Final answer:
The statement that receiving $10 today has the same value as receiving $1 today and $9 one year from now is false, as it neglects the concept of the time value of money and potential interest earnings that could make the future amount worth more present money.
Step-by-step explanation:
The statement is false because receiving $10 today is not the same value as receiving $1 today and $9 one year from now. This concept involves understanding the time value of money, which indicates that money available now is worth more than the same amount in the future due to its potential earning capacity. This is because money can earn interest or be invested, thereby generating more money. To compare amounts of money from different times, they need to be brought to their present value or future value using a given interest rate.
For example, if we assume an interest rate of 10%, and you want to compare $10 received today to $1 received today and $9 received in one year, you would calculate the future value of $1 for one year as follows: FV = $1 × (1 + 0.10)1 = $1.10. The future value of $9 in one year without any interest would just be $9 since it is already one year out. The total future value would then be $1.10 + $9 = $10.10, which is actually more than $10 today. Therefore, the two scenarios are not equivalent in value.
By the same token, if you wanted to receive $20 million in one year, and the interest rate is 5%, you'd calculate the present value as follows: PV = $20,000,000 / (1 + 0.05)1 = $19,047,619.05.