IRR vs. MIRR Valuation Methods

Firm valuation is very important for firms in their efficient planning and allocation. The value of the firm is influenced by all short and long-term measures and decisions of its managers thus it is critical to use proper valuation methods to not underestimate nor overshoot the projects/business activities that will affect its value. With proper valuation methods like using internal rate of return and its modified form give the firms a proper evaluation grounds on how to manage its assets and capitals to achieve the firm’s objectives (Mendel University, 2004).

Firm valuation is the process of determining the current worth of an asset or the company in an objective or subjective technique (Investopedia). Intuitively, a high value of a firm reflects a very good management and decision-making. Controlling for firm valuation involves conducting projects or committing to investments that will help in increasing the value of the firm. Having a strong cash flow position is one characteristic of a firm having a high value; conversely, a high value firm has the capacity to support its financing needs such as funding future investments without borrowing money to avoid paying interests to be able to put money again into the business to regenerate profit.

Valuing a firm means expressing its price in monetary equivalent while valuing a project means expressing its possible contribution in the profit generation of firm and its impact on the firm value. The firm will of course invest in a project that will give higher returns.

But how can a firm evaluate a project that will add to the firm value?

Since the value of a company is the sum of the cash flows that it produces in the future, discounted at an appropriate discount rate, it is relevant to look first at the cash flows the firm is projecting to incur upon implementation of a project.

When a firm purchases new equipments, expansion of facilities, merging or consolidating with another firms or launching research and development programs, it spends in the hope that it will generate future cash flow benefits. These capital expenditures require careful analysis and decision so as to come up with business activities that will contribute to its value and solvency (Evans, 2000, p.1).

Capital budgeting is how the firm is investing its capital assets. In analyzing, the firm must consider if the future benefits of the project will be large enough to justify the investment expenditures given the risks. It means that how we spend the money today determines the value will be tomorrow. Discounted cash flow analysis or DCF analysis is the most popular approach in looking at the present values of firm projects however it is often advised that financial analysts may have their own assumptions given different conditions and firm characteristics (i.e project time span, firm size) (Evans, 2000, p.1).

Unlike in accounting, financial management is concerned with the value of assets of today and since we want a firm’s business project to yield future benefits and one can only do this by determining its present value, discounting the future cash flows of the project to the present is needed. Discounting is taking a future amount and evaluating its value today and this future values differ from present values because of the time value of money. Discounting is done because the time value of money is changing because of inflation, uncertainty and opportunity costs. A $100 today will have less value in the future because of rising of price levels (inflation). Estimations of future returns may not be exact because of the dynamism in market. And the $100 is worth more to us than $100 in the future because we can invest it today and earn a return (Evans, 2000, p. 4).

The net-present value (NPV) and the internal rate of return (IRR) are the two most used measures for evaluating an investment. It is usually stated that a project with higher IRR and NPV will yield more profits than with lower IRRs and NPVs. The NPV computation is the process of discounting the cash flows of a project given a certain discount rate over the given project life span. It is given by:

wherein C0 is the negative income or the cost/expenditures when starting a project, Ct is the future cash flows or income the project is expected to yield, r is the discount rate and the superscript t is the time interval into the future that the income amount will be received or spent. If the NPV of a project is positive, it should be accepted because it implies that the cash flows will also be positive (Investopedia).

If our NPV is set to zero, the discount rate is the measure of the internal rate of return (IRR). Intuitively, the higher the IRR the more desirable the project is because it is the rate of growth a project can generate. Though estimated IRR will often differ from the actual rate of return, it is always safe for managers to invest in a project that has high IRR estimation. Using IRR to obtain the NPV what we know the discounted cash flow method or DCF method.

Since NPV is often used as a valuation method of firms and computing it involves the determination of IRR, it must be taken seriously that wrong estimation of IRR will lead to a wrong or less profitable business decision. It is said that IRR can be obtained when the NPV is set to zero which implies that IRR computation assumes that the project generates no interim/short-term cash flows—or these interim cash flows can be invested at the actual IRR. This is the reinvestment assumption of IRR. When the calculated IRR is higher than the true reinvestment rate for interim cash flows, the measure will overestimate the annual equivalent return from the project thus the firm will defeat its expectations and worse the project will not contribute to solvency (Kelleher, 2004, p. 1-2).

The IRR is assumed that a project has an initial cash outflow (expenses) followed by cash inflows in the future. This may not be true at all times as cash flows in the future, especially on the last period, may be negative or be a cash outflow because of some future expenses (i.e. taxes on wastes after operations) not reflected in the initial cash outflow (Xiaojuan, 2005).

