Problem 49
Question
Present Value A business is expected to yield a continuous flow of profit at the rate of \(\$ 500,000\) per year. If money will earn interest at the nominal rate of \(9 \%\) per year compounded continuously, what is the present value of the business (a) for 20 years and (b) forever?
Step-by-Step Solution
Verified Answer
The present value of the business for 20 years is approximately \$2,482,362.57 and forever is about \$5,555,555.56
1Step 1: Understand Continuously Compounding Interest Formula
We can calculate the present value using the formula for continuously compounded interest, which is \( PV = P * e^{-rt} \) where P is the principal amount, r is the interest rate, and t is the time.
2Step 2: Calculate Present Value for 20 Years
Given P = \$500,000 per year, r = 9% = 0.09, and t = 20 years, we can substitute these values into the formula to find the present value for 20 years. \( PV = \$500,000 * e^{-0.09*20} \)
3Step 3: Calculate Present Value Forever
To calculate the present value of a continuing flow, we use the formula \( PV = P / r \). So, \( PV = \$500,000 / 0.09 \).
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