Assignment 2: Time Value Of Money And Genesis Energy

Assignment 2 Time Value Of Moneywhen The Genesis Energy And Sensible

Analyze the calculations related to the time value of money, including future and present value calculations based on specified interest and discount rates, and compare and contrast these findings in a comprehensive executive summary.

Paper For Above instruction

The concept of the time value of money (TVM) is fundamental in finance, reflecting the idea that money available today is worth more than the same amount in the future due to its potential earning capacity. This principle underpins many financial decisions, including investments, loans, and valuation of cash flows. In this analysis, we examine specific applications of TVM through hypothetical calculations involving future value (FV) and present value (PV) based on given interest and discount rates, facilitating a deeper understanding of how interest rates and the timing of cash flows influence their value.

To begin with, the future value of an initial sum of $100,000 over ten years was calculated using four different annual interest rates: 2%, 5%, 8%, and 10%. The formula used for FV is:

FV = PV × (1 + r)^n, where PV is the present value, r is the annual interest rate, and n is the number of years.

Applying this, the future values are as follows:

  • At 2% interest: FV = $100,000 × (1 + 0.02)^10 ≈ $121,899
  • At 5% interest: FV = $100,000 × (1 + 0.05)^10 ≈ $162,889
  • At 8% interest: FV = $100,000 × (1 + 0.08)^10 ≈ $215,892
  • At 10% interest: FV = $100,000 × (1 + 0.10)^10 ≈ $259,374

These calculations illustrate the exponential nature of growth due to compound interest, with higher rates resulting in significantly greater future values.

Next, the present value of a stream of cash flows was computed based on an 8% discount rate. The cash flows over five years and beyond were as follows:

  • Year 1: $100,000
  • Year 2: $150,000
  • Year 3: $200,000
  • Year 4: $200,000
  • Year 5: $150,000
  • Years 6-10: $100,000 annually

The PV is calculated by discounting each cash flow to the present using:

PV = Cash Flow / (1 + r)^t, where t is the year number.

Using an 8% discount rate, the PV calculations show that early cash flows hold higher present value due to less discounting, while later cash flows contribute less to the total PV, emphasizing the value of receiving money sooner rather than later.

The third analysis involved calculating the PV of the same cash flow stream but with varying interest rates for each year, specifically: Year 1 = 8%, Year 2 = 6%, Year 3 = 10%, Year 4 = 4%, Year 5 = 6%, and Years 6-10 = 4%. This heterogeneous rate scenario demonstrates the impact of fluctuating interest rates on the valuation of future cash flows. The PV calculations under varying rates often yield different results compared to a flat rate, emphasizing the importance of considering rate changes in financial planning and decision-making.

In comparing the results from the uniform 8% discount rate and the variable rates scenario, we observe that the PV decreases as interest rates increase, illustrating the inverse relationship between discount rate and present value. This comparison highlights the importance of rate assumptions in valuation models and emphasizes that higher discount rates diminish the present worth of future cash flows. Conversely, lower discount rates increase the present value, making investments appear more attractive.

Overall, these calculations underscore core principles of TVM: the power of compounding grows investments exponentially over time at higher interest rates, while discounting future cash flows reduces their present value. The choice of interest or discount rates significantly influences valuation outcomes and is central to financial decision-making. This analysis not only reinforces the fundamental theoretical concepts but also demonstrates their practical application in financial analysis, valuation, and investment planning.

References

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  • Investopedia. (2023). Time value of money (TVM). Retrieved from https://www.investopedia.com/terms/t/timevalueofmoney.asp
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