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Contract Provision that Impact
                Cash Flow
•   Payment schedule
•   Materials
•   Mobilization
•   Monthly payments
•   Final Payment




Spring 2008,           Cash Flow Analysis      1
King Saud University   Dr. Khalid Al-Gahtani
Contractor Cash Disbursements
•   Labor
•   Equipment
•   Materials
•   Subcontractors
•   Other
     – Insurance,
     – Permit and mobilization
     – Overhead items
Spring 2008,           Cash Flow Analysis      2
King Saud University   Dr. Khalid Al-Gahtani
Factors That Minimize Contractor's
        Negative Cash Flow
1. Front end rate loading:
     – earlier items in bill of quantities carry a higher mark-
       up than later items early stages.
     – This reduces negative cash flows in contract early
       stages.
2. Reduction of delays in receiving revenue.
3. Adjustment of work schedule to late start timing.
4. Coinciding the timing of delivery of large
    materials orders with the submittal of the
    contractor's monthly pay estimate.
Spring 2008,              Cash Flow Analysis                      3
King Saud University      Dr. Khalid Al-Gahtani
Factors That Minimize Contractor's
        Negative Cash Flow
5. Delay in paying labour, plant hirers, materials
  suppliers, and subcontractors.
     – This would reduce negative cash flows but undermine
       commercial confidence in the company.
6. Increasing the mark-up and reducing the
  retentions.
7. Increasing mobilization and advance payment.
8. Achievement of maximum production in the
  field.
9. Quick settlement or claims.

Spring 2008,            Cash Flow Analysis               4
King Saud University    Dr. Khalid Al-Gahtani
The Cash Flow Analysis




Spring 2008,           Cash Flow Analysis      5
King Saud University   Dr. Khalid Al-Gahtani
The Cash Flow Analysis




Spring 2008,           Cash Flow Analysis      6
King Saud University   Dr. Khalid Al-Gahtani
Example 4.1
• The mark-up is 10% of tender value and is
  assumed to be uniformly distributed over the
  contract.
• The contractor will receive an advanced
  payment of 10% of tender value.
     – This will be deducted from each monthly revenue.
       Retention is 5% and is paid on contract completion.
• Labour cost is assumed to be 30% of total
  contract cost and is paid after one week's delay.
• The delay for other submitting is one month.
• Revenue is received after 4 weeks from
  submitting invoices.
Spring 2008,             Cash Flow Analysis                  7
King Saud University     Dr. Khalid Al-Gahtani
Example 4.1
• Assuming all the activities are scheduled on their
  early start timings, it is required to derive:
     – revenue and income curves,
     – cost and expense curves and
     – contract cash flow curves.
• Compare contract net cash flows for revenue
  received after 4 and 6 weeks from submitting
  invoices.
• Determine the effect on contract cash flow of
  scheduling the activities on their late start
  timings while the revenue is received with 4
  week’s delay.
Spring 2008,             Cash Flow Analysis        8
King Saud University     Dr. Khalid Al-Gahtani
Table 4.3 Date for example 4.1
                       D uration          P recedin g                  V alue
     A ctivity                                             O verlap
                       (w eeks)            activity                    (LE )
         A                5                                            30000
         B                4                    A                       20000
         C                5                    A              -1       15000
         D                5                    A                       15000
         E                5                    B              2        25000
         F                4                   B ,C                     16000
         G                6                    D                       18000
         H                4                    E               1       8000
         I                3                   F ,G         2 w ith G   9000
         J                2                   H .I                     4000


