You are considering two lottery payment options: Option A pays $10,000 today and Option B pays $20,000 at the end of ten years. Assume youc an earn 6 percent on your savings. Which option will you choose if you base your decision on present values? Which option will you choose if you base your decision on future values? Explain why your answers are either the same or different.
If I base my decision on present values I’d go with Option B. The PV of Option A is $10,000 as it’s year one and we have $10,000 in hand. If I elect to go with Option B than I receive $20,000 at the end of ten years, assuming 6% discount rate. Via the formula below, the present value of Option B is over $11,000. PV Option B (>$11,000) is greater than PV Option A ($10,000), thus I’d go with Option B.
PV = FV (1/(1+r)^n
Where FV = Future value; r= rate of return and n = number of periods.
However, if I’m basing my decision on the future value, and I believe I can make more than 6% on my money via the stock market, treasury bonds, corporate bonds or other alternatives than I’d choose Option A. To play this scenario out; if I make 6% on my money annually via savings interest, I’d turn my $10,000 in Option A into ~$18,000. This is not as lucrative as the $20,000 I’d get in Option B. However, if I can make 8% on my $10,000 annually than my future value would be ~$21,500. Given my risk tolerance and basic investment philosophy, I’d take my chances and try to return 8% a year. I’d included FV formula for reference.
FV = PV x (1+r)^n
Where PV = Present value; r = rate of return and n = number of periods.
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To determine which lottery payment option to choose, we need to calculate the present value and future value of each option. The present value represents the current worth of a future sum of money, while the future value represents the value of an investment over a specified period of time.
Let's start by calculating the present value of each option by using the formula for present value (PV) of a future cash flow:
PV = FV / (1 + r)^n
Where:
- FV is the future value
- r is the interest rate
- n is the number of periods
Option A pays $10,000 today, so its present value (PV) is $10,000.
Option B pays $20,000 at the end of ten years. To calculate its present value, we need to determine the present value of $20,000 received in ten years at an interest rate of 6%. Using the formula, we have:
PV = $20,000 / (1 + 0.06)^10
PV = $20,000 / (1.06)^10
PV = $20,000 / 1.790847
PV ≈ $11,169.07
If we base our decision on present values, we would choose Option A, as it has a higher present value ($10,000) compared to Option B's present value ($11,169.07).
Now, let's calculate the future value of each option by using the formula for future value (FV) of a present cash flow:
FV = PV * (1 + r)^n
Option A has a present value of $10,000. To calculate its future value in ten years at an interest rate of 6%, we use the formula:
FV = $10,000 * (1 + 0.06)^10
FV = $10,000 * (1.06)^10
FV = $10,000 * 1.790847
FV ≈ $17,908.47
Option B has a future value of $20,000 received at the end of ten years, so its future value (FV) is $20,000.
If we base our decision on future values, we would choose Option B, as it has a higher future value ($20,000) compared to Option A's future value ($17,908.47).
In this scenario, the decision based on present values and future values is different. The reason for this disparity is the effect of compounding. By choosing the higher present value, we are prioritizing the immediate value of the money. On the other hand, by choosing the higher future value, we are considering the potential growth and interest earned over time. Ultimately, the decision depends on individual preferences, financial goals, and time preferences regarding value.