Evaluate The Three Options Sally Hamilton Has To Choose

Evaluate the three options Sally Hamilton has To C

Evaluate the three alternative bonus plans for Sally Hamilton, who has earned a bonus as Chief Financial Officer of Maxtech Computer Company. The options include: (1) a $50,000 cash bonus paid immediately; (2) a $10,000 annual bonus paid over six years, with the first payment now; and (3) a three-year $22,000 annual bonus, with the first payment due three years from now. Sally is earning a 6% annual return on her investments. The task involves analyzing these options through present value calculations, understanding the timing of payments, and determining the most financially advantageous choice for Sally. Additionally, the analysis should include questions about the correct calculation methods for annuities due and deferred annuities, considering the timing of payments and the number of periods involved.

Paper For Above instruction

In the realm of executive compensation, selecting the most advantageous bonus plan requires a thorough understanding of present value calculations, time value of money, and the specific structure of each plan. Sally Hamilton’s case provides an excellent example to explore the nuances of financial decisions, especially when multiple options with different timing and payment structures are available. This analysis aims to determine which bonus plan maximizes Sally's wealth, considering her ability to earn a 6% return annually, and clarifies the essential calculations involved in each option.

Introduction

Executives often face complex decisions regarding compensation plans, which can significantly impact their financial well-being. In Sally Hamilton’s scenario, understanding the present value of each bonus option is critical for making an informed choice. The options vary in timing, amounts, and payment structure, necessitating a detailed financial analysis grounded in principles of the time value of money. This paper systematically evaluates each option, applies appropriate valuation techniques, and discusses the implications for Sally’s decision-making process.

Analysis of Bonus Option 1: Immediate Cash Bonus

The first option offers Sally a $50,000 cash bonus paid immediately. The present value of this option is straightforward, as the payment is made today, with no discounting required. This option provides instant liquidity and certainty of the amount received. Although it does not benefit from any future growth potential, it guarantees the full amount at once. This makes it particularly attractive if Sally values immediate cash or has urgent financial needs. The key aspect here is that the present value equals the nominal $50,000, as there are no further calculations needed.

Analysis of Bonus Option 2: Annuity Due with Payments Over Six Years

The second option involves an annuity due, where Sally receives $10,000 annually over six years, with the first payment occurring immediately. The structure of an annuity due indicates that payments are made at the beginning of each period, which affects the present value calculation. To determine the present value, it is essential to understand the distinction between an ordinary annuity and an annuity due. The present value (PV) of an annuity due can be calculated by first finding the present value of a regular (ordinary) annuity and then multiplying by (1 + r), where r is the interest rate per period. Specifically, the PV of an ordinary annuity of $10,000 for six periods at 6% can be obtained from standard annuity tables or formulas, and then adjusted to account for the earlier payments.

Using the annuity present value formula:

PV = P × [(1 - (1 + r)^-n) / r]

where P = $10,000, r = 0.06, n = 6.

Calculating, we get:

PV = 10,000 × [(1 - (1 + 0.06)^-6) / 0.06] ≈ 10,000 × 4.917 = $49,170.

Since these payments are an annuity due, we multiply by (1 + 0.06):

Adjusted PV ≈ 49,170 × 1.06 ≈ $52,123.

This matches the number provided in the initial evaluation. This present value reflects the value of receiving $10,000 at the start of each year, including the immediate payment. Why is this important? Because it means Sally receives a series of payments that are more valuable than the same amount received at the end of each period, due to earlier receipt and the time value of money.

Analysis of Bonus Option 3: Deferred Annuity

The third option involves a three-year, $22,000 annual bonus, commencing three years from now. This structure is a deferred annuity, and proper valuation requires understanding the timing and present value calculation. Since payments start at the end of three years, the present value at that point is simply the sum of discounted future payments, which are assumed to occur at the end of each year from year three through five.

First, calculate the present value of these future payments at the current time. Each payment is discounted back to today as follows:

PV = Σ [Payment / (1 + r)^t]

where t = 3, 4, 5 for the respective payments.

Calculations:

• Year 3 payment: 22,000 / (1 + 0.06)^3 ≈ 22,000 / 1.191 ≈ $18,491
• Year 4 payment: 22,000 / (1 + 0.06)^4 ≈ 22,000 / 1.2625 ≈ $17,439
• Year 5 payment: 22,000 / (1 + 0.06)^5 ≈ 22,000 / 1.338 ≈ $16,447

Adding these up, the total present value is approximately $18,491 + $17,439 + $16,447 ≈ $52,377.

Alternatively, if we treat it as a deferred annuity starting at year 3, and want the present value at time zero, we could also discount the three future payments to today using the same discount factors, achieving a similar total. This calculation indicates that, despite the deferred payment structure, the present value of the bonus is comparable to the other options when discounted appropriately.

Comparison and Decision-Making

Considering the above calculations, the immediate bonus (Option 1) provides certainty and immediate liquidity, with a present value of $50,000. The annuity due (Option 2) has a higher present value of approximately $52,123, suggesting it is the most financially advantageous when accounting for time value. The deferred bonus (Option 3) has an approximately equal present value of around $52,377, slightly more than Option 2, but close enough that other factors, such as risk, personal preference, and liquidity needs, should also influence Sally's decision.

Notably, the calculations depend heavily on accurate assumptions about timing and discounting. Clarifying whether payments are at the beginning or end of periods (annuity due versus ordinary annuity) is essential in precise valuation. For example, if the $10,000 payments in Option 2 are at the beginning of each period, the present value increases slightly, which favors early receipt of funds. Similarly, understanding the start time of payments in Option 3 influences its present valuation.

Questions Regarding Timing and Calculation Methods

My initial confusion about the timing of payments stems from understanding the distinction between annuity due and ordinary annuity. Specifically, for Option 2, because payments are made at the beginning of each period, I believe I should use the annuity due formula, which has an adjustment factor of (1 + r) to the ordinary annuity present value. A question arises: should I reduce the number of periods by one when calculating the present value for the annuity due, considering that the first payment occurs immediately? The answer is no; the number of periods remains the same, but the present value calculation is adjusted by multiplication, not by altering the period count.

For Option 3, the payments begin after three years, making it a deferred annuity. When calculating the present value of these payments, should I discount each payment back to the present accordingly, or is there a more straightforward approach? The correct method involves discounting each payment individually, as shown, to account for the delay in receiving payments. The question about whether to use 2 or 3 periods is relevant: since payments start after three years, from today's perspective, the first payment is discounted back three years, and similarly for subsequent payments.

Conclusion

Analyzing Sally Hamilton’s bonus options through present value calculations reveals that the second and third options are more valuable than the immediate bonus when considering her 6% investment return. These options leverage the time value of money to grow her wealth over time. However, personal preferences regarding liquidity, risk tolerance, and immediate cash needs may influence her ultimate decision. Clarifying the timing of payments and understanding the application of annuity formulas are critical in making accurate valuations. Overall, based on pure financial calculation, the deferred annuity (Option 3) appears slightly more advantageous, but Sally should align her choice with her personal financial situation and preferences.

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