How do i go about solving this one?
A cash flow sequence starts in year 1 at $3000 and decreases by $200 each year through year 10. (a) Determine the value of the gradient G; (b) determine the amount of cash flow in year 8; and (c) determine the value of n for the gradient.
also what does gradient mean?
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To solve this cash flow sequence problem, you can follow the steps below:
(a) Determine the value of the gradient G:
The gradient represents the annual decrease or increase in cash flow. In this case, the cash flow starts at $3000 in year 1 and decreases by $200 each year until year 10.
To find the value of the gradient G, subtract the cash flow in year 2 from the cash flow in year 1:
G = Cash flow in year 1 - Cash flow in year 2
G = $3000 - ($3000 - $200)
G = $3000 - $2800
G = $200
Therefore, the value of the gradient G is $200.
(b) Determine the amount of cash flow in year 8:
Given that the cash flow decreases by $200 each year, you need to calculate the cash flow in year 1, subtracting $200 for each subsequent year until year 8.
Cash flow in year 8 = Cash flow in year 1 - (Decrease per year * Number of years)
Cash flow in year 8 = $3000 - ($200 * (8 - 1))
Cash flow in year 8 = $3000 - ($200 * 7)
Cash flow in year 8 = $3000 - $1400
Cash flow in year 8 = $1600
Therefore, the amount of cash flow in year 8 is $1600.
(c) Determine the value of n for the gradient:
In this case, the gradient G is $200. The value of n represents the number of years it takes for the cash flow to decrease to zero.
To find the value of n, divide the initial cash flow by the gradient and add 1:
n = (Initial cash flow / Gradient) + 1
n = ($3000 / $200) + 1
n = 15 + 1
n = 16
Therefore, the value of n for the gradient is 16.
As for the definition of "gradient," in finance and economics, the term "gradient" refers to the rate of change in a variable over time. In this context, it represents the annual decrease or increase in cash flow.