Going back to the NPV formula, if income amounts (Ct) received in each period is higher than the projected; you will need a higher IRR to bring the NPV back to zero. This is where it is explained that higher incomes have higher IRRs (Baker, 2006).

IRR may be very attractive to be the basis for business decision-making however due to its assumption about reinvestment, it can lead to major capital budgeting mistake. Suppose we are to choose between mutually exclusive projects Y and Z with equal IRR of 30 percent. If they have identical cash flows, risk levels and time span, the manager will be confident that either of the two will bring profit and value to the firm in the future. But it is a mistake either of the two without examining the reinvestment rate for interim cash flows. If project Z’s interim cash flows could only be redeployed at 8% of the cost of capital while project Y’s cash flows could be reinvested in a follow-on project expected to generate 30 percent return per time period, then project Y is definitely preferable. Project Z will just have a growth rate of 8% per year (i.e. if project time span is 5 years, the CAGR or compound annual growth rate at the end will just be 24%) while project Y growth is 41% (Kelleher, 2004, p. 2-3) .

From this point, we can see that the major problem of IRR is its assumption of reinvestment rate but how large is the impact of this flaw? When the reinvestment rate is will be adjusted to the company’s cost of capital, the true IRR will still fall under the estimated IRR. The impact is considerable if the estimated IRR is just 10% above the true IRR. Either ways, adjusting reinvestment rate to the cost of capital will still overshoot the true IRR/return of a project given that the range of error will be just be minimal compared with the first which assumes that cash flows are reinvested at a rate that is equal to IRR (Kelleher, 2004, p. 3).

Another problem is that when NPV is set to zero and cash flows signs are changing more than once, there can be two IRRs.

Given the flaws of using IRR in discounting future values and its threat in leading to overoptimistic and/or wrong decisions, IRR was modified. Modified internal rate of return (MIRR) assumes that all the cash flows are reinvested at the firm’s cost of capital(CC) that is MIRR=cost of capital in % (Investopedia). Any types of capital have costs which are based on the rate of return required by the investors who provide the company funds. Equating MIRR to CC means that the firm managers are trying to secure firm wealth or value to return what the investors have given. Also, we can eliminate the problem of having multiple IRRs (COBA, USF) Chap.11 p.1).

MIRR reflects answers the reinvestment problem of IRR however it is problematic for MIRR to be used to compare mutually exclusive projects which have different duration and scale size (Gallinelli, 2008). Dunn and Carry (1997) suggests a method of adjusting MIRR to give rankings that are consistent with NPV of the different projects.

For illustration and application purposes, let us apply the discussed concepts in simple life situations. I am planning to buy a large waffle-maker that will be used for expanding my home-made biscuits business.

The waffle-maker that has the capacity to make 20 waffles of different ‘bread print designs’ at one heating costs $3000. It is of my dilemma whether to buy the waffle-maker or just increase my current biscuits production. It is of course my intention to increase future profits so as to sustain my future capital needs and keep my business alive. If I will choose to invest by buying it, I will incur a cash outflow as it serves as an expenditure. The life span of the waffle-maker of course is indefinite but I will assume that it would last a three-year operation. If it broke down, the life span of the investment will of course end (new expenditure because of repair or replacement).

If the net sales revenue or income stream that I will target each year from waffle-making are 1000, 1250 and 1500 respectively in three years. Using the NPV equation:

NPV = -3000 + 1000/(1+IRR) + 1250/(1+IRR)2 + 1500/(1+IRR)3

If I will use the IRR in valuing the investment that I am planning:

0 = NPV = -3000 + 1000/(1+IRR) + 1250/(1+IRR)2 + 1500/(1+IRR)3

The IRR is 11%, from here it is very attractive to buy the waffle-maker.

If I will deposit in the bank (reinvest) the net profits I earned each period with an interest of 8% per annum, it is said that my reinvestment rate will be 8%. Also, since I will not borrow money to acquire the new capital there is 0% financing rate. Finance and reinvestment rates are considered in MIRR to solve the seemingly waterloo of IRR in its reinvestment assumption. Thus, MIRR = f (values, finance rate, reinvestment rate). With the possible complexity of calculating the MIRR, I can use MS Excel in computing for it. Arranging the cash flows in sequence, the MIRR formula queried: =MIRR (year0:year4, 0, 8%) gave a result of 10% (Marshall School of Business, p. 12).

