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CHAPTER 3: Combining Factors - Coggle Diagram
CHAPTER 3: Combining Factors
SHIFTED ARITHMETIC GRADIENTS
Present worth P(G) is located 2 periods before gradient starts
Must use multiple factors to find P(T) in actual year 0
Shifted gradient begins at a time other than between periods 1 and 2
To find equivalent A series, find P(T) at actual time 0 and apply (A/P,i,n)
SHIFTED UNIFORM SERIES
Shifted series usually require the use of multiple factors
A shifted uniform series starts at a time
other than period 1
When using P/A or A/P factor, P A is always one year ahead
of first A
When using F/A or A/F factor, F
A is in same year as last A
NEGATIVE SHIFTED GRADIENTS
All other procedures are the same as for positive gradients
For negative geometric gradients, change signs on both g values
Pg = A {1 --[(1 g)/(1+i)]^n /(i g)}
For negative arithmetic gradients, change sign on G term from + to -
General equation for determining P:
P = present worth of base amount - P(G)
SHIFTED SERIES AND RANDOM SINGLE AMOUNTS
Uniform series procedures
are applied to the series amounts
Single amount formulas
are applied to the one time cash flows
SHIFTED GEOMETRIC GRADIENTS
Equation yields Pg for all cash flows (base amount A 1 is included)
Equation (i ≠ g):Pg = A 1 {1 --[(1+g)/(1+ n /(i g)}
Shifted gradient begins at a time other than between periods 1 and 2
For negative gradient , change signs on both g values