5.4 Rate of Return and Present/Annual Worth Methods Compared
5.4.2 Why Choose One Method Over the Other?
Although rate of return methods and present worth/annual worth methods give the same decisions, each set of methods has its own advantages and disadvantages. The choice of method may depend on the way the results are to be used and the sort of data the decision makers prefer to consider. In fact, many companies, by policy, require that several methods be applied so that a more complete picture of the situation is presented. A summary of the advantages and disadvantages of each method is given in Table 5.2.
Method Advantages Disadvantages
IRR Facilitates comparisons of Relatively difficult to calculate projects of different sizes Multiple IRRs may exist Commonly used
Present Gives explicit measure Difficult to compare projects worth of profit contribution of different sizes
Annual Annual cash flows may Difficult to compare projects worth have familiar meanings of different sizes
to decision makers
Payback Very easy to calculate Discriminates against
long-period Commonly used term projects
Takes into account Ignores time value of money the need to have capital Ignores the expected service recovered quickly life
Table 5.2 Advantages and Disadvantages of Comparison Methods
Rate of return methods state results in terms of rates, while present/annual worth methods state results in absolute figures. Many managers prefer rates to absolute figures because rates facilitate direct comparisons of projects whose sizes are quite different. For example, a petroleum company comparing performances of a refining division and a distribution division would not look at the typical values of present or annual worth for projects in the two divisions. A refining project may have first costs in the range of hundreds of millions, while distribution projects may have first costs in the range of thousands. It would not be meaningful to compare the absolute profits of a refining project and a distribution project. The absolute profits of refining projects will almost certainly be larger than those of distribution projects. Expressing project performance in terms of rates of return permits understandable comparisons. A disadvantage of rate of return methods, however, is the possible complication that there may be more than one rate of return.
Under such circumstances, it is necessary to calculate an ERR.
In contrast to a rate of return, a present or annual worth computation gives a direct measure of the profit provided by a project. A company’s main goal is likely to earn profits for its owners. The present and annual worth methods state the contribution of a project toward that goal. Another reason that managers prefer these methods is that present worth and annual worth methods are typically easier to apply than rate of return methods.
For completeness of coverage, we note that the payback period method may not give results consistent with rate of return or present/annual worth methods as it ignores the time value of money and the service life of projects. It is, however, a method commonly used in practice due to its ease of use and intuitive appeal.
EXAMPLE 5.11
Each of the following scenarios suggests a best choice of comparison method.
1. Edward has his own small firm that will lease injection-moulding equipment to make polyethylene containers. He must decide on the specific model to lease. He has estimates of future monthly sales.
The annual worth method makes sense here because Edward’s cash flows, including sales receipts and leasing expenses, will probably all be on a monthly basis. As a sole proprietor, Edward need not report his conclusions to others.
2. Ramesh works for a large power company and must assess the viability of locat-ing a transformer station at various sites in the city. He is looklocat-ing at the cost of the building lot, power lines, and power losses for the various locations. He has fairly accurate data about costs and future demand for electricity.
As part of a large firm, Ramesh will likely be obliged to use a specific com-parison method. This would probably be IRR. A power company makes many large and small investments, and the IRR method allows them to be compared fairly. Ramesh has the data necessary for the IRR calculations.
3. Sehdev must buy a relatively inexpensive log splitter for his agricultural firm.
There are several different types that require a higher or lower degree of manual assistance. He has only rough estimates of how this machine will affect future cash flows.
This relatively inexpensive purchase is a good candidate for the payback period method. The fact that it is inexpensive means that extensive data gather-ing and analysis are probably not warranted. Also, since future cash flows are
relatively uncertain, there is no justification for using a particularly precise comparison method.
4. Ziva will be living in the Arctic for six months, testing her company’s equipment under hostile weather conditions. She needs a field office and must determine which of the following choices is economically best: (1) renting space in an industrial building, (2) buying and outfitting a trailer, (3) renting a hotel room for the purpose.
For this decision, a present worth analysis would be appropriate. The cash flows for each of the alternatives are of different types, and bringing them to present worth would be a fair way to compare them. It would also provide an accurate estimate to Ziva’s firm of the expected cost of the remote office for planning purposes._________________________________________________쏋
R E V I E W P R O B L E M S
R E V I E W P R O B L E M 5 . 1
Wei-Ping’s consulting firm needs new quarters. A downtown office building is ideal. The company can either buy or lease it. To buy the office building will cost $6 000 000. If the building is leased, the lease fee is $400 000 payable at the beginning of each year. In either case, the company must pay city taxes, maintenance, and utilities.
Wei-Ping figures that the company needs the office space for only 15 years.
Therefore, it will either sign a 15-year lease or buy the building. If it buys the building, it will then sell the building after 15 years. The value of the building at that time is esti-mated to be $15 000 000.
What rate of return will Wei-Ping’s firm receive by buying the office building instead of leasing it?
A N S W E R
The rate of return can be calculated as the IRR on the incremental investment necessary to buy the building rather than lease it.
The IRR on the incremental investment is found by solving for i*in (6 000 000 400 000) 15 000 000(P/F,i*,15) 400 000(P/A,i*,14) 4(P/A,i*,14) 150(P/F,i*,15) 56
For i* 11 percent, the result is
4(P/A,11%,14) 150(P/F,11%,15)
4(6.9819) 150(0.20900)
59.2781 For i* 12 percent,
4(P/A,12%,14) 150(P/F,12%,15)
4(6.6282) 150(0.1827)
53.9171
A linear interpolation between 11 percent and 12 percent gives the IRR i* 11% (59.2781 56)/(59.2781 53.9171) 11.6115%
By investing its money in buying the building rather than leasing, Wei-Ping’s firm is earning an IRR of about 11.6 percent.■
R E V I E W P R O B L E M 5 . 2
The Real S. Tate Company is considering investing in one of four rental properties. Real S.
