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

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## By Muhammad Shahid Iqbal

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**Engineering**Economics By Muhammad Shahid Iqbal Module No. 10 Rate of Return**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.**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. Introduction of Rate of Return**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.**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.**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. Rate of Return**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.**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.**Rate of Return**• For the cash flow diagram shown in Fig. Compute the rate of return. 150 300 450 600 750 0 1 2 3 4 5 1,250**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.

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