Overall ROR: 30,000(0.20) + 70,000(0.14) = 100,000(x) x = 15.8% Prepare a tabulation of cash flow for the alternatives shown below.

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1 Chapter 8, Problem 2. What is the overall rate of return on a $100,000 investment that returns 20% on the first $30,000 and 14% on the remaining $70,000? Chapter 8, Solution 2. Overall ROR: 30,000(0.20) + 70,000(0.14) = 100,000(x) x = 15.8% Chapter 8, Problem 10. Prepare a tabulation of cash flow for the alternatives shown below. Machine A Machine B First cost, $ 15,000 25,000 Annual operating cost, $/year 1, Salvage value, $ 3,000 6,000 Life, years 3 6 Chapter 8, Solution 10. Year Machine A Machine B B A 0-15,000-25,000-10, , , , Chapter 8, Solution = -25, (P/A,i,6) + 26,000(P/F,i,3) 39,000(P/F,i,4) + 40,000(P/F,i,6) Solve for i by trial and error or Excel i = 17.4% (Excel) i > MARR; select machine requiring extra investment: variable speed

2 Chapter 8, Problem 15. A company that manufactures amplified pressure transducers is trying to decide between the machines shown below. Compare them on the basis of rate of return, and determine which should be selected if the company s MARR is 15% per year. Variable Dual Speed Speed First cost, $ 250, ,000 Annual operating cost, $/year 231, ,000 Overhaul in year 3, $ 26,000 Overhaul in year 4, $ 39,000 Salvage value, $ 50,000 10,000 Life, years 6 6 Chapter 8, Problem 17. A solid waste recycling plant is considering two types of storage bins. Determine which should be selected on the basis of rate of return. Assume the MARR is 20% per year. Alternative P Alternative Q First cost, $ 18,000 35,000 Annual operating cost, $/year 4,000 3,600 Salvage value, $ 1,000 2,700 Life, years 3 6 Chapter 8, Solution = -17, (P/A,i,6) + 17,000(P/F,i,3) (P/F,i,6) Solve for i by trial and error or Excel i = 6.8% (Excel) Select alternative P. Chapter 8, Problem 22. Determine which of the two machines below should be selected, using an AW-based rate of return analysis, if the MARR is 18% per year. Semiautomatic Automatic First cost, $ 40,000 90,000 Annual cost, $/year 100,000 95,000 Salvage value, $ 5,000 7,000 Life, years 2 4

3 Chapter 8, Solution 22. Find ROR for incremental cash flow over LCM of 4 years 0 = -50,000(A/P,i,4) (40, )(P/F, i,2)(a/p, i,4) (A/F,i,4) Solve for i by trial and error or Excel i = 6.1% (Excel) i < MARR; select semiautomatic machine Chapter 8, Problem 29. Mountain Pass Canning Company has determined that any one of five machines can be used in one phase of its canning operation. The costs of the machines are estimated below, and all machines have a 5-year life. If the minimum attractive rate of return is20% per year, determine the one machine that should be selected on the basis of a rate of return analysis. Annual Operating Machine First Cost, $ Cost, $/year 1 31,000 18, ,000 19, ,500 17, ,000 12, ,000 15,500 Chapter 8, Solution 29. Rank alternatives according to increasing initial cost: 2,1,3,5,4 1 vs 2: 0 = -3000(A/P,i,5) (A/P,i,5) = i = 41.0% (Excel) Eliminate 2 3 vs1: 0 = -3500(A/P,i,5) (A/P,i,5) = i = 13.2% (Excel) Eliminate 3 5 vs 1: 0 = -10,000(A/P,i,5) (A/P,i,5) = i = 7.9% (Excel) Eliminate 5

4 4 vs1: 0 = -17,000(A/P,i,5) (A/P,i,5) = i = 22.5% (Excel) Eliminate 1 Select machine 4 Chapter 8, Problem 32. Only one of four different machines is to be purchased for a certain production process. An engineer performed the following analyses to select the best machine. All machines are assumed to have a 10-year life. Which machine, if any, should the company select if its MARR is (a) 12% per year and (b) 20% per year? Machine Initial cost, $ 44,000 60,000 72,000 98,000 Annual cost, $/year 70,000 64,000 61,000 58,000 Annual savings, $/year _80, , , ,000 ROR, % Machines compared 2 to 1 3 to 2 4 to 3 Incremental investment, $ 16,000 12,000 26,000 Incremental cash flow, $/year +6,000 +3,000 +5,000 ROR on increment, % Chapter 8, Solution 32. (a) All machines have ROR > MARR of 12% and all increments of investment have ROR > MARR. Therefore, select machine 4. (b) Machines 2, 3, and 4 have ROR greater than 20%. Increment between 2 and 3 is justified, but not increment between 3 and 4. Therefore, select machine 3.

5 Chapter 8, Problem 33. The four alternatives described below are being evaluated. (a) If the proposals are independent, which should be selected when the MARR is 16% per year? (b) If the proposals are mutually exclusive, which one should be selected when the MARR is 9% per year? (c) If the proposals are mutually exclusive, which one should be selected when the MARR is 12% per year? Incremental Rate of Return, %, When Compared with Initial Alternative Alternative Investment, $ Rate of Return, % A B C A 40, B 75, C 100, D 200, Chapter 8, Solution 33. (a) Select A and C. (b) Proposal A is justified. A vs B yields 1%, eliminate B; A vs C yields 7%, eliminate C; A vs D yields 10%, eliminate A. Therefore, select proposal D (c) Proposal A is justified. A vs B yields 1%, eliminate B; A vs C yields 7%, eliminate C; A vs D yields 10%, eliminate D. Therefore, select proposal A Chapter 8, Problem 40. The incremental cash flow between two alternatives is shown below. Year Incremental Cash Flow, $ 0 20, , The equation(s) that can be used to correctly solve for the incremental rate of return is (are) (a) 0 = 20, (A/P,i,10) + 400(P/F,i,10) (b) 0 = 20, (A/P,i,10) + 400(A/F,i,10) (c) 0 = 20,000(A/P,i,10) (P/F,i,10) (d) 0 = 20, (P/A,i,10) + 400(P/F,i,10) Chapter 8, Solution 40. Answer is (d)

6 Chapter 8, Problem 43. Questions 8.41 through 8.43 are based on the following. The five alternatives are being evaluated by the rate of return method. Incremental Rate of Return, %, When Compared with Initial Alternative Alternative Alternative Investment, $ Rate of Return, % A B C D E 25, A B 35, C 40, , D E 75, If the alternatives are mutually exclusive and the MARR is 25% per year, the alternative to select is (a) A (b) D (c) E (d) None of them Chapter 8, Solution 43. Answer is (b)