I’m gonna explain to you, the special issues of capital budgeting. The first project ranking problem is about size disparity.
Size disparity arises when we are dealing with mutually exclusive projects of unequal size. Project Ranking Problems: Size Disparity
Unequal size implies that the cash flows for two projects are different.
This is why the NPV decision may not agree with the IRR or PI.
Our proposed solution is to select the project with the highest NPV.
Let’s look at the following example.
Project A is a more costly project compared to project B because its initial investment
is higher, and you will receive more cash inflows from year 1 to year 3. Now,
let’s look at project B; it has a lower initial investment and lower cash inflows subsequently. As we mentioned, when comparing these two projects, they have size disparity problems.
Based on a required return of 12%, Project A has a higher NPV,
while Project B has a higher IRR, PI, and MIRR.
For decision making, we’ll prefer Project A due to the higher NPV. A higher NPV means the project can generate more cash inflows for the company.
Another problem in project ranking is the time disparity problem.
It occurs when dealing with mutually exclusive projects that have different timing of cash flows. Project Ranking Problems: Time Disparity
The projects may have similar sizes, but they receive cash inflows at different times.
This discrepancy arises because NPV and PI assume that cash flows
are reinvested at the required rate of return for the project.
However, IRR assumes cash flows are reinvested at the IRR’s rate.
Consequently, NPV or PI decisions may not align with the IRR.
Our proposed solution is to select the project with the highest NPV.
Let’s look at the following example.
Project A and Project B have a similar initial investment size. Every year, the cash inflows are also more or less the same. However, the timing of cash inflows is different. Project B will receive more cash inflows in year 1
and year 2, whereas Project A will receive more cash inflows in year 3 and year 4.
Based on a required return of 12%, Project A has a higher NPV,
PI, and MIRR, while Project B has a higher IRR.
For decision-making, we’ll prefer Project A due to its higher NPV. A higher NPV implies that the project can generate more cash inflows for the company.
Another special issue is about mutually exclusive investments with unequal lifespan.
Suppose our firm is planning to expand and we have to select one of the two machines.
Mutually Exclusive Investments with Unequal Lifespan
They differ in terms of economic life and capacity.
How do we decide which machine to select?
As shown in this example:
Machine 1 and Machine 2 have the same initial investment, which is CF0 = $45k. However, Machine
1 will receive $20k cashflow from year 1 to year 3, while Machine 2 will receive $12k cashflow from
year 1 to year 6. To determine which machine is better, we’ll need to calculate the NPV.
Based on a 14% required return, the NPV for Machine 1 is $1,433,
and for Machine 2, it’s $1,664. So, does this mean that Machine 2 is better? No. In fact, the two NPVs cannot be compared because they have unequal lifespan.
To address this problem, we’ll use the Equivalent Annual Annuity (EAA) method. If we assume that each project will be replaced by an infinite number of times in the future,
Equivalent Annual Annuity (EAA) Method
we can convert each NPV to an annuity. That’s the concept of EAA. Simply speaking, EAA is a single average cash flow for all periods that equals the project’s NPV.
To calculate the EAA mathematically, we may divide NPV by the PVIFA, which can be found
in financial tables. Alternatively, you can use a financial calculator.
As shown here, for Machine 1, key in the NPV as PV, negative 1,433, N = 3,
I = 14, and then compute PMT, you’ll get 617.24.
By following the same method, you’ll find that PMT equals 427.91 for Machine 2.
This calculated PMT is in fact the EAA.
The EAA for Machine 1 is $617, while the EAA for Machine 2 is $428.
This information indicates that the NPV of Machine 1 is equivalent to an annuity
of $617 per year, whereas the NPV of Machine 2 is equivalent to an annuity of $428 per year.
By making this comparison, we can determine which investment is superior.
In this way, we have simplified a problem with
differing time horizons into a comparison of two annuities.
The decision rule here is to select the machine with the highest EAA,
which leads us to choose Machine 1.
The replacement chain method is the second approach used
to address the issue of unequal project lifespans.
Replacement Chain
The rationale is quite straightforward: Extend the
project’s lifespan to make both projects have equal lifespans, and then calculate the NPV.
If the projects have no common lifespan,
for example, 3 years vs. 5 years, then extend the lifespans of both projects to 15
