In: Finance
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.
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 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 |