Spring 2008,                       Cash Flow Analysis                           9
King Saud University               Dr. Khalid Al-Gahtani
Spring 2008,           Cash Flow Analysis      10
King Saud University   Dr. Khalid Al-Gahtani
Spring 2008,           Cash Flow Analysis      11
King Saud University   Dr. Khalid Al-Gahtani
Spring 2008,           Cash Flow Analysis      12
King Saud University   Dr. Khalid Al-Gahtani
Spring 2008,           Cash Flow Analysis      13
King Saud University   Dr. Khalid Al-Gahtani
Spring 2008,           Cash Flow Analysis      14
King Saud University   Dr. Khalid Al-Gahtani
Spring 2008,           Cash Flow Analysis      15
King Saud University   Dr. Khalid Al-Gahtani
Spring 2008,           Cash Flow Analysis      16
King Saud University   Dr. Khalid Al-Gahtani
Spring 2008,           Cash Flow Analysis      17
King Saud University   Dr. Khalid Al-Gahtani
Spring 2008,           Cash Flow Analysis      18
King Saud University   Dr. Khalid Al-Gahtani
Algorithm Calculations
1) calculate the net operating cash flow at the end of
  period t for t ≥ 0 is given by:
                         At = Pt Et
   – At is positive for a surplus and negative for a shortfall
   – Et = the contractor's expenses in period t, and
   – Pt = owner's payments in period t, for t = 0,1,2,...,n.
2) calculate The cumulative operating cash flow at the
  end of period t just before receiving payment Pt (for
  t ≥ 1) is:
                       Ft = Nt-1 Et
   – Nt-1 is the cumulative net cash flows from period 0 to
     period (t-1).
 Spring 2008,             Cash Flow Analysis                     19
 King Saud University     Dr. Khalid Al-Gahtani
Algorithm Calculations
3) calculate the cumulative net operating
  cash flow after receiving payment Pt at the
  end of period t (for t ≥1) is:
            Nt = Ft + Pt = Nt-1 + At
4) The gross operating profit G for a n-
  period project is defined as net operating
  cash flow at t=n and is given by:


Spring 2008,           Cash Flow Analysis      20
King Saud University   Dr. Khalid Al-Gahtani
E xa m p le 1: C on tractor's gro ss p rofit fro m a p roject

T he co ntracto r's expe nses a nd o w ner's pa ym e nts fo r a m u lt i - year co nstructio n pro ject are
g ive n in C o lu m ns 2 a nd 3, respective ly, o f T a ble 1 . E ach tim e perio d is represe nted by o ne
year, and the annu a l interest rate i is fo r bo rro w ing 11% . T he co m putatio n has bee n carried
o ut in T able 1, and the co ntracto r's gro ss pro fit G is fo und to be N 5 = $8.025 m illio n in the
la st co lu m n o f the table.


           T A B L E 1 E xa m p le o f C o ntracto r's E xpe nse s a nd O w ner's P a ym e nts ($ M illio n)
               C o ntracto r's       O w ner's         N et C ash     C u m u lat ive C a sh   C u m u lat ive N et
P erio d        E xpe nse s         P a ym e nts         F lo w       B e fo re P a ym e nts          C ash
   t                 Et                  Pt                At                   Ft                      Nt
  0              $3.782                $0              -$3.782              -$3.782                 -$3.782
  1               7.458               6.473             -0.985              -11.240                  -4.767
  2              10.425               9.334             -1.091              -15.192                  -5.858
  3              14.736              13.348             -1.388              -20.594                  -7.246
  4              11.420              16.832             + 5.412             -18.666                  -1.834
  5                5.679              15.538             + 9.859             -7.513                 + 8.025
T otal           $53.500             $61.525           + $8.025




   Spring 2008,                                    Cash Flow Analysis                                          21
   King Saud University                            Dr. Khalid Al-Gahtani
Spring 2008,           Cash Flow Analysis      22
King Saud University   Dr. Khalid Al-Gahtani
Considering the time value of money
1) Co m pute the interest per perio d


    -    If     is negat ive a nd i is the bo rro w ing rate fo r the sho rtfa ll,




    -    If      is po sit ive a nd h is the invest m e nt rate fo r the surp lus,




  Spring 2008,                     Cash Flow Analysis                            23
  King Saud University             Dr. Khalid Al-Gahtani
Considering the time value of money
2) calculate the interest accrued in period t,
  the cumulative cash flow at the end of
  period t just before receiving payment Pt
  (for t ≥1) is:


3) calculate the cumulative net cash flow after
receiving payment Pt at the end of period t
(for t ≥1) is:

Spring 2008,           Cash Flow Analysis        24
King Saud University   Dr. Khalid Al-Gahtani
Considering the time value of money

4) calculate the gross operating profit at the
  end of a n-period project including interest
  charges is:



     w here            is the cu m u lative net cash flo w fo r t = n.



