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# 8.the rate of return method

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### 8.the rate of return method

1. 1. Building Economy ARE 431 Dr. Mohammad A. Hassanain ١ The Rate of Return Method ٢ The Present Worth Method. The Equivalent Uniform Annual Worth Method. Today’s Lecture
2. 2. Building Economy ARE 431 Dr. Mohammad A. Hassanain ٢ ٣ Rate of Return Method The objective of the rate of return method is to find the rate of return (% - percentage) for an investment over a specific service life. The rate of return method considers all the cash follows that occur during the life cycle of an investment. There are two methods to find the rate of return for an investment. These are: The Present Worth Method. The Equivalent Uniform Annual Cost (EUAC) Method. ٤ Rate of Return Method Rate of Return Calculation by the Present Worth Method: Procedure (3 Steps): 1. Draw a cash flow diagram. 2. Set up the rate of return equation in the form: +_=0 P + n Σj = 1 F (P/F, i%, n) A (P/A, i%, n)+_ 3. Select values of i by trail and error until the equation is balanced.
3. 3. Building Economy ARE 431 Dr. Mohammad A. Hassanain ٣ ٥ Rate of Return Method Rate of Return Calculation by the Present Worth Method: Example: If \$5,000 is invested now, this is expected to yield \$100 per year for 10 years and \$7,000 at the end of 10 years, What is the rate of return? A = \$100 642 0 1 3 5 7 8 i = ?% 9 \$5,000 10 \$7,000 Draw the Cash Flow Diagram ٦ Rate of Return Method Using the equation: +_=0 P n Σj = 1 F (P/F, i%, n) A (P/A, i%, n)+_ _=0 5,000 + 7,000 (P/F, i%, 10)100 (P/A, i%, 10) + Try i = 5% _=0 5,000 + 7,000 (P/F, 5%, 10)100 (P/A, 5%, 10)+ =0 + \$69.46 +_
4. 4. Building Economy ARE 431 Dr. Mohammad A. Hassanain ٤ ٧ Rate of Return Method Try i = 6% _=0 5,000 + 7,000 (P/F, 6%, 10)100 (P/A, 6%, 10)+ =0 _ \$355.19 By interpolation \$69.46 _ \$355.19 5% 0 i % 6% \$69.46 0_ \$69.46 ( \$355.19)_ _ = 5% _ i % 5% _ 6 % i = 5.16% ٨ Rate of Return Method Rate of Return Calculation by the EUAC Method: Procedure (3 Steps): 1. Draw a cash flow diagram. 2. Set up the rate of return equation in the form: 3. Select values of i by trail and error until the equation is balanced. +_=0 P (A/P, i%, n) A+_ +_ F (A/F, i%, n)Σj = 1 n
5. 5. Building Economy ARE 431 Dr. Mohammad A. Hassanain ٥ ٩ Rate of Return Method Rate of Return Calculation by the EUAC Method: Example: If \$5,000 is invested now, this is expected to yield \$100 per year for 10 years and \$7,000 at the end of 10 years, What is the rate of return? A = \$100 642 0 1 3 5 7 8 i = ?% 9 \$5,000 10 \$7,000 Draw the Cash Flow Diagram ١٠ Rate of Return Method Using the equation: _=0 5,000 7,000 (A/F, i%, 10) + 100(A/P, i%, 10) + Try i = 5% =0 + \$9.02 _=0 5,000 7,000 (A/F, 5%, 10) + 100(A/P, 5%, 10) + +_=0 P (A/P, i%, n) A+_ +_ F (A/F, i%, n)Σj = 1 n
6. 6. Building Economy ARE 431 Dr. Mohammad A. Hassanain ٦ ١١ Rate of Return Method Try i = 6% =0 _ \$48.26 By interpolation \$9.02 _ \$48.26 5% 0 i % 6% \$9.02 0_ \$9.02 ( \$48.26)_ _ = 5% _ i % 5% _ 6 % i = 5.16% =0 5,000 7,000 (A/F, 5%, 10) + 100(A/P, 5%, 10) +_