365) = $31.16

Net Return: $31.16 - $30 = $1.16

Yield: ($1.16 / $5,000) * (365 / 91) = 0.00931 = 0.09%

The yield for XYZ Corporation's investment is 0.09%.