Spring 2008,                     Cash Flow Analysis                      25
King Saud University             Dr. Khalid Al-Gahtani
Example 2
E xa m p le 2: E ffe cts of C on stru ction F in an cin g

T he co m putatio n o f the cu m u lat ive ca sh flo w s inc lud ing interest charges at i = 11% fo r
E xa m p le 1 is sho w n in T a ble 2 w ith gro ss pro fit   =      = $1.384 m illio n. T he resu lts o f
co m putatio n are a lso sho w n in F igure 2 .


T A B L E 2 E xa m p le C u m u lat ive C a sh F lo w s Inc lu d ing Interests fo r a C o ntractor ($ M illio n)
  P erio d      C o nstructio n        O w ner's         A nnua l          C u m u lat ive        C u m u lat ive
  (year)          E xpe nse s         P a ym e nts       Interest      B e fo re P a ym e nts   N et C ash F lo w
     t                Et                   Pt
      0             $3.782               0                   0               -$3.782                -$3.782
      1             7.458              $6.473            -$0.826             -12.066                 -5.593
      2             10.425             9.334              -1.188             -17.206                 -7.872
      3             14.736             13.348             -1.676             -24.284                -10.936
      4             11.420             16.832             -1.831             -24.187                 -7.354
      5             5.679              15.538             -1.121             -14.154                + 1.384


   Spring 2008,                               Cash Flow Analysis                                            26
   King Saud University                       Dr. Khalid Al-Gahtani
Example 2




Spring 2008,            Cash Flow Analysis      27
King Saud University    Dr. Khalid Al-Gahtani
Example 2




Spring 2008,            Cash Flow Analysis      28
King Saud University    Dr. Khalid Al-Gahtani
E xa m p le 3: E ffe cts of In flation
S uppo se that both expe nses a nd rece ipts fo r the constructio n pro ject in the E xa m p le 1 are
no w expressed in the n -current do llars (w ith a nnua l inflat io n rate o f 4% ) in T able 3 . T he
m arket interest rate reflect ing this inflatio n is no w 15% . In co nsidering these e xpe nses a nd
rece ipts in then -curre nt do llars a nd using an interest rate o f 15% inc lud ing inflat io n, w e can
reco m pute the cu m u lat ive net cash flo w (w ith interest). T hus, the gro ss pro fit le ss fina nc ing
co sts beco m es     =    = $0.4 m illio n. T here w ill be a lo ss rather tha n a pro fit a fter deducting
fina nc ing co sts and ad just ing fo r the effects o f inflatio n w ith this pro ject.


       T A B L E 3 E xa m p le o f O verdra ft F ina nc ing B a sed o n Inflated D o llars ($ M illio n)
                                                                             C u m u lat ive    C u m u lat ive
  P erio d        C o nstructio n          O w ner's          A nnua l          B e fo re        N et C ash
  (year)            E xpe nse s           P a ym e nts        Interest        P a ym e nts          F lo w
     t                  Et                     Pt
     0               $3.782                   0                  0             -$3.782            -$3.782
     1               7.756                  $6.732           -$1.149           -12.687             -5.955
     2               11.276                 10.096            -1.739           -18.970             -8.874
     3               16.576                 15.015            -2.5 74          -28.024            -13.009
     4               13.360                 16.691            -2.953           -29.322             -9.631
     5               6.909                  18.904            -1.964           -18.504            + 0.400


   Spring 2008,                              Cash Flow Analysis                                            29
   King Saud University                      Dr. Khalid Al-Gahtani
Example 4: Effects of Work
    Stoppage at Periods of Inflation
T A B L E 4 E xa m p le o f the E ffects o f W o rk Sto ppage and Inflat io n o n a C o ntracto r ($ Million)
                                                                            C u m u lat ive   C u m u lat ive
  P erio d       C o nstructio n          O w ner's         A nnua l           B e fo re       N et C ash
  (year)           E xpe nse s           P a ym e nts       Interest         P a ym e nts         F lo w
     t                 Et                     Pt
     0               $3.782                  0                  0             -$3.782           -$3.782
     1               7.756                 $6.732           -$1.149           -12.687            -5.955
     2               11.276                10.096            -1.739           -18.970            -8.874
     3                 0                     0               -1.331           -10.205           -10.205
     4               17.239                15.015            -2.824           -30.268           -15.253
     5               13.894                16.691            -3.330           -32.477           -12.786
     6               7.1 85                18.904            -2.457           22.428             -3.524




