ABC Incorporated is considering the following projects for possible investment next year. Each project has a 5-year useful life and no salvage value. For 15% MARR, and a capital outlay of $25,000, which projects should be funded under ROR?

Question

Project	1	2	3	4	5	6	7	8
First Cost	$5,000	$4,500	$2,500	$3,000	$5,000	$5,500	$6,000	$7,000
Annual Benefit	$1,319	$1,673	$836	$771	$1,492	$1,759	$1,963	$2,341

Accepted Answer

The solution procedure comprises the following steps. If the RORs are given, skip step 1.

Step 1: Evaluate the ROR of each project

All the projects have a 5-year useful life, i.e., n = 5. Calculate the ROR of each project as learned in Chapter 7. For example, for project 3, we have:

[latex]2,500=836({P}/{A},i,5)[/latex]

Thus,

[latex]({P}/{A},i,5) = {2,500}/{836}[/latex]

[latex]=2.9904[/latex]

From the interest tables, for the above value of the factor, [latex]i\approx 20\%[/latex]. Thus, the rate of return for the third project is 20%. Once all the RORs have been evaluated, they are tabulated, as follows.

Project	First Cost	Annual Benefit	Computed ROR, %
1	$5,000	$1,319	10
2	$4,500	$1,673	25
3	$2,500	$836	20
4	$3,000	$771	9
5	$5,000	$1,492	15
6	$5,500	$1,759	18
7	$6,000	$1,963	19
8	$7,000	$2,341	20

Step 2: Discard the unattractive projects
Check to see which of the projects have ROR less than the desired MARR, and discard them. In this case, for 15% MARR, projects 1 and 4 are discarded.

Step 3: Arrange the remaining projects
Arrange the remaining projects in descending order of ROR, as follows .

Project	First Cost	Annual Benefit	Computed ROR, %
2	$4,500	$1,673	25
3	$2,500	$836	20
8	$7,000	$2,341	20
7	$6,000	$1,963	19
6	$5,500	$1,759	18
5	$5,000	$1,492	15

Step 4: Allocate the available capital
Begin to allocate the available capital. Since project 2 tops the list due to its highest ROR, its required capital of $4,500 is allocated first. The next two projects, 3 and 8, have the same ROR, so they are allocated together, but 3 is preferred due to its lower capital need.
The allocations can be tabulated in another column, as follows.

Project	First Cost	Annual Benefit	Computed ROR, %	Allocation
2	$4,500	$1,673	25	$4,500
3	$2,500	$836	20	$2,500
8	$7,000	$2,341	20	$7,000
7	$6,000	$1,963	19
6	$5,500	$1,759	18
5	$5,000	$1,492	15

The allocation process is continued until all the available capital has been used up. To keep track of this constraint another column is created, as below, to record the cumulative allocation.

Project	First Cost	Annual Benefit	Computed ROR, %	Allocation	Cumulative Allocation
2	$4,500	$1,673	25	$4,500	$4,500
3	$2,500	$836	20	$2,500	$7,000
8	$7,000	$2,341	20	$7,000	$14,000
7	$6,000	$1,963	19
6	$5,500	$1,759	18
5	$5,000	$1,492	15

As seen in the last column, we have thus far allocated $14,000 out of the available $25,000. So the allocation continues. With the next allocation, the cumulative allocation increases to $20,000.

Step 5: Is there any remaining capital?
After allocating to as many projects as possible, you may be left with some capital. What to do with the remaining capital? There are two choices depending on how much is left.

a. If the remaining capital is significantly lower than what is needed to fund the next best project, it is usually returned to the company capital pool for use elsewhere.
b. If the remaining capital is closer to what is needed to fund the next best project, and then try to acquire the required additional capital and fund the next project.

In this particular case, after allocating the best four projects at a total cost of $20,000, we are left with $5,000 (= $25,000 – $20,000). The next best project, namely 6, requires a capital of $5,500. If we had another $500 we could fund project 6 too. This fact should be discussed with the capital budgeting authority through the department manager. Negotiate with the budget officer, providing additional information on the project if needed, and highlighting its merits. The budgeting authority might release the additional $500 provided project 6 is among the other worthy ones within the company.

Question 15.4: ABC Incorporated is considering the following projects for p...

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