It can be observed that the IRR of the project is higher than the MIRR. Our simple situation followed that of in theory that MIRR tend to be smaller than IRR. But does this mean that whichever I choose means that I will still yield a positive cost of capital return? Do I still need to consider the option not to expand the business? Do I still need to calculate for the NPV to really determine if the project will give future desirable returns? Which is the better valuation measurement (IRR or MIRR)?

Using the IRR as the discount rate r, the NPV using the Excel calculator is 1221.60 while the NPV when we used MIRR as the discount rate, the total return of the project will be 6912.09. The NPV are both positive so we can be sure that if we buy the waffle-maker, it will give me a positive return in the future and thus the project is a good one. The analysis is simple because I only evaluated whether or not the investment will yield future positive returns and did not focus on choosing whether to just increase the production without buying the waffle-maker. Thus the theory of MIRR, IRR and NPV relationships apply when we just evaluate one project. If we add another project as another option for investing, say, hiring one baker, the relationships of the three valuation measurement still apply. The investor will just choose the project with higher NPV. However, this analysis works only when the projects are of the same scale (small or large budget) and duration (project life span). Cary and Dunn (1997) suggested ways on how to adjust IRR and MIRR given that different projects can have varying initial outflows and cash inflows.

We are now going down to the primary question of this paper: IRR or MIRR?

In our simple example, the IRR is higher but the actual total value of returns (NPV) is lower. If a manager will base his or her decision on the magnitude of IRR, he or she will be driven to an overoptimistic decision in the conclusion that higher IRR means higher return.

On the other hand, even if the MIRR is lower than the IRR (which is the rule of thumb usually followed by managers in decision-making); the actual return of the project is higher. MIRR is unappealing because of the mentality that what we are measuring is the “rate of return” so lower percentage means lower returns. This may be the reason why MIRR is often preferred by academes because they recognize that the two are different so the interpretations must be different. The solution to the unrealistic capital reinvestment assumption of the IRR is answered by the MIRR thus the modified IRR reflects what is really happening in our real world. Sometimes, assumptions can make our picture of reality an illusion especially when we are not cautious about them.

Short-term and long-term decisions of the firm affect them in any ways. Choosing a project for its capital budgeting will reflect present and future effects to the value of the firm: either it will contribute to the firm solvency or to the bankruptcy. Firm valuation gives the stakeholders a hint of their company’s financial capabilities thus overshooting or underestimating its value will drive them to business activities that will not realize their optimal capabilities. The same is through with project valuations: given economic conditions and firm capabilities, the firm must choose to invest in activities that will bring them positive NPVs or the one with highest NPV among options. NPV can only be estimated right given an appropriate discount rate or rate of return.

MIRR is better than IRR because it considers much realistic assumptions and therefore gives us a hint of the real mechanics of proper valuation of business activities. And lastly, proper valuation leads to proper decision-making thus the ‘real’ internal rate of return must be estimated properly.

References

Baker, Samuel L. (2006, September 26). Perils of the Internal Rate of Return. Retrieved October 21, 2008, from http://hspm.sph.sc.edu/COURSES/ECON/invest/invest.html

Cary, David, Dunn, Michael. (1997). Adjustment of Modified Internal Rate of Return for Scale and Time Span Differences. Academy of Accounting and Financial Studies, 2, 57-63.

Evans, Matt H. (200). Course 3: Capital Budgeting Analysis.from http://www.exinfm.com/training/pdfiles/course03.pdf

Gallinelli, Frank (2008). NPV, IRR, FMRR, MIRR, CpA – Stirring the Alphabet Soup of Real Estate Investment (Part 2). Retrieved October 21, 2008, from http://realdata.com/ls/alphabet-soup-part2.html

Investopedia. (2008). Retrieved October 21, 2008, from www.investopedia.com

Kelleher, John C., MacCormack, Justin J. (August 2004). Internal rate of return: A cautionary tale. The McKinsey Quarterly, 1-4. Retrieved October 21, 2008 from http://mdm.gwu.edu/forman/IRR%20A%20Cautionary%20Tale.pdf

Marshall School of Business: University of Southern Carolina. (1998, August 19). Information Resources: Excel 2000 Intermediate. Retrieved October 21, 2008, from http://www.marshall.usc.edu/assets/003/5240.pdf

Mendel University of Agriculture and Forestry. (2004). Possible Approaches to the valuation of a firm. Agricultural Economics – Czechoslovakia, 5, 204-206.

Xiaojuan, Grace. (2005, October 13). A Powerpoint lecture presentation. Retrieved October 22, 2008, from econ.uscb.edu.ppt