1 / 15

Combining Factors – Shifted Uniform Series

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. 0 1 2 3 4 n+4.

paprika
Télécharger la présentation

Combining Factors – Shifted Uniform Series

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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 0 1 2 3 4 n+4

  2. Combining Factors – Shifted Uniform Series $P 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. 0 1 2 3 4 n+4

  3. Combining Factors – Shifted Uniform Series $P 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 = 5%. A = $200 P4 = $200(P/A,5%,10) = $200 x 7.7217 = $1544.34 P = P4(P/F,5%,4) = $1544.34 x 0.8227 = $1270.53 P = $200(P/A,5%,10) (P/F,5%,4) 0 1 2 3 4 14 $200

  4. Combining Factors – Shifted Uniform Series $P Example: How much will be in 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 = $2000 + $2000(P/A,6,10) P = $2000 + $2000(7.3601) = $16720.2 0 1 2 3 4 10 $2000

  5. Combining Factors – Shifted Uniform Series $F Example: What is F for the following cash flow. Installments of $200 are paid for periods 5 through 14. Assume i = 5%. A = $200 F = $200(F/A,5%,10) F = $200(12.5779) = $2515.58 What is the account worth in period 20 (no installments made after period 14)? 0 1 2 3 4 14 $200

  6. Combining Factors – Single Amounts and Uniform Series $P 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. 0 1 2 3 4 10 $200 $P1 $P2 0 1 2 3 4 10 0 1 2 3 4 5 10 $200 $200

  7. Combining Factors – Single Amounts and Uniform Series $P 0 1 2 3 4 10 $200 P = $200(P/A,i%,10) + $200(P/F,i%,5) $P1 $P2 0 1 2 3 4 10 0 1 2 3 4 5 10 $200 $200

  8. Combining Factors – Multiple Uniform Series $P 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. 0 1 2 3 4 10 $200 $P1 $P2 0 1 2 3 4 10 $200 $200

  9. Combining Factors – Multiple Uniform Series $P 0 1 2 3 4 10 $200 P = $200(P/A,i%,10) + $200(P/A,i%,3)(P/F,i%,4) $P1 $P2 0 1 2 3 4 10 $200 $200

  10. Combining Factors – Shifted Gradients $175 $150 $125 $100 0 1 2 3 4 5 6 7 8 $P

  11. Combining Factors – Shifted Gradients $175 $150 $125 $100 0 1 2 3 4 5 6 7 8 $P P = P1+ P3 $75 $100 $50 $25 0 1 2 3 4 5 6 7 8 $P3 $P2 $P1

  12. Combining Factors – Shifted Gradients $75 $100 $50 $25 0 1 2 3 4 5 6 7 8 0 1 2 3 4 5 6 7 8 $P3 $P2 $P1 P = P1+ P3 P = $100(P/A,i%,8) + 25(P/G,i%,4)(P/F,i%,4) Note, P2 = $25(P/G,i%,4) term is for 4 periods.

  13. Combining Factors – Shifted Decreasing Gradients $1000 $850 $700 $550 0 1 2 3 4 5 6 7 8 $P

  14. Combining Factors – Shifted Decreasing Gradients $1000 $1000 $850 $700 $550 0 1 2 3 4 5 6 7 8 0 1 2 3 4 5 6 7 8 => - $450 $P $P1 $300 $150 0 1 2 3 4 5 6 7 8 $P3 $P2

  15. Combining Factors – Shifted Decreasing Gradients $1000 $450 $300 - $150 0 1 2 3 4 5 6 7 8 0 1 2 3 4 5 6 7 8 $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.

More Related