Evaluation of Projects with Unequal Lives

In finance, it is the basic notion that we choose projects with positive Net Present Value (NPV). What will be the problem in decision making if projects have different lives?

Example 1: A company has two projects in hand Plant A and Plant B. Plant A has 2 years of life and Plant B has 3 years of life. Cost of capital of 12%.

If we must choose one Plant out of these two Plants, we may usually go for Plant B as it will contribute to shareholders’ wealth with its higher NPV (CU 303.99) as compared to Plant A (CU 262.76).  Our evaluation with this NPV results can lead us to wrong decision because these two Plants have different lives so their NPVs cannot be compared to reach at any conclusion, because expiry of plant life does not mean that company will stop producing after that period. Company can generate same value in second cycle of the new Plant in both cases.

Equivalent Annual Benefit (EAB)

Let’s compute the EAB for the two plants stated above.

Based on EAB, Plant A will be selected with higher EAB i.e., CU 155.47 million against Plant B which has EAB of CU 126.56 million. Computation of Equivalent Annual Benefit (EAB) is simple, and decision based on EAB is a stress-free approach i.e., just select project with higher EAB.

But the question is what does this EAB mean?

Meaning of EAB

EAB is just the indicator that helps decision maker to choose the projects with different lives. In pragmatic terms, it is the recasting of earlier cash flow streams which may not be equal into equal cash flow streams over the period of the project.

Now each year’s cash flow assumed to be produced by two plants are comparable i.e., each year CU 155.47 is better than each year CU 126.56. But Plant B is producing cash flows for 3 years and Plant A for 2 years leaving our analysis and results incomplete. It does not mean that company will stop production after 2 years in case of Plant A or after 3 years in case of Plant B. Company will buy another similar plant for each life cycle of the Plant which may go infinitely. However, for the sake of comparison let us take fixed period that coincides exactly by replacement of different life cycles of the two plants.  This can be derived by taking Least Common Multiples (LCM) of life of the two plants i.e., 2 x 3 = 6 years.

Consider Plant A which require replacement for 2 times in 6 years after its first investment i.e., first replacement at the end of 2^nd year and second replacement at the end of 4^th year as below.

This way NPV of the Plant A in 6 years will be CU 639.21 million. This can be derived from recast of equal annual cash flow as below:

Similar calculation can be done for Plant B with two alternatives cash flow streams which produces same NPV in 6 years period with 2 life cycle of Plant B. To enable easy comparison in order to reach a conclusion, alternative cash flows of the two plants can be taken as below:

In 6 years, period, Plant A will have 3 cycles each of 2 years and Plant B will have 2 cycles each of 3 years. NPV in 6 years’ period is higher for Plant A so Plant A shall be selected but decisions are taken on the basis of equal annual benefits (assumed cash flow) i.e. CU 155.47 against CU 126.56.

Equivalent Annual Costs (EAC)

Unlike EAB, we may be required to evaluate projects with their related costs. Projects will normally generate cash inflows more than cash outflows making it financially viable. However, when two different projects have same production capacity or generate same revenue (cash inflows) but their lifespan, initial costs and their running costs differ from each other; then they can be evaluated based on their related costs only.

Example 2: Suppose Plant M and Plant N both have annual production capacity of 10,000 units and company’s annual demand is limited to 8,000 units now and will remain same in future as well. It means revenue of the company shall not be altered because of choice of the plant either M or N. But Plant M costs CU 1,000 million and lasts for 2 years and Plant N costs CU 800 million and has lifespan of 3 years. However, although initial cost of Plant N is lower, its running costs are higher over its lifespan as compared to Plant M which is depicted in table below. Assume running costs are net of disposal value of Plants, if any. The Equivalent Annual Costs (EAC) of both plants shall be computed in the same manner as we have calculated EAB but considering their initial costs and running costs as below.

Plant M has lower Present Value (NPV) of total costs (CU 1,417.73) over the life of the project in comparison to Present Value of total costs of Plant N (CU 1,871.77). But company can utilize Plant N for production of goods for next 3 years with its higher NPV cost whereas Plant M can be utilized for next 2 years with its lower NPV costs. Thus, NPVs of costs are not comparable for decision making. In this case, like EAB, EAC shall be calculated as shown in the same table above.

The EAC of Plant M is CU 838.87 million and Plant N is CU 779.31 million. The interpretation of the EAC is like EAB. Therefore, Plant N is better for production because both plants will generate same amount of revenue, but annual equivalent cost (annuity) is lower that of Plant N.

Replacement Cycle of Single Asset

In example 1 and 2 above, we evaluated two different plants (projects) with different lifespan. However, we can evaluate single project having certain life with different replacement cycles. It means if any asset (project) has 4 years of lifespan then we can replace this asset at any time before four years. The question may arise why we may need to replace the assets before its useful economic life.

The answer is simple because with the passage of time, repair and maintenance costs or running costs of the assets will increase and in other hand disposal value will gradually decrease.

Example 3: Suppose a company can invest in a Plant for CU 1,000 million which lasts for 3 years. Running costs of the Plant is in increasing trend i.e., CU 200 million, CU 250 million and CU 300 million in next 3 years respectively. The company can replace this Plant before its expiry (3 years) with the new one so that lower running costs can be maintained. In addition, higher disposal value will be realized from the Plant if it is sold before end of its lifespan i.e., CU 700 million in Year 1 and CU 500 million in Year 2. However, the plant will be scraped at CU 50 million if disposed at the end of Year 3.

Here, shorter replacement cycle will benefit company in two ways i.e., lower running costs and maximizes disposal value (cash inflow) but frequent replacement will demand huge amount of investment in new plant. So, to evaluate appropriate replacement cycle, we need to compute Equivalent Annual Cost (EAC) for each different cycle as below:

Replacement Cycle every Year

Replacement Cycle every Two Year

Replacement Cycle every Three Year

Summary of three different replacement cycles:

Conclusion: 2-year replacement cycle is better as every year equivalent costs is lower i.e. CU 579.43 as compared to other two different replacement cycles.

Extracted from the Article “Evaluation of Projects with Unequal Lives” from the Journal of The Institute of Chartered Accountants of Nepal, June 2024 page no. 35 (Source for full article:

https://en.ican.org.np/_browsable/file/journals/June2024.pdf)