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# Calculating the fair value of the given annuity

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You are considering three insurance settlement offers. The first offer includes annual payments of \$5,000, \$10,000, \$15,000, etc., where the payment for each year is \$5,000 more than the payment for the previous year, over the next ten years. The first payment of \$5,000 will be made exactly one year from today and the last payment, equal to \$50,000 will be made ten years from today. The second offer is the payment of one lump sum amount today. The third offer is to receive an equal amount at the end of each year, over the next ten years. Assume there are no tax effects and your discount rate is 12% per year. What is the minimum amount that you will accept today if you are to select the lump sum offer? What is the minimum amount of each of the 10 equal annual payments that you should be willing to accept

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#### Solution Preview

Please refer attached file for better clarity of tables.

Solution:

What is the minimum amount that you will accept today if you are to select the lump sum offer?

Minimum lump sum amount should be equal to PV of cash stream offered in alternative 1.

Let us calculate the PV of cash stream offered in alternative 1.

Year End Cash Flow PV factor, PVF PV
n Cn 1/(1+12%)^n PVF*Cn
1 ...

#### Solution Summary

Solution describes the steps to calculate the lump sum amount that can be accepted in place of the given annuity.

\$2.19