Question

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.

Answer 1

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

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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 PVIFA_{r=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