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# Management Accounting Financial Management b

By Juan Shaw,2014-05-17 09:07
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Management Accounting Financial Management b

Subject: Financial Management

Chapter no. 11: Capital Budgeting

Chapter No. 11 Capital Budgeting

How do you get IRR by calculation?

IRR is obtained by “trial and error” method. Suppose we are given a set of cash flows, both outflow at the beginning

and inflows over a period of time in future. We start with some rate as the discounting rate and start determining the

NPV till we get NPV= zero. In case the rate lies between two rates, we fix the range and mention that the IRR lies in

this range. Let us illustrate this with an example.

Example no. 4

Let us take project 2 in our Example no. 3. The present value is the closest to our original investment of Rs. 500 lacs.

The discounting rate is 15%. p.a. our target present value is Rs. 500 lacs. How do we get to this figure? By increasing

the rate of discount or reducing the rate of discount? As the present value is inversely related to the rate of discount,

we have to increase the rate. Let us try it out for 20%.

Year Future value Present no. of cash flow value @

20% 1 100 82.0 2 120 80.76 3 200 110.8 4 250 114 5 250 94.25 Total 481.81 This means that the discounting rate of 20% is high and has to be reduced so as to reach the target present value of Rs.

500 lacs. Le us try it out at 19% and redo the exercise.

Year Future value Present no. of cash flow value @

19% 1 100 82.80 2 120 82.32 3 200 114 4 250 118.75 5 250 99.00 Total 496.87 Punjab Technical University, Online Virtual Campus 1

Subject: Financial Management

Chapter no. 11: Capital Budgeting

This means that we have to reduce the rate of discount to 18%. The IRR lies between 18% and 19%. This is called the

“trial and error” method. However if we want to find out the exact IRR, we will have to adopt the following steps

further:

1. Find out the Present value by @ 18% discount rate

2. Employ the “method of interpolation”

Let us do this exercise so that the students will be familiar with determining accurate IRR.

Year Future value Present no. of cash flow value @

18% 1 100 83.60 2 120 84.0 3 200 117.40 4 250 123.50 5 250 104.0 Total 512.50 Compare the present values @ 19% and 18% discount rates. It clearly shows that the IRR is closer to 19% than to 18%. 1 and determine the exact IRR. Let us now adopt the method of interpolation

At 18% discounting, PV = Rs. 512.50 lacs

At 19% discounting, PV = Rs. 496.87 lacs and

Our target PV = Rs. 500 lacs

By employing the method of interpolation we find that the IRR =

18% + 512.5 500____ = 18.80%

512.5 496.87

This vindicates what we have mentioned in the previous paragraph we have mentioned that IRR is closer to 19%

rather than 18%. How do we take the values in this method?

1. In the denominator, the values at the extremes of the given range are taken and difference is the denominator

2. One may start from the lower rate in which case in the numerator, the values taken are the target value and the

value corresponding to the lower rate

3. On the other hand, if we want to go from the higher rate, the equation will be =

19% (-) 500 496.87____ = 18.80%

512.5 496.87

Thus whether we go up from the lower rate or come down from the higher rate, there is no difference in the end

result. The above example tells us clearly how to adopt the trial and error method to fix the range of interest rates

within which our IRR lies and then proceed to adopt “interpolation method” to determine the exact IRR.

1 Method of interpolation is just the opposite of method of extrapolation. This is adopted whenever the target parameter (in this case the discount rate) lies between a range of values. In the given example, the target discount rate (IRR) lies between 18% and 19%.

Punjab Technical University, Online Virtual Campus 2

Subject: Financial Management

Chapter no. 11: Capital Budgeting

When we employ IRR method of financial evaluation of more than one project, that project with the higher IRR is

chosen.

Merits:

1. It tells us the rate at which the project should get a return taking into consideration the risks associated with the

project

2. It takes into consideration the time value of money and hence reliable as a tool for evaluation of projects

3. It is very useful to a lender who is always interested in NPV = zero at a given rate and in a given period.

Demerits:

1. It takes a long time to calculate

2. Based on this comparison cannot be made between projects of unequal size. A smaller project could get selected

because of higher IRR as against a project in which wealth maximisation is very good (NPV being very high)

only because its IRR is less than the previous one.

3. Multiple IRRs (more than one IRR) will be the outcome in case there is a negative sign in the project cash flows in

the future. This means that should it happen that in one-year project cash inflow is negative (cash outflows being

more than cash inflows) it will give rise to more than one IRR.

Profitability Index (PI)

The profitability index or benefit-cost ratio of a project is the ratio of present value of future net cash flows to the

initial cash outflow. It can be expressed as

Present value as per NPV and IRR methods

Initial investment in the project

Example no. 5

In our above example the present value of future cash flows at 15% was Rs. 556.29 lacs in the case of project no. 2 as

against original investment of Rs. 500 lacs. Hence PI = 556.29/500 = 1.113

This is more often employed in social projects like infrastructure projects undertaken by the governments or public

sector and less employed in commercial projects.

The merits and demerits are the same as for the NPV method as above.

Punjab Technical University, Online Virtual Campus 3

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