Opportunity cost of a capital is a term unique to economics and finance. It is unique in the sense that you will not find mention of opportunity cost of capital in the accounting books. It is not an explicit cost which is paid out of the pocket. Hence, there is no mention of this cost in the accounting records. Rather, it is an implicit cost which results out of our investment decisions. This article will explain about opportunity cost of capital and how it must be used while making financial decisions: Show
Alternate Uses of MoneyOpportunity cost of capital represents alternate uses of money. Let’s say, if I have a $1000 to invest and I decide to invest the money in the stock market, I am committing my resources. By investing $1000 in the stock market, I will now not be able to use the same $1000 for any other purposes now. I must therefore ensure that I am committing my resources to the best possible project. Let’s say, I have a choice between real estate and stock market investment, when I choose the stock market investment, I make it my best possible choice. Opportunity cost of capital tells us what we are foregoing to choose that best possible alternative. Opportunity cost of capital is therefore the value of the second best alternative. Alternate Projects Must Share Similar Risk ProfileHowever, we must ensure that we compare opportunity costs of capital across similar projects. This will ensure that we do not see a biased picture and end up choosing the wrong projects. Consider a comparison between a stock market investment and government bonds. Usually, stock markets will offer more return compared to government bonds. So, using government bonds as the opportunity cost will always make them look good. But stock market investments and government bond investments have very different risk profiles. One guarantees a fixed rate of return whereas there are no guarantees in the other. Hence, using one as the opportunity cost of capital for another will provide a skewed picture and the risky alternative will always be chosen. Hence, only projects with similar risk must be used for opportunity cost of capital calculation. This makes these calculations very subjective and open to debate. Alternate Uses Represent Implicit CostsThe investment decision is all about prioritizing. It is about choosing the best possible alternative. So, if we have 2 alternatives, one which offers a $100 return potential whereas another which offers an $80 return potential, then by choosing one alternative we are alternatively foregoing the other one. So, if we choose to get a $100 return, we are foregoing the $80 return. Corporate finance captures this implicit tradeoff in the expected rate of return number. How Opportunity Cost Helps in Decision Making ?Opportunity cost helps in choosing the right project when faced with a variety of alternatives. Here is how the decision is affected: Related ArticlesView All Articles Equivalent annual costsAt some stage you have probably bought an asset such as a car, a washing machine or a computer and you may have considered how long you should keep that asset prior to replacing it. If the asset is kept for a longer period its initial cost, less any residual value, is spread over more years which is likely to reduce your cost per year of ownership. However, as the asset ages it is likely to require more and more maintenance and may operate less effectively which will increase your costs per year. Determining the optimal time to replace the asset (the optimal replacement cycle) is difficult. As a general rule you and I don’t worry too much about this. Indeed most of us will make a decision based on our ‘gut feel’ and other factors such as image for example. Indeed I tend to keep my car until such time as I have lost confidence in its ability to get me reliably from A to B or it has deteriorated so much I no longer want to be seen in it! Companies also face exactly the same asset replacement decisions. However as the amounts involved can often be very significant, making decisions based on ‘gut feel’ is not really accurate enough. The calculation of equivalent annual costs is a tool that can be used to assist in this decision-making process. The equivalent annual cost method involves the following steps:
A machine has a cost of $3,500. The annual maintenance costs of the machine are forecast to be $900 in the first year, $1,000 in the second year and $1,200 in the third year of ownership. The residual value of the machine is expected to be $2,100 after two years and $1,600 after three years. The cost of capital of the company is 11% per year. Calculate the optimal replacement cycle for the machine.
