Equivalence for Repeated Cash Flows
Name: Piyush AkkineniEKU ID : 901589527Chapter 4: Equivalence for Repeated Cash Flows [5 points] If i = 10%, for what value of B is the present value = 0?[pic 1]SolutionP = F(1+i)-n1st YearPresent Value of B1 = B × (1+0.1)-1 = 0.909B2nd YearPresent Value of B2 = -1.25B × (1+0.1)-2 = -1.033BPresent Value of 900 = 900 × (1+0.1)-2 = 743.83rd YearPresent Value of B3 = -B × (1+0.1)-3 = -0.75BPresent Value of 900 = 900 × (1+0.1)-3 = 676.184th YearPresent Value of B4 = -1.75B × (1+0.1)-4 = -1.19B
Present Value of 900 = 900 × (1+0.1)-4 = 614.7On solving for the value of B using Excel SpreadsheetB = 982.6387. [pic 2][5 points] These cash flow transactions are said to be equivalent in terms of economic desirability at an interest rate of 15% compounded annually. Determine the unknown value of A?[pic 3]Solution[pic 4][pic 5][pic 6][pic 7]P = + [pic 8][pic 9] = + [pic 10][pic 11] = 1155 + 670.4 = 1825.4 … (1)[pic 12] = 2.855A … (2)[pic 13]On equating equations (1) and (2),2.855A = 1825.4A = [pic 14]A = 639.369Chapter 5: Present Worth Analysis[10 points] An industrial engineer has been studying a lean process line to determine if the company should switch from a labor-intensive line to a more automated system. If the company wants to earn at least 12% over a 10-year planning horizon, given the following cash flow estimates and using a Present Worth Analysis, which alternative is preferred?Labor Intensive LineAutomated LineInitial Cost$ 0$ 100,000Installation Cost×$ 0$ 100,0001st-Year Maintenance Costs$ 2,000$ 15,000Annual Increase in Maintenance Costs$ 250$ 5001st-Year Labor Costs$ 95,000$ 50,000Annual Increase in Labor Costs3%3%Salvage Value (End of Year 10)$ 10,000$ 20,000