 Spring 2008,                               Cash Flow Analysis                                             30
 King Saud University                       Dr. Khalid Al-Gahtani
Example 4: Effects of Work
  Stoppage at Periods of Inflation




Spring 2008,           Cash Flow Analysis      31
King Saud University   Dr. Khalid Al-Gahtani
Example 4: Effects of Work
  Stoppage at Periods of Inflation




Spring 2008,           Cash Flow Analysis      32
King Saud University   Dr. Khalid Al-Gahtani

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Cash flow

  • 1. Contract Provision that Impact Cash Flow • Payment schedule • Materials • Mobilization • Monthly payments • Final Payment Spring 2008, Cash Flow Analysis 1 King Saud University Dr. Khalid Al-Gahtani
  • 2. Contractor Cash Disbursements • Labor • Equipment • Materials • Subcontractors • Other – Insurance, – Permit and mobilization – Overhead items Spring 2008, Cash Flow Analysis 2 King Saud University Dr. Khalid Al-Gahtani
  • 3. Factors That Minimize Contractor's Negative Cash Flow 1. Front end rate loading: – earlier items in bill of quantities carry a higher mark- up than later items early stages. – This reduces negative cash flows in contract early stages. 2. Reduction of delays in receiving revenue. 3. Adjustment of work schedule to late start timing. 4. Coinciding the timing of delivery of large materials orders with the submittal of the contractor's monthly pay estimate. Spring 2008, Cash Flow Analysis 3 King Saud University Dr. Khalid Al-Gahtani
  • 4. Factors That Minimize Contractor's Negative Cash Flow 5. Delay in paying labour, plant hirers, materials suppliers, and subcontractors. – This would reduce negative cash flows but undermine commercial confidence in the company. 6. Increasing the mark-up and reducing the retentions. 7. Increasing mobilization and advance payment. 8. Achievement of maximum production in the field. 9. Quick settlement or claims. Spring 2008, Cash Flow Analysis 4 King Saud University Dr. Khalid Al-Gahtani
  • 5. The Cash Flow Analysis Spring 2008, Cash Flow Analysis 5 King Saud University Dr. Khalid Al-Gahtani
  • 6. The Cash Flow Analysis Spring 2008, Cash Flow Analysis 6 King Saud University Dr. Khalid Al-Gahtani
  • 7. Example 4.1 • The mark-up is 10% of tender value and is assumed to be uniformly distributed over the contract. • The contractor will receive an advanced payment of 10% of tender value. – This will be deducted from each monthly revenue. Retention is 5% and is paid on contract completion. • Labour cost is assumed to be 30% of total contract cost and is paid after one week's delay. • The delay for other submitting is one month. • Revenue is received after 4 weeks from submitting invoices. Spring 2008, Cash Flow Analysis 7 King Saud University Dr. Khalid Al-Gahtani
  • 8. Example 4.1 • Assuming all the activities are scheduled on their early start timings, it is required to derive: – revenue and income curves, – cost and expense curves and – contract cash flow curves. • Compare contract net cash flows for revenue received after 4 and 6 weeks from submitting invoices. • Determine the effect on contract cash flow of scheduling the activities on their late start timings while the revenue is received with 4 week’s delay. Spring 2008, Cash Flow Analysis 8 King Saud University Dr. Khalid Al-Gahtani
  • 9. Table 4.3 Date for example 4.1 D uration P recedin g V alue A ctivity O verlap (w eeks) activity (LE ) A 5 30000 B 4 A 20000 C 5 A -1 15000 D 5 A 15000 E 5 B 2 25000 F 4 B ,C 16000 G 6 D 18000 H 4 E 1 8000 I 3 F ,G 2 w ith G 9000 J 2 H .I 4000 Spring 2008, Cash Flow Analysis 9 King Saud University Dr. Khalid Al-Gahtani