Step 1 – Calculate the NPV of cost for each potential replacement cycle. As we have not been given the residual value after one year of ownership, we cannot calculate an NPV of cost for a one-year replacement cycle. Hence, our decision here will be between a two- or three-year replacement cycle. NPV of cost – two-year replacement cycle: Please note that the normal assumptions with regard to the timings of the cash flows continue to be made. Hence, the maintenance costs are shown at the end of each year, whereas in reality they will arise throughout the year. One complication that arose in a past question was that the maintenance was an annual overhaul required at each year end rather than ongoing maintenance occurring throughout each year. Logically the maintenance/overhaul cost was not incurred in the year of disposal as a company would be unlikely to overhaul an asset just prior to selling it. Hence, in the two-year replacement cycle above, if the maintenance had been an annual overhaul the $1,000 cost at time 2would be excluded. NPV of cost – three-year replacement cycle: Whilst there is an element of repetition in these calculations I would still advise using the above simple and logical format or something similar. Although I have seen formats which try to combine the calculations, they are more complex and tend to lead to mistakes being made. A classic mistake to be avoided is including the residual value after two years in the calculation of the NPV of cost for the three-year replacement cycle. For the three-year replacement cycle, the sale will occur at the end of the three years. Please remember if you buy the asset once you can only sell it once! The two NPVs calculated should not be compared as quite obviously buying and keeping an asset for a longer period is likely to cost more than buying and keeping it for a shorter period as there is less benefit to the owner. This has proved to be the case here. In order to make a fair comparison we must calculate the equivalent annual costs. Step 2 – For each potential replacement cycle an equivalent annual cost is calculated. The costs calculated in Step 1 are spread over the period for which they will give benefit. Hence, the NPV of cost for the two-year cycle is spread over two years and the NPV of cost for the three-year cycle is spread over three years. This is done by using annuity factors to turn each NPV of cost into an equivalent annual cost (EAC) at the end of each year of ownership. Remember if you have equal annual cash flows for a number of years and want to calculate a present value (PV) you must multiply the annual cash flow by an annuity factor: so to calculate the equivalent annual cost or EAC from an NPV of cost we must divide by the relevant annuity factor. EAC – two-year cycle: EAC = $3,418/1.713 = $1,995 per year This is the equivalent annual cost at time 1and time 2which equates to an NPV of cost of $3,418. EAC – three-year
cycle: EAC = $4,831/2.444 = $1,977 per year This is the cost at time 1, time 2and time 3which equates to an NPV of cost of $4,831. While some textbooks will continue to put brackets around these cost figures, I am content to show them as positive as we are describing them as costs. The decision: As the calculated equivalent annual costs are both annual costs, they can be compared to come to a decision. Hence, as an annual cost of $1,977 is less than an annual cost of $1,995, the three-year replacement cycle is said to be the optimal replacement cycle. Weaknesses Having worked through an example we should now consider the weaknesses of the approach we have used. These include the following:
Without going into great detail it is worth being aware that a similar technique can be used in other circumstances. These include:
Equivalent annual benefitIf a company is faced with mutually exclusive projects, where only one out of a number of projects can be accepted, then the general rule is that the company should choose the project that generates the highest NPV as this creates the biggest increase in shareholder wealth. However, if the situation is such that it is anticipated that the same projects could be repeated in perpetuity and the projects have different lives then the equivalent annual benefit approach can be used. This is simply a further variation on the equivalent annual cost approach and is demonstrated in the following example.
Two mutually exclusive projects are being considered:
The cost of capital of the company is 13% per year. Calculate which project the company should accept.
Step 1 – Calculate the NPV for each potential project. Project A – $47m Step 2 – Calculate the equivalent annual benefit for each potential project. Project A – equivalent annual benefit = $47m/2.361 = $19.9m per year The decision: As Project A has the highest equivalent annual benefit it should be chosen instead of Project B, which has the higher NPV, so long as the project can be repeated for the foreseeable future. This result arises because although the shorter project produces the lower NPV that NPV will be obtained more frequently than the NPV of the longer project. The equivalent annual benefit technique suffers similar weaknesses to the EAC technique. ConclusionAlthough this topic is a relatively small one within your Financial Management syllabus, it is a topic well worth mastering as when it has been examined in the past those with the necessary knowledge have been able to earn very good marks. Equally, I would not expect any significant question on this topic to be wholly calculative and hence students should be ready to discuss the reasons for the approach used and the weaknesses or limitations of that approach. William Parrott, freelance tutor and senior FM tutor, MAT Uganda When a project's internal rate of return equals its opportunity cost of capital then?When a project's internal rate of return equals its opportunity cost of capital, then: The net present value will be negative.
What is the relationship between NPV and cost of capital?The cost of capital represents the minimum desired rate of return (i.e., a weighted average cost of debt and equity capital). The net present value (NPV) is the difference between the present value of the expected cash inflows and the present value of the expected cash outflows.
When a project's internal rate of return equals its opportunity cost of capital then quizlet?The internal rate of return is most reliable when evaluating: a single project with only cash inflows following the initial cash outflow. When a project's internal rate of return equals its opportunity cost of capital, then the: net present value will be zero.
What is the difference between IRR and opportunity cost of capital?The internal rate of return is the discount rate for which the net present value of a project is zero. On the other hand, the opportunity cost of capital is usually the discount rate considered for ascertaining the net present value of a project.
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