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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%.

https://brainmass.com/economics/barriers-to-growth/perpetuities-227498

#### Solution Summary

The solution explains some calculations relating to perpetuities

\$2.19

## Differences between perpetuities and annuities

Describe the differences between perpetuities and annuities. Give examples of both types of products.

https://personal.vanguard.com/us/funds/byobjective/detail?category=LifeCycle
http://www.johnhancock.com/products/annuities.html

? Find one example of a perpetuity.
? Find one example of an annuity.
? How is the perpetuity structured?
? How is the annuity structured?
? Why would an investor prefer one product over the other?
? Keeping the time value of money in mind with respect to the initial cash out-lay, what does a preference of one product over the other say about the investors feeling of the time value of money?
? How does the time value of money impact the eventual returns of both products?
? If the investor had a short life expectancy, which investment would they prefer?
? If the investor had a long life expectancy, which investment would they prefer?

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