# Cost of capital and irr relationship

### Internal Rate of Return (IRR) - A Guide for Financial Analysts

the IRR is less than the cost of capital the project should be rejected. There is a close relationship between IRR and WACC as these concepts together make. If the IRR exceeds the WACC, the net present value (NPV) of a corporate project Financial ratios can either have direct or inverse relationships, depending on. Note it is the cost of debt and not the weighted average cost of capital. See below the relationship between the cost of debt and equity IRR.

C0 initial investment todayC1, C2, The future cash flows are random variables, but, from now on, we refer to their expected values. Note that, now, we usually already know what is the amount of money to be spent at the outset. If the future cash flows have a present value higher than C0, then we shall be in a favorable situation.

It is possible to construct a complete, clean probabilistic model of behavior of the future cash flows, and to define the risk pattern of the collection of future cash flows just like we did for a security over one year. The model is more intricate than for a security. It is then possible to find an entirely known security S "behaving like the future cash flows of I". Then, the profitability of S is called the opportunity cost of capital of I. Why this barbaric sounding name? So, the profitability of S the benefit of which we give up is the opportunity cost of I.

Finally, we can compute the present value of these future cash flows by discounting them with the opportunity cost of capital of I. We won't go into the mathematics of the model, but will stay at an intuitive level. This is a favorable situation: In other words, the investment I has a net present value of 20,37 mio euros. The general formula for the PV present value of a series of future cash flows is this where r is the opportunity cost of the collection of cash flows: This formula has an interesting interpretation: The "raw" cash flows are not comparable, because they don't correspond to the same years ; but, when each of them is properly discounted, they become comparable: Differences between one security and an investment At this point, it is important to stress the similarities and the differences between investing into one security and selling it one year later and making an investment into a project which will produce a stream of future cash flows.

The money or sums of money we shall receive in the future are unsure quantities, so we work with a probabilistic model. We need to know or estimate distributions of probability, means, variances, etc. We did it in the case of a single payoff in one year ; we did not do it in the case of a stream of cash flows, because we need, first, to study several random variables produced in the same experiment E, joint distributions of probability, dependence and independence, etc.

And then we need to define clearly what is the risk pattern of a collection of future random cash flows, the present value of a cash flow in two years, etc.

So we decided to stay at an intuitive level. If we have the time, later in the course, we will study a little bit two random variables produced in the same experiment. So securities in the stock market have a price which is their present value, and, therefore, their NPV is always zero. Concerning physical investments, things are different.

Usually we know how much money we must spend today to produce a stream of future cash flows, and, usually, the initial investment C0 is different from the PV present value of the future expected cash flows.

Sometimes the NPV is positive - the investment is worth considering ; sometimes the NPV is negative - the investment project must be discarded. How to find the opportunity cost of capital of an investment? The theory says "find a security which has the same risk pattern as your investment, then the profitability of that security is your opportunity cost of capital".

Now, let's plunge and try to swim In the most general situation, we shall use the ROCE of firms in the same industry. More precisely, we must figure out the beta of the project see laterand this will lead to the proper discount rate for the investment cash flows. If we are the financial officer of a firm and the management considers a new investment project I. We are asked the compute its NPV.

How do we do it?

Project IRR and Equity IRR Case Study CA Final Level

Briefly stated, people putting money into the firm that ends up recorded on the liability side of the balance sheet give up other opportunities with the same risk as the firm, therefore, they expect from the firm a cash generation with the same expected profitability. It is called the cost of capital for the firm, and "main stream" investments made by the firm should have at least this profitability, otherwise the investors will turn away from that firm.

More on this later.

### Internal Rate of Return IRR and MIRR Meaning, Calculation and Use

Each bar represents the net of cash inflows and outflows for one two-month period. Positive values are net inflows, and negative values are net outflows.

The complete set of net cash flow events is a cash flow stream. This stream shows expected cash flow results from one action, while the cash flow stream for another act might show a different cash flow profile. When comparing IRRs for different streams, other things being equal, analysts view the proposed action with the higher IRR as the better choice.

## Internal Rate of Return (IRR)

Notice especially the shape, or profile of this example stream. This figure represents a typical investment curve because: The IRR metric, in fact, "expects" this kind of cash flow profile—costs first and benefits later. As a result, when the cash flow stream has this profile, an interpretable IRR probably exists. When cash flow events have another profile, instead, the stream may not have an IRR.

Also, other strange IRR results may also appear when the profile is something other than an investment curve. Consequently, in such cases, the resulting IRRs are either very difficult to interpret or meaningless Internal Rate of Return: They specify, that is, an IRR rate that incoming proposals must reach or exceed to qualify for approval and funding. Two possible reasons for IRR's popularity may be the following: