The Discounted Cash Flow Method ( D. C. F.) is commonly used for determining the financial viability of any project. Discounting is based on the concept of Time Value of Money and is essentially the reverse of compounding. In simplified terms, Ti
me Value of Money indicates that a rupee earned today is more valuable than a rupee earned after a year.
One calculates the future value using the compounding method while one calculates the present value ( the value as of today) using the discounting method. The formula for compounding used is the one we have learnt in our school days: A = P ( 1+ R)^ 100 The formula used for discounting for calculating Present value is thus: P = A . ( 1+ R)^ 100 Under DCF we can use the either the Net Present Value ( N. P. V.) or the Internal Rate of Return ( I. R. R) method. Of the two IRR is more popular. This is because NPV gives a result in absolute units while IRR gives a result in %. As it is common practice to express financial returns in %, project managers and financiers are more comfortable with using IRR. Let us begin by revising IRR. How is IRR calculated? Conceptually, IRR is the rate ( R %) at which NPV is zero.
NPV = C1 + C2 + C3 – C0 ( 1+ R)^ 1 ( 1+ R)^ 2 ( 1+ R)^ 3 100 100 100 Where C0, C1, C2, C3 are cash flows for Y0, Y1, Y2, Y3 respectively.
In the IRR method , we set the NPV value to zero and calculate the value of R ( the discount rate).
Remember given one equation, we can always calculate the value of one variable, in this case R (%).
This R is the IRR. How can IRR be used to determine the viability of a project? Once IRR is calculated using the above equation, we will compare it with the Cost of capital ( funding cost). This funding cost is also called W. A. C. C. ( Weighted Average Cost of Capital).
If IRR > WACC, the project is accepted. This is obvious for ex&le the return is say 11% and the cost of funds is say 7%, then the project is worthy of acceptance as it is earning more than the cost of funds.
IF IRR < WACC, the project is rejected. This again is simple, for ex&le, if the return on the project is say 9% and the funding cost is 12%, we will reject the project as the returns are less than the cost.
Illustrate an ex&le of IRR calculations.
Let us consider the following project: Project STU WACC 10% Year Cash Flow 0 – 40 1 25 2 30 IRR 23% This project can be accepted as IRR of 23% is greater than Cost of funds ( WACC) of 10%. It is logical that greater the IRR over WACC the better it is. So , in case, multiple projects have IRRs greater than WACC, we will tend to accept the one with the highest IRR. However, IRR should be used very carefully and one needs to be aware of the pitfalls of using IRR. What are the pitfalls of using the IRR method? Professionals are advised not to blindly use the IRR method. This is because we could have the problem of multiple IRRs as illustrated below : Year Cash Flow 0 – 20000 1 90000 2 – 80000 First value of IRR 21.92% NPV at 21.92% 0.00 Second value of IRR 228.08% NPV at 228.08% 0.00 By definition, NPV is zero at IRR. As can be seen in the above case, NPV is zero at both the values of 21.92% and 228.08%. Thus both 21.92% and 228.08% are IRR values for the above case.
Why do we have the problem of multiple IRR? Let us revise elementary algebra to answer this question. As one would recall a polynomial polynomial equation of power has roots. For ex&le, a quadratic equation has two roots. Thus x2 – 4x + 3 = 0 has two roots x= 3 and x= 1. Both these values of x i. e. 3 & 1 satisfy the above equation. The same logic needs to be applied to the illustration given in Q4.
90000 + (- 80000) – 20000 = 0 ( 1+ R)^ 1 ( 1+ R)^ 2 100 100 Thus the above equation has two roots 21.92% and 228.08%, giving rise to the problem of multiple IRRs. It needs to be noted here that if one blindly uses the Excel formula of IRR, this problem can go unnoticed. This is because Excel is pr
