To determine which cash flow a rational person would prefer, we need to consider the time value of money. The idea is that money available now is worth more than the same amount in the future due to its potential earning capacity.
Let's analyze each option:
a. $5,000 per year for 10 years, starting one year from today. This is an annuity and has a present value that needs to be calculated.
b. $5,000 per year for 10 years, starting today. This is also an annuity but starts immediately, which gives it a higher present value compared to option (a).
c. $50,000 paid today. This is the full amount available immediately without any waiting period.
d. $25,000 paid today and $25,000 paid next year. This gives a present value of $25,000 + the present value of $25,000 in one year.
e. $49,000 paid today. This is almost the same as option (c) but slightly less.
To compare these options directly, it's best to think in terms of present values:
- Options (a) and (b) both provide annuities, the one starting today (b) has a higher present value.
- Option (c) is straightforward; $50,000 today is a significant amount.
- Option (d) provides $25,000 today and $25,000 a year later, which is less than $50,000 today but more than $49,000 today (option e).
Considering these comparisons, a rational person would likely prefer:
c. $50,000 paid today
This option offers the highest present value without waiting, maximizing immediate access to funds.