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Chapter 12: Problem 49

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?

Short Answer

Expert verified
The present value of the business for 20 years is approximately \$2,482,362.57 and forever is about \$5,555,555.56

Step by step solution

01

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.
02

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. \( PV = \$500,000 * e^{-0.09*20} \)
03

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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Most popular questions from this chapter

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