Internal Rate of Return and the Discounted Cash Flow Model

Valuing a business can often be a subjective process, and there are no hard and fast rules. When asked how to value a business, many people would probably first think of a multiple of its net profits, or perhaps it's asset (book) value, both of which look at the historical performance of the company. However, sometimes it is more appropriate to consider the future potential of the company, and this article examines ways in which businesses can be valued on the basis of expected future income and profits.

This is known as an investment approach to valuation and it use tools commonly known as discounted cash flow (DCF), net present value (NPV) and internal rate of return (IRR).


Discounted cash flow and net present value

Put simply, discounted cash flow calculates a company's current value by estimating the amount of money it will make in the future. To take into account that money received today is worth more than money received in the future, this income is then discounted at a rate that takes into account its 'time value'. The selection of this discount rate is problematic as it is an expression of the risk and uncertainty of actually receiving the projected income together with many other factors, such as the rate of inflation and the opportunity cost of investing the money elsewhere. The value that an investor arrives at for this income stream is known as the net present value (NPV), and can be defined as showing the value of a stream of future cash flows discounted back to the present by some percentage that represents the minimum desired rate of return.

One popular discount rate can be the long-term cost of capital. When applying an NPV calculation as a method to value a business, a purchaser might assume income of £100,000 per year for 5 years. (See the cash flow diagram below.) If the purchaser's desired rate of return is 7%, then the final income in year 5 needs to be discounted at 7% over 5 years, as does the income in year 4, and so on. Looking at the calculation, we can see that the NPV is £434,295. As such, if the seller wants £450,000 for the business this will not be a good purchase for someone with a required rate of return of 7%.

Year 1 £100,000 £100,000
Year 2 £100,000 £93,000
Year 3 £100,000 £86,490
Year 4 £100,000 £80,000
Year 5 £100,000 £74,805
Total £434,295

Every investor using discounted cash flow analysis will have a different discount rate for each type of investment, other things being equal (i.e. inflation), to reflect risk. This level of risk will vary according to the business's circumstances - for example, a start-up business would carry a higher discount rate than a management buy-out. In the case of purchasing a business, the discount should be increased in each of the following instances (least risky first):

Buying and integrating a similar business in a similar geographical market

Buying a similar business in an existing market and running it as a standalone company.

Buying a business in a different market sector in a similar geographical market.

Buying a foreign business in a similar market sector

Buying a foreign business in a different market sector


Another issue to be addressed in discounted cash flow analysis is the terminal value (i.e. the price that the purchaser expects to get when selling the business on) to be included in the valuation. Quite understandably, private equity houses include the estimated disposal value of the acquired company because their investment rationale is based on an exit within five years. Corporate acquirers should be making long term acquisitions and the terminal value should be the realisable disposal value of the assets on a piecemeal basis rather than the value of the company, otherwise comparisons cannot be made on a consistent basis.

It is important to note that these techniques are best used to compare different investments and decide on the best one rather than deciding whether to invest at all.


Internal rate of return

Many investors use the internal rate of return (IRR) to compare potential investments. IRR is the flip side of net present value (NPV) and is based on the same principles and the same maths.

While NPV shows the value of a stream of future cash flows discounted back to the present by some percentage that represents the minimum desired rate of return (often your company's cost of capital), IRR, on the other hand, computes a break-even rate of return. It shows the discount rate below which an investment results in a positive NPV (and should be made) and above which an investment results in a negative NPV (and should be avoided). It is the break-even discount rate, the rate at which the value of cash outflows equals the value of cash inflows.

IRR can also be defined as a cut off rate of return; avoid an investment or project if its IRR is less than your cost of capital or minimum desired rate of return. Once an investor has established a rate of return that they desire, then a number of investments can be evaluated and compared. However, the same principle of setting a required rate of return is needed as the investor may need different required rates for different types of business depending on risk.

Calculating the IRR of an initial investment and cash flows involves initial estimations of rates of return. The diagram below shows a purchase price of £1m in year 0 for an income of £300k per year:

IRR 10% 15% 20%
Yr 0 - £m - £m - £m - £m
Yr 1 +£300k £273k £261k £250k
Yr 2 +£300k £248k £227k £208k
Yr 3 +£300k £225k £197k £174k
Yr 4 +£300k £205k £172k £145k
Yr 5 +£300k £186k £149k £121k
Total NPV+£500k +£137k +£6k -£102k


As the IRR is the break-even discount rate (i.e. the rate at which the value of the money paid to purchase a business equals the value of cash inflows), then we are aiming for a Net Present Value of 0. Therefore, the closest rate illustrated above is 15%, which gives us an NPV of £6,000. Looked at another way, if our required IRR was 15% then we could afford to pay a little more than £1m, £6000 in fact. If our required IRR is 20%, then we would need to pay £102,000 less than £1m, i.e. £898k. So what internal rates of return do purchasers of businesses use? The British Venture Capital Association states that private equity buyers will generally be looking for an IRR of over 20%, however this will vary greatly according to the stage and sector of the business. For example, an industrial business looking to assimilate a supplier which has scope to increase capacity may look for an IRR of 15%, while venture capitalists financing an early stage company often require IRRs of between 35% and 50%.


Drawbacks

There are some problems with using the IRR method and so it should be used with caution. Like NPV, it doesn't measure the absolute size of the investment or its return. And because of the way the maths works, the timing of periods of negative cash flow can affect the value of IRR without accurately reflecting the underlying performance of the investment.

IRR can also produce misleading results because, as classically defined, it assumes that the cash returned from an investment is reinvested at the same percentage rate, which may not be realistic. This error is magnified when comparing two investments of different durations. To counter this, spreadsheets can be used to compute an optional "modified IRR" that allows the user to specify a different reinvestment rate.


In conclusion, the results are no better than projections made by the investor since risk factors and assumptions may outweigh the mathematical calculation. As such, the IRR and NPV tools should only be used to compare very similar proposals where the investor's aims or required returns are the same. The IRR can also be a useful benchmark for management - for instance, if a business purchase cannot produce a return over the required IRR, then it means there will be an increased need to justify the purchase.

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