  • 10. Spring 2008, Cash Flow Analysis 10 King Saud University Dr. Khalid Al-Gahtani
  • 11. Spring 2008, Cash Flow Analysis 11 King Saud University Dr. Khalid Al-Gahtani
  • 12. Spring 2008, Cash Flow Analysis 12 King Saud University Dr. Khalid Al-Gahtani
  • 13. Spring 2008, Cash Flow Analysis 13 King Saud University Dr. Khalid Al-Gahtani
  • 14. Spring 2008, Cash Flow Analysis 14 King Saud University Dr. Khalid Al-Gahtani
  • 15. Spring 2008, Cash Flow Analysis 15 King Saud University Dr. Khalid Al-Gahtani
  • 16. Spring 2008, Cash Flow Analysis 16 King Saud University Dr. Khalid Al-Gahtani
  • 17. Spring 2008, Cash Flow Analysis 17 King Saud University Dr. Khalid Al-Gahtani
  • 18. Spring 2008, Cash Flow Analysis 18 King Saud University Dr. Khalid Al-Gahtani
  • 19. Algorithm Calculations 1) calculate the net operating cash flow at the end of period t for t ≥ 0 is given by: At = Pt Et – At is positive for a surplus and negative for a shortfall – Et = the contractor's expenses in period t, and – Pt = owner's payments in period t, for t = 0,1,2,...,n. 2) calculate The cumulative operating cash flow at the end of period t just before receiving payment Pt (for t ≥ 1) is: Ft = Nt-1 Et – Nt-1 is the cumulative net cash flows from period 0 to period (t-1). Spring 2008, Cash Flow Analysis 19 King Saud University Dr. Khalid Al-Gahtani
  • 20. Algorithm Calculations 3) calculate the cumulative net operating cash flow after receiving payment Pt at the end of period t (for t ≥1) is: Nt = Ft + Pt = Nt-1 + At 4) The gross operating profit G for a n- period project is defined as net operating cash flow at t=n and is given by: Spring 2008, Cash Flow Analysis 20 King Saud University Dr. Khalid Al-Gahtani
  • 21. E xa m p le 1: C on tractor's gro ss p rofit fro m a p roject T he co ntracto r's expe nses a nd o w ner's pa ym e nts fo r a m u lt i - year co nstructio n pro ject are g ive n in C o lu m ns 2 a nd 3, respective ly, o f T a ble 1 . E ach tim e perio d is represe nted by o ne year, and the annu a l interest rate i is fo r bo rro w ing 11% . T he co m putatio n has bee n carried o ut in T able 1, and the co ntracto r's gro ss pro fit G is fo und to be N 5 = $8.025 m illio n in the la st co lu m n o f the table. T A B L E 1 E xa m p le o f C o ntracto r's E xpe nse s a nd O w ner's P a ym e nts ($ M illio n) C o ntracto r's O w ner's N et C ash C u m u lat ive C a sh C u m u lat ive N et P erio d E xpe nse s P a ym e nts F lo w B e fo re P a ym e nts C ash t Et Pt At Ft Nt 0 $3.782 $0 -$3.782 -$3.782 -$3.782 1 7.458 6.473 -0.985 -11.240 -4.767 2 10.425 9.334 -1.091 -15.192 -5.858 3 14.736 13.348 -1.388 -20.594 -7.246 4 11.420 16.832 + 5.412 -18.666 -1.834 5 5.679 15.538 + 9.859 -7.513 + 8.025 T otal $53.500 $61.525 + $8.025 Spring 2008, Cash Flow Analysis 21 King Saud University Dr. Khalid Al-Gahtani
  • 22. Spring 2008, Cash Flow Analysis 22 King Saud University Dr. Khalid Al-Gahtani
  • 23. Considering the time value of money 1) Co m pute the interest per perio d - If is negat ive a nd i is the bo rro w ing rate fo r the sho rtfa ll, - If is po sit ive a nd h is the invest m e nt rate fo r the surp lus, Spring 2008, Cash Flow Analysis 23 King Saud University Dr. Khalid Al-Gahtani
  • 24. Considering the time value of money 2) calculate the interest accrued in period t, the cumulative cash flow at the end of period t just before receiving payment Pt (for t ≥1) is: 3) calculate the cumulative net cash flow after receiving payment Pt at the end of period t (for t ≥1) is: Spring 2008, Cash Flow Analysis 24 King Saud University Dr. Khalid Al-Gahtani
