Question

An investment is expected to generate annual cash flows forever. The first annual cash flow is expected in 1 year and all subsequent annual cash flows are expected to grow at a constant rate annually. We know that the cash flow expected in 3 years from today is expected to be $9,000 and the cash flow expected in 7 years from today is expected to be $10,000. What is the cash flow expected to be in 5 years from today?

Answer 1

Let Cash Flows in 1^st year be $x and constant growth rate be g%

Cash Flows in 3^rd year = $9,000
$x * (1 + g)^2 = $9,000                                   ... (1)

Cash Flows in 7^th year = $10,000
$x * (1 + g)^6 = $10,000                                 ... (2)

Dividing (1) and (2)

[$x * (1 + g)^6] / [$x * (1 + g)^2] = $10,000 / $9,000
(1 + g)^4 = 1.1111
(1 + g) = 1.0267
g = 0.0267
g = 2.67%

Putting g in equation (1)

$x * 1.0267^2 = $9,000
$x = $8,537.985

Expected Cash Flows in 5^th year = $x * (1 + g)^4
Expected Cash Flows in 5^th year = $8,537.985 * 1.0267^4
Expected Cash Flows in 5^th year = $9,487