NPV Method. Payback Period

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Drusilla Bryant
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1 1. Why the payback method is often considered inferior to discounted cash flow in capital investment appraisal? A. It does not take account of the time value of money B. It does not calculate how long it will take to recoup the money invested C. It is more difficult to calculate D. It only takes into account the future income of a project (Ans.: A) Explanation: NPV Method Under the net present value method, a business estimates all the cash flows, both positive (revenue) and negative (costs), of pursuing a project, now and in the future. It then adjusts, or "discounts," the value of future cash flows to reflect what they're worth in the present day. It makes this adjustment using a "discount rate" that takes into account inflation, the risk of the project and the cost of capital -- either interest paid on borrowed money or interest not earned on money spent to pursue the project. Finally, it adds up the present values of all the positive and negative cash flows to arrive at the net present value, or NPV. If the NPV is positive, the project is worth pursuing; if it's negative, the project should be rejected. When deciding between projects, choose the one with the higher NPV. Payback Period Under the payback period method, a company estimates how much it will cost to launch the project and how much money the project will generate once it's up and running. It then calculates how long it will take the project to "break even," or generate enough money to cover the startup costs. Companies using the payback period method typically choose a time horizon -- for example, 2, 5 or 10 years. If a project can "pay back" the startup costs within that time horizon, it's worth doing; if it can't, the project will be rejected. When deciding between projects, choose the one with the shorter payback period. Pros and Cons The payback period method has some key weakness that the NPV method does not. One is that the payback method doesn't take into account inflation and the cost of capital. It essentially equates $1 today with $1 at some point in the future, when in fact the purchasing power of money declines over time. Another is that the payback method ignores all cash flows beyond the time horizon -- and those cash flows may be substantial. Big moneymakers, after all, sometimes take a while to get going. On the other hand, the big drawback of the NPV method lies in its assumptions. If you don't get your

2 estimate of the discount rate correct, your calculation will be off -- and you won't know it until the project turns into a big money-loser. Combining Methods Many businesses use a combination of methods when making capital budgeting decisions. A company could use the payback period method to narrow down its options, then apply the NPV method to identify the best of the remaining projects. Or it could use the NPV method to separate the "winners" from the "losers" among possible projects, then look at payback periods to see which projects return their costs more quickly.

3 2. Guddu is considering the purchase of an asset for Rs.120,000. This asset will generate the following cash flows: Year Rs. Year 1 15,000 Year 2 25,000 Year 3 40,000 Year 4 40,000 Year 5 35,000 Year 6 30,000 Using a discount rate of 20% the discounted payback period would be: A. 6 years B. 4 years C. The investment does not pay back D. 5 years (Ans.: C) Explanation: The discounted payback can be calculated in the following way: Year Cash Flow (Rs.) Discount Factor Discounted Cash Flow (Rs.) Cumulative Cash Flow (Rs.) 0 (120,000) (120,000) (120,000) 1 15, ,495 (107,505) 2 25, ,350 (90,155) 3 40, ,160 (66,995) 4 40, ,280 (47,715) 5 35, ,070 (33,645) 6 30, ,660 (23,985) The project does not pay back the original cost of the asset.

4 3. A project that has been tested for its feasibility has already incurred market research costs of Rs.50,000. The actual cost of the asset is Rs.100,000 and the project is expected to yield the following returns: Year 1 Rs. 90,000 Year 2 Rs. 80,000 Year 3 Rs.70,000 If the discount rate is 12% the NPV of the project will be: A. Rs.140,000 B. Rs.44,000 C. Rs.94,000 D. Rs.294,000 (Ans.: C) Explanation: The market research expenditure that has already been incurred is a sunk cost and is irrelevant in the decision to accept or reject the project. The appraisal for the project is: Year Cash Flow (Rs.) Discount Rate Discounted Cash Flow (Rs.) Year 0 (100,000) (100,000) Year 1 Rs. 90, ,370 Year 2 Rs. 80, ,440 Year 3 Rs.70, ,840 93,650 The NPV of the project is approximately Rs.94,000.

