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4-91. An electronic device is available that will reduce this year’s labor costs by $8,000. The...

4-91. An electronic device is available that will reduce this year’s labor costs by $8,000. The equipment is expected to last for 10 years. Labor costs increase at a rate of 5% per year and the interest rate is 10% per year.(4.12)

a. What is the maximum amount that we could justify spending for the device? Draw a cash flow diagram to represent the situation.

b. What is the uniform annual equivalent value (A) of the labor costs over the eight-year period?

A very similar question was answered in the Chegg Textbook Solutions for Engineering Economy (16th edition) Chapter 4 Question 4-91, but I need a cash flow diagram to help visualize the situation.

Solutions

Expert Solution

Year Savings in labor costs
1 $8,000
2 $7,600.00
3 $7,220.00
4 $6,859.00
5 $6,516.05
6 $6,190.25
7 $5,880.74
8 $5,586.70
9 $5,307.36
10 $5,042.00

a) The maximum amount we could justify spending for the device is the present value of the labor cost savings over a period of 10 years

Present value of labor cost savings = $ 8000 1.101 + $ 7600  1.102 + $ 7220 1.103 + $ 6859 1.104 + $ 6516.051.105 + $ 6190.251.106 + $ 5880.74 1.107 + $ 5586.701.108 + $ 5307.36 1.109 + $ 50421.1010

Present value of labor cost savings = $ 41,021.92

Maximum amount that we could justify spending for the device = $ 41,021.92

_________________________________________________________________

b) The data on the labor is not given hence assuming the labor cost for year 1 is $ 1000

The present value of labor cost over eight year period = $ 1000 1.101 + $ 1050  1.102 + $ 1102.50 1.103 + $ 1157.63 1.104 + $ 1215.511.105 + $ 1276.281.106 + $ 1340.10 1.107 + $ 1407.101.108

The present value of labor cost over eight year period = $ 6215.12

Uniform annual equivalent value (A) of the labor costs over the eight-year period = Present value labor costs PVIFAr=10%, n = 8 years

Uniform annual equivalent value (A) of the labor costs over the eight-year period = $ 6215.12 5.334926

Uniform annual equivalent value (A) of the labor costs over the eight-year period = $ 1,164.987

Year Labor cost
1 $1,000
2 $1,050.00
3 $1,102.50
4 $1,157.63
5 $1,215.51
6 $1,276.28
7 $1,340.10
8 $1,407.10

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