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# Mike buys a perpetuity-immediate with varying annual payments. During the first 5 years, the…

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Mike buys a perpetuity-immediate with varying annual payments. During the first 5 years, the payment is constant and equal to 10. Beginning in year 6, the payments start to increase. For year 6 and all future years, the current year’s payment is K% larger than previous year’s payment. At an annual effective interest rate of 9.2%, the perpetuity has a present value of 167.50. Calculate K given K<9.2. You can solve this problem in following steps. Or consider it as a stock with varying annual dividends.

a. Draw the time diagram. Hint: Separate this perpetuity into a 5-year annuity and a perpetuity with constant growth rate after 5 years.

b. What is the present value for the 5-year annuity?

c. What is the remaining value, or present value of perpetuity at time t=0?

d. What is the value of this perpetuity at time=5?

e. Calculate K.