  • 25. Considering the time value of money 4) calculate the gross operating profit at the end of a n-period project including interest charges is: w here is the cu m u lative net cash flo w fo r t = n. Spring 2008, Cash Flow Analysis 25 King Saud University Dr. Khalid Al-Gahtani
  • 26. Example 2 E xa m p le 2: E ffe cts of C on stru ction F in an cin g T he co m putatio n o f the cu m u lat ive ca sh flo w s inc lud ing interest charges at i = 11% fo r E xa m p le 1 is sho w n in T a ble 2 w ith gro ss pro fit = = $1.384 m illio n. T he resu lts o f co m putatio n are a lso sho w n in F igure 2 . T A B L E 2 E xa m p le C u m u lat ive C a sh F lo w s Inc lu d ing Interests fo r a C o ntractor ($ M illio n) P erio d C o nstructio n O w ner's A nnua l C u m u lat ive C u m u lat ive (year) E xpe nse s P a ym e nts Interest B e fo re P a ym e nts N et C ash F lo w t Et Pt 0 $3.782 0 0 -$3.782 -$3.782 1 7.458 $6.473 -$0.826 -12.066 -5.593 2 10.425 9.334 -1.188 -17.206 -7.872 3 14.736 13.348 -1.676 -24.284 -10.936 4 11.420 16.832 -1.831 -24.187 -7.354 5 5.679 15.538 -1.121 -14.154 + 1.384 Spring 2008, Cash Flow Analysis 26 King Saud University Dr. Khalid Al-Gahtani
  • 27. Example 2 Spring 2008, Cash Flow Analysis 27 King Saud University Dr. Khalid Al-Gahtani
  • 28. Example 2 Spring 2008, Cash Flow Analysis 28 King Saud University Dr. Khalid Al-Gahtani
  • 29. E xa m p le 3: E ffe cts of In flation S uppo se that both expe nses a nd rece ipts fo r the constructio n pro ject in the E xa m p le 1 are no w expressed in the n -current do llars (w ith a nnua l inflat io n rate o f 4% ) in T able 3 . T he m arket interest rate reflect ing this inflatio n is no w 15% . In co nsidering these e xpe nses a nd rece ipts in then -curre nt do llars a nd using an interest rate o f 15% inc lud ing inflat io n, w e can reco m pute the cu m u lat ive net cash flo w (w ith interest). T hus, the gro ss pro fit le ss fina nc ing co sts beco m es = = $0.4 m illio n. T here w ill be a lo ss rather tha n a pro fit a fter deducting fina nc ing co sts and ad just ing fo r the effects o f inflatio n w ith this pro ject. T A B L E 3 E xa m p le o f O verdra ft F ina nc ing B a sed o n Inflated D o llars ($ M illio n) C u m u lat ive C u m u lat ive P erio d C o nstructio n O w ner's A nnua l B e fo re N et C ash (year) E xpe nse s P a ym e nts Interest P a ym e nts F lo w t Et Pt 0 $3.782 0 0 -$3.782 -$3.782 1 7.756 $6.732 -$1.149 -12.687 -5.955 2 11.276 10.096 -1.739 -18.970 -8.874 3 16.576 15.015 -2.5 74 -28.024 -13.009 4 13.360 16.691 -2.953 -29.322 -9.631 5 6.909 18.904 -1.964 -18.504 + 0.400 Spring 2008, Cash Flow Analysis 29 King Saud University Dr. Khalid Al-Gahtani
  • 30. Example 4: Effects of Work Stoppage at Periods of Inflation T A B L E 4 E xa m p le o f the E ffects o f W o rk Sto ppage and Inflat io n o n a C o ntracto r ($ Million) C u m u lat ive C u m u lat ive P erio d C o nstructio n O w ner's A nnua l B e fo re N et C ash (year) E xpe nse s P a ym e nts Interest P a ym e nts F lo w t Et Pt 0 $3.782 0 0 -$3.782 -$3.782 1 7.756 $6.732 -$1.149 -12.687 -5.955 2 11.276 10.096 -1.739 -18.970 -8.874 3 0 0 -1.331 -10.205 -10.205 4 17.239 15.015 -2.824 -30.268 -15.253 5 13.894 16.691 -3.330 -32.477 -12.786 6 7.1 85 18.904 -2.457 22.428 -3.524 Spring 2008, Cash Flow Analysis 30 King Saud University Dr. Khalid Al-Gahtani
  • 31. Example 4: Effects of Work Stoppage at Periods of Inflation Spring 2008, Cash Flow Analysis 31 King Saud University Dr. Khalid Al-Gahtani
  • 32. Example 4: Effects of Work Stoppage at Periods of Inflation Spring 2008, Cash Flow Analysis 32 King Saud University Dr. Khalid Al-Gahtani