Tate will rent out whatever property it buys for four years and then sell it at the end of that period. The data concerning the properties is shown below:
Rental Purchase Net Annual Sale Price at the Property Price Rental Income End of Four Years
1 $100 000 $ 7200 $100 000
2 120 000 9600 130 000
3 150 000 10 800 160 000
4 200 000 12 000 230 000
On the basis of the purchase prices, rental incomes, and sale prices at the end of the four years, answer the following questions.
(a) Which property, if any, should Tate invest in? Real S. Tate uses a MARR of 8 percent for projects of this type.
(b) Construct a graph that depicts the present worth of each alternative as a function of interest rates ranging from 0 percent to 20 percent. (A spreadsheet would be helpful in answering this part of the problem.)
(c) From your graph, determine the range of interest rates for which your choice in part (a) is the best investment. If the MARR were 9 percent, which rental prop-erty would be the best investment? Comment on the sensitivity of your choice to the MARR used by the Real S. Tate Company.
A N S W E R
(a) Since the “do nothing” alternative is feasible and it has the least first cost, it becomes the current best alternative. The IRR on the incremental investment for property 1 is given by:
100 000 100 000(P/F,i*,4) 7200(P/A,i*,4) 0
The IRR on the incremental investment is 7.2 percent. Because this is less than the MARR of 8 percent, property 1 is discarded from further consideration.
Next, the IRR for the incremental investment for property 2, the alternative with the next-highest first cost, is found by solving for i* in
120 000 130 000(P/F,i*,4) 9600(P/A,i*,4) 0
The interest rate that solves the above equation is 9.8 percent. Since an IRR of 9.8 percent exceeds the MARR, property 2 becomes the current best alternative. Now the incremental investments over and above the first cost of property 2 are analyzed.
Next, property 3 challenges the current best. The IRR on the incremental investment for property 3 is
(150 000 120 000) (160 000 130 000)(P/F,i*,4)
(10 800 9600)(P/A,i*,4) 0
30 000 30 000(P/F,i*,4) 1200(P/A,i*,4) 0
This gives an IRR of only 4 percent, which is below the MARR. Property 2 remains the current best alternative and property 3 is discarded.
Finally, property 4 challenges the current best. The IRR on the incremental investment from property 2 to property 4 is
(200 000 120 000) (230 000 130 000)(P/F,i*,4)
(12 000 9600)(P/A,i*,4) 0
80 000 100 000(P/F,i*,4) 2400(P/A,i*,4) 0
The IRR on the incremental investment is 8.5 percent, which is above the MARR. Property 4 becomes the current best choice. Since there are no further challengers, the choice based on IRR is the current best, property 4.
(b) The graph for part (b) is shown in Figure 5.11.
(c) From the graph, one can see that property 4 is the best alternative provided that the MARR is between 0 percent and 8.5 percent. This is the range of interest rates over which property 4 has the largest present worth.
If the MARR is 9 percent, the best alternative is property 2. This can be seen by going back to the original IRR computations and observing that the
–60 000 –40 000 –20 000 0 20 000 40 000 60 000 80 000
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2
Interest rate
Property 1 Property 2 Property 3 Property 4
Present worth ($)
Figure 5.11 Present Worth for Review Problem 5.2
results of the analysis are essentially the same, except that the incremental investment from property 2 to property 4 no longer has a return exceeding the MARR. This can be confirmed from the diagram (Figure 5.11) as well, since the property with the largest present worth at 9 percent is property 2.
With respect to sensitivity analysis, the graph shows that, for a MARR between 0 percent and 8.5 percent, property 4 is the best choice, and for a MARR between 8.5 percent and 9.8 percent, property 2 is the best choice. If the MARR is above 9.8 percent, no property has an acceptable return on investment, and the
“do nothing” alternative would be chosen.■
R E V I E W P R O B L E M 5 . 3
You are in the process of arranging a marketing contract for a new Java applet you are writing. It still needs more development, so your contract will pay you $5000 today to finish the prototype. You will then get royalties of $10 000 at the end of each of the second and third years. At the end of each of the first and fourth years, you will be required to spend $20 000 and $10 000 in upgrades, respectively. What is the (approximate) ERR on this project, assuming a MARR of 20 percent? Should you accept the contract?
A N S W E R
To calculate the approximate ERR, set
FW(receipts @ MARR) FW(disbursements @ ERR)
5000(F/P,20%,4) 10 000(F/P,20%,2) 10 000(F/P,20%,1)
20 000(F/P,i*ea ,3) 10 000
5000(2.0736) 10 000(1.44) 10 000(1.2)
20 000(F/P,i*ea ,3) 10 000 (F/P,i*ea ,3) 1.3384
(1 i*ea)3 1.3384
i*ea(1.3384)(1/3)1
10.2%
The (approximate) ERR is 10.2 percent. Since this is below the MARR of 20 percent, the contract should not be accepted.■
S U M M A R Y
This chapter presented the IRR method for evaluating projects and also discussed the relationship among the present worth, annual worth, payback period, and IRR methods.
The IRR method consists of determining the rate of return for a sequence of cash flows. For an independent project, the calculated IRR is compared with a MARR, and if