Question

The cash flows in the table below represent the potential annual savings associated with two different types of production​ processes, each of which requires an investment of ​$34,000. Assume an interest rate of 6​%.

                                                                                                                                                                                                                                                                    

(a) Determine the equivalent annual savings for each process.

The equivalent annual savings for process A are ​$_________. ​(Round to the nearest​ dollar.)

The equivalent annual savings for process B are ​$_________. ​(Round to the nearest​ dollar.)

(b) Determine the hourly savings for each process if will be in operation of 5,000 hours per year.

The hourly savings for process A are $______. (Round to the nearest cent.)

The hourly savings for process B are $______. (Round to the nearest cent.)

(c) Which process should be selected? Choose the correct answer below.

Yes or No

Answer 1

(a)

First, Present Worth (PW) of savings is computed as follows.

PW, Process A ($) = -34,000 + 16,910 x P/F(6%, 1) + 15,330 x P/F(6%, 2) + 13,750 x P/F(6%, 3) + 12,170 x P/F(6%, 4)

= -34,000 + 16,910 x 0.9434** + 15,330 x 0.8900** + 13,750 x 0.8396** + 12,170 x 0.7921**

= -34,000 + 15,953 + 13,644 + 11,545 + 9,640

= 16,782

PW, Process B ($) = -34,000 + 12,000 x P/A(6%, 4) = -34,000 + 12,000 x 3.4651** = -34,000 + 41,581 = 7,581

Therefore,

Equivalent Annual savings, Process A ($) = PW of Process A / P/A(6%, 4) = 16,782 / 3.4651** = 4,843

Equivalent Annual savings, Process B ($) = PW of Process B / P/A(6%, 4) = 7,581 / 3.4651** = 2,188

(b)

Hourly saving, Process A ($) = Equivalent Annual savings / Number of hours per year = 4,843 / 5,000 = 0.97

Hourly saving, Process B ($) = Equivalent Annual savings / Number of hours per year = 2,188 / 5,000 = 0.44

(c)

Since Process A has higher hourly saving, Process A should be selected.

**From P/A and P/F Factor tables