5 4. A company is considering investing in a machine with a capital cost of Rs.300,000 with a useful life of 4 years. Annual running costs are expected to amount to Rs.276,000 including straight line depreciation of Rs.70,000 per annum. It is estimated that the machine can be disposed of at its net book value at the end of its life. The capacity of the machine will be 6 million items for the first two years but this will fall to 5 million items in years 3 and 4. It is estimated that the company will be able to sell whatever the machine produces. The average contribution is Rs.60 per 1,000 units. What is the payback period for the machine? A years B years C years D years (Ans.: B) Explanation: The machine will generate the following profits: Year ContribCumulative Annual costs Investment Cash flow Cost/scrap Cash flow (Rs.) value (Rs.) running (Rs.) (Rs.) 0 300,000 (300,000) 1 360, , ,000 (146,000) 2 360, , ,000 10, , ,000 94, , , ,000 20, , ,000 The project pays back between years 1 and 2. We can interpolate to find the exact payback period as follows: Payback period = 1 year + (2 years - 1 year) * (Rs.146,000/(Rs.146,000 + Rs.10,000)) Payback period = 1 year + (1 year) * (0.94) Payback period = 1.94 years, i.e. almost two years.

6 5. The discount factor used to appraise capital investment decisions is a measure of: A. The current high street interest rate B. The opportunity cost of capital of all businesses in the same industry C. The current inflation rate D. The opportunity cost of capital of the business (Ans.: D) Explanation: The opportunity cost of capital is the incremental return on investment that a business foregoes when it elects to use funds for an internal project, rather than investing cash in a marketable security. Thus, if the projected return on the internal project is less than the expected rate of return on a marketable security, one would not invest in the internal project, assuming that this is the only basis for the decision. The opportunity cost of capital is the difference between the returns on the two projects.

7 Answer question 6 8 based on the information given below. Table below shows the information related to a project that involves the merger of two marketing firms (in days). Activity Immediate Predecessor(s) Estimated Duration (days) A - 10 B - 15 C A 2 D B 12 E C, D 14 F B 8 G D, F 15 H E 10 I E, G 6 J F, I 9 6. What is the critical path? (Ans.: A) A. Start-B-D-G-I-J-Finish B. Start-A-C-E-I-J-Finish C. Start-B-D-E-I-J-Finish D. Start-A-C-E-H-Finish 7. What is the project completion duration? (Ans.: B) A. 58 days B. 57 days C. 55 days D. 56 days 8. If there is an option to delay one activity without delaying the entire merge project, which activity would you delay? A. Activity A B. Activity B C. Activity A and Activity C D. None of these (Ans.: C) Explanation: The project schedule is as follows: Activity Earliest Start Latest Start Earliest Finish Latest Finish Slack Start A

B 0 0 15 15 0 C 10 23 15 28 13 D 15 15 27 27 0 E 27 28 41 42 1 F 15 19 23 27 4 G 27 27 42 42 0 H 41 47 51 57 6 I 42 42 48 48 0 J 48 48 57 57 0 Finish

8 B C D E F G H I J Finish The critical activities are: B-D-G-I-J The project completion duration is 57 days. Activity A or C since they have the largest slack times.

9 Answer question 9 14 based on the information given below. Consider the network information shown in the previous problem (Problems 7-9) and assume that the duration of some activities is not known with certainty. The estimates of these activities are shown below, assuming that the duration for the other activities remains unchanged. Activity Optimistic Most Likely Pessimistic A C D G H What is the critical path? A. Start-B-D-G-I-J-Finish B. Start-A-C-E-I-J-Finish C. Start-B-D-E-I-J-Finish D. Start-A-C-E-H-Finish (Ans.: A) 10. What is the project s expected completion time? A. 58 days B. 57 days C. 55 days D. 56 days (Ans.: B) 11. What is the variance of the expected completion time? A B C D (Ans.: C) 12. What is the probability that the project will be completed in 60 days or more? A. 0.10% B. 0.20% C. 0.15% D. 0.05% (Ans.: A) 13. What is the probability that the project will be completed in 55 days or more?

