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Perpetuities

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5. Perpetuities are often used to value merger and acquisition targets.
a) What is the present value of a stable perpetuity of $100,000 per year that
starts at the end of year one and continues to infinity? The appropriate
discount rate is 10%.
b) What is the present value of a stable perpetuity of $100,000 per year that
starts at the end of year five and continues to infinity? The appropriate
discount rate is 10%.
c) What is the present value of a growing perpetuity that starts at $50,000 at
the end of year one and grows at a 4% annual rate? The appropriate
discount rate is 10%.
d) What is the present value of a growing perpetuity that starts at $50,000 at
the end of year five and grows at a 4% annual rate? The appropriate
discount rate is 10%.

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The solution explains some calculations relating to perpetuities

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