a) Calculate the PV of a perpetuity with a cash flow of $111.11 received every year. The first cash flow occurs in year 1. The interest rate is 11% simple annual rate.
b) Calculate the PV of a perpetuity with a cash flow of $222.22 received every second year. The first cash flow occurs in year 2. The interest rate is 11% simple annual rate.
c) Calculate the PV of a perpetuity with a cash flow of $333.33 received every third year. The first cash flow occurs in year 3. The interest rate is 11% simple annual rate.
Answer a.
Annual payment = $111.11
Interest rate = 11%
Present value of perpetuity = Annual payment / Annual interest
rate
Present value of perpetuity = $111.11 / 0.11
Present value of perpetuity = $1,010.09
Answer b.
Payment every two years = $222.22
Interest rate = 11%
Present value of perpetuity = $222.22/1.11^2 + $222.22/1.11^2 +
….
Present value of perpetuity = ($222.22/1.11^2) / (1 -
(1/1.11)^2)
Present value of perpetuity = $222.22 / (1.11^2 - 1)
Present value of perpetuity = $222.22 / 0.2321
Present value of perpetuity = $957.43
Answer c.
Payment every three years = $333.33
Interest rate = 11%
Present value of perpetuity = $333.33/1.11^3 + $333.33/1.11^3 +
….
Present value of perpetuity = ($333.33/1.11^3) / (1 -
(1/1.11)^3)
Present value of perpetuity = $333.33 / (1.11^3 - 1)
Present value of perpetuity = $333.33 / 0.367631
Present value of perpetuity = $906.70
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