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What is the value of a apple orchard that is expected to generate no cash flows...

What is the value of a apple orchard that is expected to generate no cash flows for several years and then generate fixed annual cash flows of 12,800 dollars forever if the first annual cash flow of 12,800 dollars is expected in 6 years and the appropriate discount rate for the apple orchard is 8.27 percent?

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Answer #1

Perpetuity may be defined as infinite series of equal cash flows occurring at regular intervals.

As the first cash flow is expected in 6 years, first the value of the perpetuity will be calculated at 6 years with perpetuity formula, after that simply the present value will be calculated of the future value of perpetuity for 6 years with Present value formula.

(it is assumed the cash flow is generated at the end of 6th year)

PV of the perpetuity = annual cash flow / discount rate

PV of the perpetuity at 6 years from now = 12,800 / 0.0827

= $ 154,776 (approx)

This the the present value at 6 year, to calculate present value today, we will use the below formula-

PV (today) = 154,776 / ( 1 + 0.0827)6

= $ 96,085 (approx)

Hope it helps!

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