By Muhammad Shahid IqbalModule No. 10Rate of ReturnEngineering Economics

Introduction of Rate of ReturnThe internal rate of return (IRR) is a rate of return used in capital budgeting to measure and compare the profitability. 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. 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.An investment is considered acceptable if its IRR is greater than an established cost of capital.

Break-Even Interest RateThe IRR on 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.Rate of return (ROR) is the break-even interest rate, i*, which equates the present worth of a projects cash outflows to the present worth of its cash inflows. Mathematical Relation:

Example: A bank lends $10,000 and receives annual repayment of $4,021 over 3 years. what is ROR?

The first step is to find the net present worth of the cash flows: PW = - P + R1/(1 + i)1 + R2/(1 + i)2 + .+ Rj/(1 + i)j +.+ Rn /(1 + i)n + S/(1 + i)n P = Initial investmentRj = 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

Using Trial and Error: The general procedure of using a PW-based equation is as follows: Draw a cash flow diagram. Set up the rate of return equationSelect values of i by trial and error until the equation is balanced.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.If the NPV is negative r is decreased.Rate of Return

Rate of Return Decision RulesDecision Criterion for a Single Project: If IRR > MARR, accept the project.If IRR = MARR, remain indifferent.If IRR < MARR, reject the project.

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 Decision Rules

Period012345Cash flow-100,00030,00030,00030,00030,00030,000

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

Alternative A1 A2 A3Investment1,50,0002,10, 0002,55,000Ann. Net Income45,57058,26069,000

For the cash flow diagram shown in Fig. Compute the rate of return.Rate of Return0 1 2 3 4 5 150 300 450 600 7501,250

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.Rate of Return

Initial Investment Yearly revenueAlternative 15,00,0001,70,000Alternative 28,00,0002,70,000

Engineers with Monarch Paints have recommended an investment of $200,000 now that will reduce the amount of wastewater, packaging materials and other solid waste in their consumer paint manufacturing facility. Estimated savings are $15,000 per year for each of the next 10 years and an additional savings of $300,000 at the end of 10 years in facility and equipment upgrade costs. Determine the rate of return?PW = - 200,000+15,000(P/A,9%,10)+300,000(P/F,9%,10)PW = 22,986The result is positive, indicating that return is more than 9%. Try i = 11%.PW = - 200,000+15,000(P/A,11%,10)+300,000(P/F,11%,10)PW = - 6002Interest rate of 11% is too high, linearly interpolate between 9% and 11%.Rate of Return

Other Computational Methods

Direct SolutionDirect SolutionTrial & Error MethodLogQuadraticnProject AProject BProject C0-$1,000-$2,000-$75,000101,30024,400201,50027,3403055,76041,500

Direct Solution MethodsProject A

Project B

Trial and Error Method ProjectStep 1: Guess an interest rate, say, i = 15%Step 2: Compute PW(i) at the guessed i value.

PW (15%) = $3,553Step 3: If PW(i) > 0, then increase i. If PW(i) < 0, then decrease i.

PW(18%) = -$749

Step 4: If you bracket the solution, you use a linear interpolation to approximate the solution $3,5530-$74915%i18%Note: This method works onlyfor finding i* for simple investments.