ENG2000 Chapter 16 Evaluating and Comparing Projects: The MARR. ENG2000: R.I. Hornsey CM: 1

Transcription

1 ENG2000 Chapter 16 Evaluating and Comparing Projects: The MARR ENG2000: R.I. Hornsey CM: 1

2 Overview So, we have seen that the act of investing is to sacrifice something of present value in the expectation of receiving more value at a future time As an engineer making a decision about whether to go ahead with a project, your job is to determine whether the future returns merit the present investment In order to compare options, we must convert the transactions into a common value present worth annual worth payback period ENG2000: R.I. Hornsey CM: 2

3 Assumptions Decisions are made on a purely financial basis clearly this is not always the case, e.g. safety or environment one can theoretically calculate the value of a safe workplace or the fines avoided by being environmentally sound, but it s impossible in practise Future cash flows are known accurately there are techniques for dealing with this uncertainty We do not account for inflation can also be handled in more complex treatments All options are equally feasible in reality, some may be excluded because of insufficient resources etc ENG2000: R.I. Hornsey CM: 3

4 No taxes yeah, right! All projects have an initial cash flow called first costs and that all projects have subsequent cash flows that equal or exceed the first costs ENG2000: R.I. Hornsey CM: 4

5 Relationships between projects When there are several possible projects available, we need to know what (if any) relationship there is between them independent mutually exclusive related but not mutually exclusive ENG2000: R.I. Hornsey CM: 5

6 Independent projects In this case, neither the expected costs nor the expected benefits of the possible projects are in any way related and so the numbers do not change if one or other (or both) projects go ahead In reality, there may not be enough funds to pursue two otherwise independent projects but, in the current scenario, this violates one of the assumptions In the case of independent projects, each is treated on its own merits and the costs are compared directly ENG2000: R.I. Hornsey CM: 6

7 Mutually exclusive projects In many cases, we will pursue either one option or the other but not all e.g. we will build either an office block or a factory on the land we own we ll buy Agilent equipment rather than National Instruments we will buy a BMW or a Lexus (mutually exclusive in most cases!) Again, each option can be considered on its own merits ENG2000: R.I. Hornsey CM: 7

8 Related but not mutually exclusive Here, costs and benefits of one option depend on whether or not a different option is chosen e.g. opening two Starbucks franchises in close proximity clearly the returns will be different if one or both go ahead and costs may be reduced if both are constructed simultaneously In this case, we can make four logical groups open both open #1 open #2 open neither In general n related projects can be grouped into 2 n sets which are mutually exclusive ENG2000: R.I. Hornsey CM: 8

9 Contingent projects A special case of the related but not exclusive is where one project is contingent on another e.g. you can buy a PC and a printer, or a PC without a printer but you re not likely to buy a printer without a PC hence the printer purchase is contingent on the purchase of a PC When there are several related projects 2 n can be a large number this can be reduced by determining feasibilities using a matrix technique such as a morphological chart ENG2000: R.I. Hornsey CM: 9

10 Summary relations Set of n projects related but not mutually exclusive divide into 2 n mutually exclusive sets independent: evaluate each one separately mutually exclusive: rank and pick the best ENG2000: R.I. Hornsey CM: 10

11 Minimum acceptable rate of return The minimum acceptable rate of return (MARR) is a lower limit for investment acceptability the MARR is an effective interest rate that must be earned by a project in order to make the project acceptable in comparison to competing investment opportunities Hence, projects making a higher return that the MARR are desirable those projects earning a lower return are undesirable since the money can get better returns elsewhere In order to attract investors, a company must participate in projects returning more than the MARR the minimum return required by investors is called the company s cost of capital ENG2000: R.I. Hornsey CM: 11

12 The MARR represents an opportunity cost investors have a choice of investing in your company or elsewhere if the company invests in one project, it gives up the opportunity to invest in another project which would pay the MARR The A in MARR is sometimes attractive The point is clearer if one imagines that the money to be spent on the project is being borrowed at a specified interest rate so the project must give a return in excess of that interest rate however, investors or management may set a different level for the MARR ENG2000: R.I. Hornsey CM: 12

13 Example 4.2 Alex Student notices that students frequently have to wait for computer terminals he proposes to offer an alternative location in a nearby mall it will cost Alex $ to set up the service the annual net cash flow (after expenses) is expected to be $30,000 for five years (after which the new university terminal room will be available) the salvage value of the 5-year-old equipment is negligible If investors in such a hi-tech venture expect an annual return of 20%, is Alex s proposal a good investment? ENG2000: R.I. Hornsey CM: 13

14 Example 4.3 A mechanical engineer is considering building automated materials handling equipment for a production line on one hand the equipment would substantially reduce the manual labour required for the materials handling on the other hand, it will consume energy, require insurance, and maintenance Option 1 continue with present method; labour costs $9 200/year Option 2 build new equipment with a life of 10 years First cost $15 000; labour $3 300/year; power $400/year; maintenance $2 400/year; tax & insurance $300/year Which is preferable if the MARR is 9%? ENG2000: R.I. Hornsey CM: 14

15 Present worth (PW) comparison PW analysis compares the present worth of all the cash flows using the MARR as the interest rate the highest PW is preferable and indeed the value of a company can be assessed as the sum of the PWs of all the current projects The PW of a project exactly at the MARR is zero since the future receipts exactly balance the initial disbursement and the project is deemed marginally acceptable In order to be acceptable we need our project to have a PW > 0 otherwise the do nothing option (= invest elsewhere) is preferable ENG2000: R.I. Hornsey CM: 15

