### Examples Arithmetic Gradient Factors (P/ G and A/ G)

A local university has initiated a logo-licensing program with the clothier Holister, Inc. Esti-

mated fees (revenues) are $80,000 for the ﬁ rst year with uniform increases to a total of $200,000

by the end of year 9. Determine the gradient and construct a cash ﬂ ow diagram that identiﬁ es

the base amount and the gradient series.

Solution

The cash ﬂ ow diagram (Figure 2–13) shows the base amount of $80,000 in years 1 through 9 and the $15,000 gradient starting in year 2 and continuing through year 9.

EXAMPLE 2.9

Neighboring parishes in Louisiana have agreed to pool road tax resources already designated for bridge refurbishment. At a recent meeting, the engineers estimated that a total of $500,000 will be deposited at the end of next year into an account for the repair of old and safety-questionable bridges throughout the area. Further, they estimate that the deposits will increase by $100,000 per year for only 9 years thereafter, then cease. Determine the equivalent (a) present worth and (b) annual series amounts, if public funds earn at a rate of 5% per year.

Solution

(a) The cash ﬂ ow diagram of this conventional arithmetic gradient series from the perspective of the parishes is shown in Figure 2–16. According to Equation [2.19], two computations must be made and added: the ﬁrst for the present worth of the base amount PA and the second for the present worth of the gradient PG. The total present worth PT occurs in year 0. This is illustrated by the partitioned cash ﬂ ow diagram in Figure 2–17. In $1000 units, the total present worth is

(b) Here, too, it is necessary to consider the gradient and the base amount separately. The total annual series AT is found by Equation [2.20] and occurs in years 1 through 10.

## 0 comments:

## Post a Comment