What is geometric gradient cash flow series?

A geometric gradient series is a cash flow series that either increases or decreases by a constant percentage each period. The uniform change is called the rate of change.

How do you find the geometric gradient?

Geometric Gradient Series

1. g = gradient percent (as a decimal in calculations) i = interest percent (as a decimal in calculations)
2. P = A1 ( P/ A1, g, i, n ) = A1 [ 1 – ( 1 + g ) n ( 1 + i ) –n ] / ( i – g )
3. = 100 [ 1 – 2.0114 * 0.6499] / (-0.06)
4. = 100 [ 1 – 1.628894627 * 0.463193488] / (0.03)

What is G in arithmetic gradient?

G = constant arithmetic change in cash flows from one time period to the next; G may be positive or negative. Figure (2–5): Cash flow diagram of an arithmetic gradient series. It is important to realize that the base amount defines a uniform cash flow series of the size A that occurs each time period.

What is arithmetic gradient present worth factor?

The general equation to find the present worth of an arithmetic gradient cash flow series is: P = present worth of base amount + present worth of gradient amount = A (P/A,i,n) + G (P/G, i,n) where: A = amount of money in period 1 G = change in amount between periods 1 and 2 n = number of periods from 1 thru end of …

What is the difference between geometric gradient series and arithmetic gradient series?

Only Cash flows in last period can be considered separately in geometric series while can’t be considered separately when working with arithmetic series. c. Only Cash flows in last period can be considered separately in arithmetic series while can’t be considered separately when working with geometric series.

What is a linear gradient series?

Linear Gradient Series A Strict Gradient Series Gradient Series as a Composite Series of a Uniform Series of N Payments of A1 and the Gradient Series of Increments of Constant Amount G. 3. Example 3.21 Linear Gradient: A textile mill has just purchased a lift truck that has a useful life of five years.

What is G in engineering economics?

A = An end-of-period cash receipt or disbursement in a uniform series continuing for n periods. G = Uniform period-by-period increase or decrease in cash receipts or disbursements.

What is the formula for arithmetic gradient future value factor?

To compute a future amount from a linear gradient series use: The term in the brackets is called the arithmetic-gradient series future worth factor. The general equations for calculating total present worth are PT = PA + PG and PT = PA – PG.

What is P A and P f?

P = A present sum of money. F = A future sum of money. A = An end-of-period cash receipt or disbursement in a uniform series continuing for n periods.

What is the gradient in the given cash flow diagram of the uniform gradient in a cash flow?

Answer: In a uniform gradient cash flow the cash flow changes by the same amount in each payment period. For example, if the cash flow in period 1 is $2000, and in period two it is $2100 it would be a uniform gradient if the subsequent amounts increased by $100 in each subsequent period.

What is a geometric gradient series?

A defi nition and description of new terms follow. A geometric gradient series is a cash flow series that either increases or decreases by a constant percentage each period. The uniform change is called the rate of change Note that the initial cash flow A1 is not considered separately when working with geometric gradients.

Is initial cash flow considered separately when working with geometric gradients?

Note that the initial cash flow A1 is not considered separately when working with geometric gradients. Figure 2–21 shows increasing and decreasing geometric gradients starting at an amount A1 in time period 1 with present worth Pg located at time 0.

How to calculate the PG of a cash flow diagram?

Cash flow diagram of (a) increasing and (b) decreasing geometric gradient series and present worth Pg. The (P A,g,i,n) factor calculates Pg in period t = 0 for a geometric gradient series starting in period 1 in the amount A1 and increasing by a constant rate of g each period.

How do you find the annual worth of a gradient?

AG = annual worth of gradient. Alternately, the annual worth of the gradient cash flow could be obtained by first finding the present worth, P, of the cash flow (as in the example above) and then converting the P value into an A value using the relation A = P(A/P, i,n).