Equivalence for Repeated Cash Flows

Name: Piyush Akkineni

EKU ID : 901589527

Chapter 4: Equivalence for Repeated Cash Flows

1. [5 points] If i = 10%, for what value of B is the present value = 0?
   
   [pic 1]

Solution

P = F(1+i)-n

1st Year

Present Value of B1 = B × (1+0.1)-1

                           = 0.909B

2nd Year

Present Value of B2 = -1.25B × (1+0.1)-2

                           = -1.033B

Present Value of 900 = 900 × (1+0.1)-2

                            = 743.8

3rd Year

Present Value of B3 = -B × (1+0.1)-3

                           = -0.75B

Present Value of 900 = 900 × (1+0.1)-3

                            = 676.18

4th Year

Present Value of B4 = -1.75B × (1+0.1)-4

                           = -1.19B

Present Value of 900 = 900 × (1+0.1)-4

    = 614.7

On solving for the value of B using Excel Spreadsheet

B = 982.6387.        

[pic 2]

1. [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 = 1825.4

A = [pic 14]

A = 639.369

Chapter 5: Present Worth Analysis

1. [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?