10 (Ans.: B) A B C D If the company wants a 96% probability of completing the project on time, state the latest time each activity should have started and completed. A. 57 days B days C days D. 60 days (Ans.: B) Explanation: The mean and variance for activities for which the duration is not known with certainty: Activity a m b t e σ 2 A C D G H The critical path is Start-B-D-G-I-J-Finish. The expected project completion time is 57 days and its variance is = The probability that the project will be completed in 60 days or more: P(X 60) = P(X z), where z = = Therefore, P(X 3.198) = = or 0.1 % The probability that the project will be completed in 55 days or less: P(X 50) = P(X z), where z = = Therefore, P(X 2.13) = = or 2.12 % Z 0.96 = 1.76, the project completion time X = = days. Therefore to meet this completion time, the latest start and finish times for each activity should be as follows: Activity Latest Start Latest Finish Start A B C D E F G H I J Finish

11 15. A company has to make a choice between two projects, because the available resources in money and kind are not sufficient to run both at the same time. Each project would take 9 months and would cost $250,000. The first project is a process optimization which would result in a cost reduction of $120,000 per year. This benefit would be achieved immediately after the end of the project. The second project would be the development of a new product which could produce the following net profits after the end of the project: YEAR PROFIT 1 st year $15,000 2 nd Year $125,000 3 rd Year $220,000 Assumed a discount rate of 5% per year. Looking at the present values of the benefits of these projects in the first 3 years, what is true? A. Both projects are equally attractive. B. The first project is more attractive by approx. 7%. C. The second project is more attractive by approx. 5%. D. The first project is more attractive by approx. 3%. (Ans.: D) PV=FV/(1+R)^Y Project 1 Yr1 $ 120,000/(1+0.05)^1 = $ 114,286 Yr2 $ 120,000/(1+0.05)^2 = $ 108,844 Yr2 $ 120,000/(1+0.05)^3 = $ 103,661 Total $ 326,791 Project 2 Yr1 $ 15,000/(1+0.05)^1 = $ 14,286 Yr2 $ 125,000/(1+0.05)^2 = $ 113,379 Yr2 $ 220,000/(1+0.05)^3 = $ 190,044 Total $ 317,709 Conclusion: Project 1 has better return by 3% (326,791/317,709 = ). Benefit Cost Ration ( BCR ) = / = This means Payback is 1.3 times of the cost.

12 16. The objective of project crashing is to: A) Reduce the project duration and revise the network critical path and completion times when the schedule falls hopelessly behind B) Minimize the cost of crashing C) Reduce indirect costs such as interest on investments D) More than one statement above is true (Ans.: D)

13 17. Shared slack in an activity network is defined as: A) The amount of time an activity can be delayed without delaying the entire project. B) The amount of slack that an activity has in common with another activity. C) The amount of unused resources for an activity. D) The amount by which a time estimate can be in error without affecting the critical path computations. (Ans.: B)

14 18. Based on the list of activities below which of the following can be said? Activity IP A - B - C A, B D A, C A) Activity D can begin as soon as both activities A and B are complete. B) Activity C can begin as soon as activity B is complete. C) Activity D can begin as soon as both activities A and C are complete. D) Activity C can begin as soon as activity A is complete. (Ans.: C)

15 19. An expected project completion time follows a normal distribution with a mean of 21 days and a standard deviation of 4 days. What is the probability that the project will be completed in a time between 22 to 25 days inclusive? A) B) C) D) (Ans.: C)

16 20. The latest finish time for an activity: A) Equals the min. of EST + t for all immediate successors. B) Equals the max. of EST + t for all immediate predecessors. C) Equals the min. of LFT t for all immediate successors. D) Equals the max. of LFT t for all immediate predecessors. (Ans.: C)

Answer Questions 21 25 based on the information given above: Indirect cost for a project is $12 000 per week for as long as the project lasts.

