1. Contemporary Engineering Economics
Gradient Series
Lecture No. 8
Chapter 3
Contemporary Engineering Economics
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2. Linear Gradient Series

3. Linear Gradient Series
An Increasing Linear Strict Gradient Series
!!! Most problems do not correspond to this form

4. Linear 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

5. Example 1: Find P, given A1, G, N, and i
Maintanence cost of a machine is $1,000 during the first year. As the machine ages, maintanence cost is expected to increase at a rate of $250 per year over the remaining life time. Life time of machine is 5 years. You want to open a maintanence cost account today that earns 12% annual interest. How much should you deposit now?

6. Example 2: Find F, given A1, G, N, and i
Given: A1 = $1,200, G = -$200, N = 5 years, and i = 10% per year
Find: F

7. Gradient-to-Equal-Payment Series Conversion Factor, (A/G, i, N)

8. Example 3: Find A, given A1, G, i, and N
John and Barbara open two savings accounts. John puts $1,000 at the end of year 1 and increase this amount by $300 for each of the next 5 years. Barbara simply deposits the same amount each year. What should Barbara deposit so that the accounts will have the same balance?

9. Geometric Gradient Series
Cash flows that increase or decrease over time by a constant percentage (g%) (e.g. construction costs) (g>0 or g<0)

10. Example 4: Find P, given A1, g, i, and N
A manufacturer uses a compressor that runs 70% of time for 250 workdays and 24 hours. It requires 260 kW of electricity at a rate of $0.05/kWh. The company has two options: Option 1: Operate with current system (running costs will increase by 7% per year for the next 5 years). Option 2: Replace the old machine with a new one that costs $28,570. The new machine uses 23% less power. Which option to choose (i=12%)?

11. Solution

12. Example 5: Find A1, given F, g, i and N