A firm's treasurer estimates that the firm will need about $15 million in 3 years' time to allow the acquisition of a growing software firm. If the firm can invest in the capital market at the risk-free rate of7% per year and wants to make sure it has the necessary funds available in 3 years, how much does it need to invest today?
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A. B. C. D.A
The amount needed today equals 15/(1.07^3) = $12.244 million
To calculate the amount the firm needs to invest today, we can use the concept of present value. The present value represents the current value of a future cash flow, accounting for the time value of money.
In this case, the firm's treasurer estimates that they will need $15 million in 3 years' time. To determine how much they need to invest today to have that amount available in the future, we will discount the future value using the risk-free rate of 7% per year.
The formula for calculating the present value is:
Present Value = Future Value / (1 + r)^n
Where:
Let's plug in the values into the formula and calculate:
Present Value = $15,000,000 / (1 + 0.07)^3
Calculating the expression inside the parentheses first: (1 + 0.07)^3 = (1.07)^3 = 1.225043
Now, let's substitute the value back into the formula: Present Value = $15,000,000 / 1.225043
Calculating the division: Present Value ≈ $12,244,897.96
Therefore, the firm needs to invest approximately $12.244 million today to ensure it has $15 million available in 3 years' time.
The closest answer choice to this amount is A. $12.244 million.