To determine which cash flow option a rational person would prefer, we can consider the time value of money, which states that money today is worth more than the same amount in the future because of its potential earning capacity.
Let's analyze the options:
a. $5,000 per year for 10 years with the first payment made one year from today: This is an annuity. Over 10 years at a certain interest rate, the future value will be less than its present value.
b. $5,000 per year for 10 years with the first payment made today: This is a slightly better annuity since the first payment is made immediately, increasing its overall present value.
c. $50,000 paid today: This is a lump sum payment received immediately, giving the full amount for investment or consumption right away.
d. $25,000 paid today and $25,000 paid next year: This option provides some immediate cash flow and another payment after one year. The present value of the second payment will reduce the overall value compared to a lump sum today.
e. $49,000 paid today: This is a lump sum payment that is less than option c, but still received immediately.
Comparing these options, the preference will typically go toward the option that gives the most total value when present-valued. Here’s a simplified comparison based on the time value of money:
- Option c ($50,000 paid today) provides a higher cash flow today than any other option.
- Option b provides a total for future payments, but less than $50,000 total present value.
- Option d has a future payment, thus additional reduced present value.
- Option e is less than option c but still received immediately.
- Option a is an annuity with future payments and will provide less overall value compared to other earlier payments.
In summary, a rational person would prefer Option c: $50,000 paid today as it provides the highest present value immediately.
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