16 Present and annual cost While we have been talking about the worth of a project, we can also compare costs This assumes that the major benefits of the projects are identical and can therefore be neglected in the calculations, since they are the same for each option This approach also assumes that the value of each project clearly exceeds its costs i.e. they are all viable projects and we are looking for the lowest cost viable option ENG2000: R.I. Hornsey CM: 16

17 Example 4.2 Alex Student notices that students frequently have to wait for computer terminals he proposes to offer an alternative location in a nearby mall it will cost Alex $ to set up the service the annual net cash flow (after expenses) is expected to be $ for five years (after which the new university terminal room will be available) the salvage value of the 5-year-old equipment is negligible If investors in such a hi-tech venture expect an annual return of 20%, is Alex s proposal a good investment? ENG2000: R.I. Hornsey CM: 17

18 4.2 Solution ENG2000: R.I. Hornsey CM: 18

19 Example 4.3 A mechanical engineer is considering building automated materials handling equipment for a production line on one hand the equipment would substantially reduce the manual labour required for the materials handling on the other hand, it will consume energy, require insurance, and maintenance Option 1 continue with present method; labour costs $9200/year Option 2 build new equipment with a life of 10 years First cost $15,000; labour $3,300/year; power $400/year; maintenance $2,400/year; tax & insurance $300/year Which is preferable if the MARR is 9%? ENG2000: R.I. Hornsey CM: 19

20 4.3 solution ENG2000: R.I. Hornsey CM: 20

21 Annual worth (AW) comparisons These are essentially the same as the PW calculations except that the PW is converted to an annual series at the MARR using the capital recovery factor, (A/P,i,n) One gets the same result with PW and AW provided the lifes are the same The difference between AW and PW is often perceptual it s often easier to grasp an annual cost, rather than a single present worth ENG2000: R.I. Hornsey CM: 21

22 Unequal lives It is important to cover the same time periods for even the PW calculations so the full advantages and costs are included in both There are two approaches to unequal lives Use a repeated lowest common multiple from the choices known as repeated service lives each repetition has the same cash flows may not be valid for equipment which quickly becomes obsolete Use a defined study period define a time period for the calculations affects the salvage value that can be assumed ENG2000: R.I. Hornsey CM: 22

23 4.3 revisited (MARR = 9%) Option 1: build equipment first cost $ labour $3 300/year power $400/year maintenance $2 400/year tax & insurance $300/year a life of 10 years Option 2: buy off-the-shelf equipment first cost $25,000 labour $1 450/year power $600/year maintenance $3 075/year tax & insurance $500/year a life of 15 years ENG2000: R.I. Hornsey CM: 23

24 New 4.3 solution ENG2000: R.I. Hornsey CM: 24

25 Payback method Useful for assessing the economic viability of projects roughly giving the amount of time needed to recover an initial investment (i.e. pay for itself) The payback period is the number of years taken for an investment to be recouped with 0% interest rate Payback period = first cost annual savings e.g. an initial investment of $20,000 saves $8,000 per year, gives a payback period of 2.5 years ENG2000: R.I. Hornsey CM: 25

26 If the annual returns are not equal, simply subtract each return from the first cost until it vanishes e.g. $ investment saves $5 000 in year 1, $6 000 in year 2, $7 000 in year 3,etc. now $ $ $ $8 000 = $ so the payback period is either 4 years (if the $8 000 is not received until the end of the year) or 3.25 years if the $8 000 is spread out throughout the year Now, the project with the shorted payback period is the preferred option typically a payback between 2 and 4 years is considered reasonable, although it depends a lot on the circumstances ENG2000: R.I. Hornsey CM: 26

27 Advantages of payback approach Straightforward and easy to understand Easy to calculate Identifies period of cash-flow and speed of recovery of capital Given uncertainties about future returns on investments, a more precise calculation may be unwarranted ENG2000: R.I. Hornsey CM: 27

28 Disadvantages of payback approach Tends to make long-term projects seem unattractive Timings of cash flows within the payback period are ignored no account taken of the time value of money Ignores service life and benefits that occur outside the payback period ENG2000: R.I. Hornsey CM: 28

29 Discounted payback period A better estimate can be obtained (at the expense of more complex calculations) id the PW of each year s savings are deducted from the first cost If you invest $5 000 and receive $2 000 per year in benefits but the interest rate is 10% Year Year 1 Year 2 Year 3 Year 4 Present worth $2 000(P/F,10%,1) = $1 818 $2 000(P/F,10%,2) = $1 653 $2 000(P/F,10%,3) = $1 503 $2 000(P/F,10%,4) = $1 366 Cumulative $1 818 $3 471 $4 974 $6 340 compare with standard technique, which gives 5000/2000 = 2.5 years ( P / F,i,N) = 1 ( 1+i) N ENG2000: R.I. Hornsey CM: 29

30 Example 4.10 Self Defence Systems is going to upgrade their paper shredding facility and have a choice between two models Model 007 first cost: $ life: 7 years saving: $10 000/year Model MX first cost: $ life: 20 years saving: $1 500/year MARR is 8% ENG2000: R.I. Hornsey CM: 30

31 Example 4.10 solution ENG2000: R.I. Hornsey CM: 31

32 Summary Here we considered how to choose between different projects independent mutually exclusive related nut not mutually exclusive For these situations we primarily examined the present worth method where all cash flows are converted to the present worth for comparison although this can be converted to an annual worth simply We also looked at the payback period a rough way of determining how long it takes to recover an initial investment ENG2000: R.I. Hornsey CM: 32