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Bridget Jones has a contract in which she will receive the following payments for the next...

Bridget Jones has a contract in which she will receive the following payments for the next five years: $17,000, $18,000, $19,000, $20,000, $21,000. She will then receive an annuity of $24,500 a year from the end of the sixth year through the end of the 15th year. The appropriate discount rate is 18 percent.

a. What is the present value of all future payments?

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Answer #1

Value at year 5 = Annuity * [1 - 1 / (1 + r)^n] / r

Value at year 5 = 24500 * [1 - 1 / (1 + 0.18)^10] / 0.18

Value at year 5 = 24500 * [1 - 0.191064] / 0.18

Value at year 5 = 24500 * 4.494086

Value at year 5 = 110,105.1142

Present value of all cash flows = 17,000 / (1 + 0.18)^1 + 18,000 / (1 + 0.18)^2 + 19,000 / (1 + 0.18)^3 + 20,000 / (1 + 0.18)^4 + 21,000 / (1 + 0.18)^5 + 110,105.1142 / (1 + 0.18)^5

Present value of all cash flows = 14,406.77966 + 12,927.31974 + 11,563.98658 + 10,315.7775 + 9,179.29354 + 48,127.96

Present value of all cash flows = $106,521.12

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