1. By Muhammad Shahid Iqbal
Engineering
Economics
Module No. 10
Rate of Return
By Muhammad Shahid Iqbal

2. Introduction of Rate of Return
The internal rate of return (IRR) is a rate of return used in capital budgeting to measure and compare the profitablity.
In the context of savings and loans the IRR is also called the effective interest rate.
The term internal refers to the fact that its calculation does not incorporate environmental factors.
The IRRon an investment or project is the "annualized effective compounded return rate" or discount rate that makes the net present value of all cash flows (both positive and negative) from a particular investment equal to zero.
More specifically, the IRR of an investment is the interest rate at which the NPV of costs (-ve cash flows) of the investment equals the NPV of the benefits (+ve cash flows) of the investment.

3. Introduction of Rate of Return
Internal rates of return are commonly used to evaluate the desirability of investments or projects.
The higher a project's internal rate of return, the more desirable it is to undertake the project.
Assuming all other factors are equal among the various projects, the project with the highest IRR would probably be considered the best and undertaken first.
internal rate of return is a rate quantity, it is an indicator of the efficiency, quality, or yield of an investment.
This is in contrast with the net present value, which is an indicator of the value of an investment.
An investment is considered acceptable if its IRR is greater than an established cost of capital.

4. Rate of Return
The first step is to find the net present worth of the cash flows:
PW = - P + R1/(1 + i)n-1 + R2/(1 + i)n-2 + ……………….+ Rj/(1 + i)j +………….+ Rn /(1 + i)n + S/(1 + i)n
P = Initial investment
Rj = Net revenue at the end of jth year.
S = Salvage value at the end of nth year.
In this analysis expenditures are always assigned negative sign and revenues/inflows are assigned positive signs.
The above function is to be evaluated for different values of I until the present worth function reduces to zero.

5. Rate of Return
The IRR is calculated by a trial and error process, Starting with a guess at the IRR, r, the process is as follows:
The NPV is calculated using discount rate r.
If the NPV is close to zero then r is the IRR.
If the NPV is positive r is increased.

6. Rate of Return
A person is planning a new business. The initial outlay and cash flow pattern is given below. The expected life of business is five years. Find the rate of return for the new business.
Period 1 2 3 4 5
Cash flow
-100,000
30,000

7. Rate of Return
A company is trying to diversify its business in a new product line.
The life of the project is ten years with no salvage value at the end of its life.
The initial outlay of the project is Rs. 20,00,000.
The annual net profit is Rs. 3,50,000.
Find the rate of return for the new business.

8. Rate of Return
A firm has identified three mutually exclusive investment proposals whose details are as follows. The life of is five years with negligible salvage value. The minimum attractive rate of return is 12%.
Find the best alternative based on the rate of return comparison.
Alternative
A A A3
Investment
1,50,000
2,10, 000
2,55,000
Ann. Net Income
45,570
58,260
69,000

9. Rate of Return
For the cash flow diagram shown in Fig. Compute the rate of return.
1,250

10. Initial Investment Yearly revenue
Rate of Return
A company is planning to expand its present business. it has two alternatives, the corresponding cash flows are given below. Each alternative has a life of five years and negligible salvage value. The minimum attractive rate of return is 12%. Suggest the best alternative.
Initial Investment Yearly revenue
Alternative 1
5,00,000
1,70,000
Alternative 2
8,00,000
2,70,000