1. Combining Factors – Shifted Uniform Series
Question: What is P for the following cash flow, a shifted uniform series of n equal installments? The first installment occurs at the end of period 5.
P = ?
n+4
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2. Combining Factors – Shifted Uniform Series
P = ?
n+4
Approaches for finding P:
Use (P/F) for each of the n payments.
Use (F/P) for each of the payments to find FT, then use FT(P/F,i%,n+4) to find P.
Use (P/A) to find the P4, then use P4(P/F,i%,4) to find P.
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3. Combining Factors – Shifted Uniform Series
P = ?
$200
Example: What is P for a computer you purchase in which installments of $200 are paid for 10 months, with the first payment deferred until the 5th month after purchase. Assume i = 0.5% per month.
A = $200
P4 = ________________________________
P = _________________________________
A = $200
P4 = $200(P/A,0.5%,10) = $200 x = $
P = P4(P/F,0.5%,4) = $ x = $
P = $200(P/A,0.5%,10) (P/F,0.5%,4)
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4. Combining Factors – Shifted Uniform Series
P = ?
i = 6%
$2000
Example: What is the present worth of an account in which you invest $2000 beginning now and at the end of each year for 10 years? The account pays interest at 6%.
P = ____________________________
P = $ $2000(P/A,6,10)
P = $ $2000(7.3601) = $
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5. Combining Factors – Shifted Uniform Series
$200
Example: What is F for the cash flow shown above, in which installments of $200 are paid at the end of periods 5 through 14? Assume i = 5%.
A = _________________
F = _________________
What is the account worth in period 20 (no installments made after period 14)?
A = $200
F = $200(F/A,5%,10)
F = $200( ) = $
F20 = (F/P, 5%, 6) = (1.3401) =
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6. Combining Factors – Single Amounts and Uniform Series
P = ?
i = 10%
$200
$400
How might you approach the above cost flow? $200 paid in periods 1,2,3,4,8,9,10; and $400 paid in periods 5.
P1 = ?
P2 = ? 5
$200
$200
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7. Combining Factors – Single Amounts and Uniform Series
P = ?
$200
$400
P = $200(P/A,10%,10) + $200(P/F,10%,5) = _________
P = 200(6.1446) + 200(0.6209) =
P1 = ?
P2 = ? 5
$200
$200
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8. Combining Factors – Multiple Uniform Series
$200
$400
How might you approach the above cost flow? $200 paid in periods 1,2,3,4,8,9,10; and $400 paid in periods 5,6,7.
P1 = ?
P2 = ? 5
$200
$200
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9. Combining Factors – Multiple Uniform Series
$200
$400
P = $200(P/A,i%,10) $200(P/A,i%,3)(P/F,i%,4)
P1 = ?
P2 = ? 5
$200
$200
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10. Combining Factors – Shifted Gradients
$175
$150
$125
$100 P
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11. Your turn – draw the cash flow diagram(s) ….
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12. Combining Factors – Shifted Gradients
$75
$100
$50
$25 P3 P2 P1
P = ________
P = ___________________________________
Note, P2 term is for ____ periods.
P = P1+ P3
P = $100(P/A,i%,8) + 25(P/G,i%,4)(P/F,i%,4)
Note, P2 term is for 4 periods.
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13. Combining Factors – Shifted Decreasing Gradients
$1000
$850
$700
$550 P
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14. Draw the cash flow diagrams …
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15. Combining Factors – Shifted Decreasing Gradients
$1000
$1000
$850
$700
$550  P1 -
$450 P
$300
$150 P3 P2
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16. Combining Factors – Shifted Decreasing Gradients
$1000 -
$450
$300
$150 P3 P2 P1
P = P1- P3
P = $1000(P/A,i%,7) - 150(P/G,i%,4)(P/F,i%,3)
Note, P2 = $150(P/G,i%,4) term is for 4 periods.
P = _______
P = _______________________________
Note, P2 term is for ___ periods.
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