Explanation Formula used: The internal rate of return on the investment is the value of r that satisfies the equation C ( 1 + r ) n − R 1 ( 1 + r ) n − 1 − R 2 ( 1 + r ) n − 2 − R 3 ( 1 + r ) n − 3 − … − R n = 0 , where r denotes the interest rate per period earned on the investment, R 1 , R 2 , … , R n are the returns at the end of each year and C is the initial outlay in the investment. Method used: Newton’s Method: 1. Pick an initial estimate x 0 of the root c. 2. Find a new estimate using the iterative formula x n + 1 = x n − f ( x n ) f ′ ( x n ) ( n = 0 , 1 , 2 , … ) . 3. Compute | x n + 1 − x n | . If this number is less than a prescribed positive number, stop. The required approximation to the root x = c is x = x n + 1 . Calculation: It is given that executive limousine service acquired limousines worth $12000 and the projected returns over 3 years. The time period the limousines will be in service are $80000 end of first year, $60000 at the end of the second year, and $40000 at the end of fourth year. That is, R 1 = $ 80000 , R 2 = $ 60000 , R 3 = $ 40000 , n = 3 , C = $ 120000 . Substitute R 1 = $ 80000 , R 2 = $ 60000 , R 3 = $ 40000 , n = 3 , C = $ 120000 in the above equation and obtain the value of f ( x ) as shown below: f ( x ) = 120000 ( 1 + r ) 3 − 800000 ( 1 + r ) 2 − 600000 Let x = 1 + r . Replace x with 1 + r and C with 12000 and simplify the above equation as, f ( x ) = 120000 ( 1 + r ) 3 − 800000 ( 1 + r ) 2 − 600000 f ( x ) = 120000 x 3 − 800000 x 2 − 600000 Differentiate f ( x ) with respect to x and obtain the value of f ′ ( x ) as, f ( x ) = 120000 x 3 − 800000 x 2 − 600000 f ′ ( x ) = 360000 x 2 − 160000 x Thus, the values of f ( x n ) , f ′ ( x n ) are as follows: f ( x n ) = 120000 x n 3 − 800000 x n 2 − 600000 f ′ ( x n ) = 360000 x n 2 − 160000 x n Using the above formula and obtain the value of x n + 1 as follows: x n + 1 = x n − f ( x n ) f ′ ( x n ) = x n − 120000 x n 3 − 800000 x n 2 − 600000 360000 x n 2 − 160000 x n Thus, x n + 1 = x n − 120000 x n 3 − 800000 x n 2 − 600000 360000 x n 2 − 160000 x n

APPLIED CALCULUS FOR MGRL, LIFE, SOC SCI

10th Edition

ISBN: 9780357465400

Author: Tan

Publisher: CENGAGE L

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Chapter 11.7, Problem 33E

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The internal rate of return on the investment, accurate to four decimal places.

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Chapter 11.7, Problem 32E

Chapter 11.7, Problem 34E

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Chapter 11 Solutions

APPLIED CALCULUS FOR MGRL, LIFE, SOC SCI

Ch. 11.1 - Prob. 1CQ Ch. 11.1 - Prob. 2CQ Ch. 11.1 - Prob. 1E Ch. 11.1 - In Exercises 110, find the first three Taylor...Ch. 11.1 - Prob. 3E Ch. 11.1 - Prob. 4E Ch. 11.1 - Prob. 5E Ch. 11.1 - Prob. 6E Ch. 11.1 - Prob. 7E Ch. 11.1 - Prob. 8E

Ch. 11.1 - In Exercises 110, find the first three Taylor...Ch. 11.1 - Prob. 10E Ch. 11.1 - Prob. 11E Ch. 11.1 - Prob. 12E Ch. 11.1 - Prob. 13E Ch. 11.1 - Prob. 14E Ch. 11.1 - In Exercises 1120, find the nth Taylor polynomial...Ch. 11.1 - Prob. 16E Ch. 11.1 - Prob. 17E Ch. 11.1 - Prob. 18E Ch. 11.1 - Prob. 19E Ch. 11.1 - Prob. 20E Ch. 11.1 - Prob. 21E Ch. 11.1 - Prob. 22E Ch. 11.1 - Prob. 23E Ch. 11.1 - Prob. 24E Ch. 11.1 - Prob. 25E Ch. 11.1 - Prob. 26E Ch. 11.1 - Prob. 27E Ch. 11.1 - Prob. 28E Ch. 11.1 - Prob. 29E Ch. 11.1 - Prob. 30E Ch. 11.1 - Prob. 31E Ch. 11.1 - Prob. 32E Ch. 11.1 - Prob. 33E Ch. 11.1 - Prob. 34E Ch. 11.1 - Let f(x) = ex. a. 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The internal rate of return on the investment, accurate to four decimal places.

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Chapter 11 Solutions