17 Answer Questions based on the information given above: Indirect cost for a project is $ per week for as long as the project lasts. The project manager has supplied the cost and time information and precedence network diagram shown in Figure and the table given below: Activity Crashing Potential (Weeks) Cost per Week to Crash A 3 $11,000 B 3 $3,000 (1 st Week), $4,000 (2 nd Week) C 2 $6,000 D 1 $1,000 E 3 $6,000 F 1 $2, What is the total duration of the project after all activities are crashed? A. 23 Weeks B. 22 Weeks C. 21 Weeks D. 20 Weeks (Ans.: D) 22. What is the total cost of the project involved after all activities are crashed? A. Rs. 276,000 B. Rs. 271,000 C. Rs. 273,000 D. Rs. 279,000 (Ans.: A) 23. Which activity/activities is/are crashed in the 1 st iteration? A. Activity A

18 B. Activity B C. Both A and B D. None of these (Ans.: B) 24. Which activity/activities is/are crashed in the 2 nd iteration? A. Only activity B B. Only activity F C. Both B and F D. Both F and E (Ans.: C) 25. Which activity/activities is/are crashed in the 3 rd iteration? A. Only activity A B. Only activity B C. Only activity E D. Both B and E (Ans.: D) Explanation: Calculate path lengths and identify the critical path: Path Duration (weeks) S-A-B-End 24 (critical path) S-C-D-End 19 S-E-F-End 23 Rank critical activities according to crash costs: Activity Cost per Week to Crash B $3000 first week, $4000 after that A Activity B should be shortened one week since it has the lower crashing cost per week. This would reduce indirect costs by $ at a cost of $3000, for a net savings of $9000. At this point, paths S- A-B-End and S-E-F-End would both have a length of 23 weeks, so both would be critical. Rank activities by crashing cost on the two critical paths: Path Activity Cost per Week to Crash S-A-B-End B $ A $ S-E-F-End F $ E $6000

Choose one activity (the least costly) on each path to crash: B on S-A-B-End and F on S-E-F-End, for a total cost of $4000 + $2000 = $6000 and a net savings of $12 000 - $6000 = $6000.

19 Choose one activity (the least costly) on each path to crash: B on S-A-B-End and F on S-E-F-End, for a total cost of $ $2000 = $6000 and a net savings of $ $6000 = $6000. Note: There is no activity common to the two critical paths. Check to see which path(s) might be critical: S-A-B-End and S-E-F-End would be 22 weeks in length, and S-C-D-End would still be 19 weeks. Rank activities on the critical paths: Path Activity Cost per Week to Crash A-B..... B $ A $ E-F..... E $ F (no further crashing possible) Crash B on path S-A-B-End and E on S-E-F-End for a cost of $ $6000 = $10 000, for a net savings of $ $ = $2000. At this point, no further reduction is cost-effective: paths S-A-B-End and S-E-F-End would be 21 weeks in length, and one activity from each path would have to be shortened. This would mean activity A at $ and E at $6000 for a total of $17 000, which exceeds the $ potential savings in indirect costs. Note that no further crashing for activity B is possible. The following table summarizes the results, showing the length of the project after crashing n weeks: Path n = S-A-B-End S-C-D-End S-E-F-End Activity crashed B B,F B,E Crashing costs ($000)

A convenient analytical and visual technique of PERT and CPM prove extremely valuable in assisting the managers in managing the projects.

A convenient analytical and visual technique of PERT and CPM prove extremely valuable in assisting the managers in managing the projects. Introduction Any project involves planning, scheduling and controlling a number of interrelated activities with use of limited resources, namely, men, machines, materials, money and time. The projects