Question

Assume i=8% year. How much money do I have to deposit today(year 0) in an account that will generate $25000 from year 12 to infinity.

Answer 1

Need to deposit $134,026 today (year 0) to generate $25,000 from year 12 to perpetuity

Explanation

C₁= Initial cash flow = $25,000

r = rate per period = 8% = 0.08

Compute Present value of a stream of cash flows one period before the initial payment

Since perpetuity is to be generated from year 12 to infinity

Therefore computing PV₁₁ one period before

PV₁₁ = C₁ / r = $25,000 / 0.08 = $312,500

Continue discounting this PV back one year at a time to finally yield the value today, period 0. The formula to cover this entire period from period 11 to 0 to give PV₀ is

PV₀ = PV₁₁ / (1 + r)¹¹

        = $312,500 / (1 + 0.08)¹¹ = $312,500 / (1.08)¹¹ = $312,500 / 2.3316

        = $134,026

Need to deposit $134,026 today (year 0)