 A Guide to the Project Management Body of Knowledge,
Chapter 7 (1996 & 2000 edition)
 PMBOK Q&A, PMI 
Project Planning, Scheduling & Control, Lewis, James P., 1995, Chapter 10 
Project Management, A Managerial Approach,, Chapters 5 (pg. 206), 7, 10. Meridith & Mantel 
The New Project Management, Frame, J. Davidson, 1994, Chapters 89, 11 
Earned Value Project Management, Chapters 7, 8, 9. Flemming and Koppleman 
PMP Challenge, ESI International, Cost Section 
PV  =  __M _ (1 + r)**t 

M  =  amount of payment t years from now  
r  =  interest rate (also called discount rate) 
Given the following problem and assume today's date is Jun. 30.:




1. What is the net present value of an annual income flow of $1600 at 10% over the next 3 years?  

2. What is the present value of $1000 at 12% at the end of 5 years?  
3. Given the following:






Given $100,000 depreciated over 4 years, what would be
the depreciation per year for the straightline,
doubledeclining, and sumoftheyearsdigits methods?



Question  Answer  Notes 

1  $55  $67 = $12  The Cost Variance is the difference between the estimated cost of an activity and the actual cost of that activity. In earned value that is CV = BCWP  ACWP. The current date for the problem is June 30. As of June 30, the BCWP is $55. This figure is obtained by adding up the budgeted cost of work performed for units A, B, C, D, and E. The BCWP is 10 + 4 + 8 + 13 + 20 = 55. Similarly, the ACWP is $67. (12 + 5 + 8 + 12 + 30 = 67). Using the cost variance formula, we have CV = BCWP  ACWP, or CV = 55  67 = 12. Therefore, the cost variance is $12. 
2  $55  $56 = $1  The schedule variance is the difference between the scheduled completion of an activity and the actual completion of that activity. In earned value that is SV = BCWP  BCWS. Per question #1, the BCWP was calculated to be 55. The BCWS is calculated by adding the budget for units A, B, C, D, and E. In other words, BCWS = 10 + 5 + 6 +15 + 20 = 56. Now SV = BCWP  BCWS = 55  56 = 1. Therefore, the schedule variance is $1. 
3  55 / 67 = 0.82  The cost performance index (CPI) is the ratio of budgeted costs to actual cost, BCWP / ACWP. The BCWP is already known to be 55. (from previous problems). The ACWP is already known from previous problems to be 67. So the CPI = BCWP / ACWP = 55 / 67 = 0.82. 
4  55 / 56 = 0.98  The schedule performance index (SPI) is the ratio of work performed to work scheduled, BCWP / BCWS. The BCWP is known to be 55. Also, the BCWS has been calculated to be 56. So SPI = BCWP / BCWS = 55 / 56 = 0.98. 
5  147  The budget at completion (BAC) is the estimated total cost of the project when done. In this case it is the budgeted total of all units. In other words, BAC = A + B + C + D + E + F + G + H + I + J = 147. 
6  147 / 0.82 = $179.27  The estimate at completion (EAC) is the expected total cost of an activity, a group of activities, or of the project when the defined scope of work has been completed. For the calculation, we need to add the actual cost of the work completed to the budget (estimate) of the work still needed. The EAC is calculated as BAC / CPI. From #5, we calculated BAC to be 147. From #3, we calculated CPI to be 0.82. Therefore EAC = BAC / CPI = 147 / 0.82 = 179.27. 
7  $179.27  $67 = $112.27  The estimate to completion (ETC) is the expected additional cost needed to complete an activity, a group of activities, or the project. The ETC is the estimate at completion minus the actual cost of work performed. In other words, ETC = EAC  ACWP. The EAC was calculated to be 179.27. The ACWP was calculated to be 67. Therefore, ETC = EAC  ACWP = 179.27  67 = 112.27. 
8  55 / 147 = 0.37 = 37%  The percent complete (PC) is the percentage of work that has been completed on an activity or group of activities. It is calculated by dividing the budgeted cost of work performed by the budget at completion. In other words, it is BCWP / BAC. The BCWP has been calculated as 55 and BAC as 147. Therefore, PC = BCWP / BAC = 55 / 147 = 0.37 = 37%. 
9  67 / 147 = 0.46 = 46%  The percent spent (PS) is the percentage of budget consumed by the actual work completed. It is calculated by dividing the actual cost by the BAC. The ACWP is 67 and BAC is 147. Therefore, PS = ACWP / BAC = 67 / 147 = 0.46 = 46%. 
10  Over cost, a little behind schedule  The CV is negative which indicates that the project is over budget. A CPI less than one also indicates an over budget project. A negative SV indicates that the project is behind schedule. An SPI less than one also indicates a behind schedule project. 
Question  Answer  Notes  

1 

  
2  PV(5) = 1000/(1.12)**5 = $567.00  What is the present value of $1000 at 12% at the end of 5 years?  
3 

 
Question  Answer  Notes 

A  SL: Same amount depreciated each year / period.   
B  Accelerated   
C  DDB: 50% during the first year, then dividing into half each following year. Since we're depreciating it over 4 years, we depreciate the remainder in year 4.   
D 
SYD: No. of years left/Sum of the years.
Year 1: 4/10 or 40% Year 2: 3/10 or 30% Year 3: 2/10 or 20% Year 4: 1/10 or 10% 
 