3
Exam 1, Problem 1.
An engineer has proposed a design to improve the quality of an existing product. The design is
expected to have a life of fifteen years. Its projected costs are $250,000 to design and install,
$20,000 per year to operate and this cost is expected to increase by $3,000 per year every year
after the first. Additional maintenance is expected at years 5, 10 and 15. This cost will be
$20,000 the first time and will increase by $10,000 each time thereafter. What must the value of
the improvement be per year to recover all costs and economic growth of 10% per year in the
first seven years of usage?
Using Present-Worth analysis, we can determine the total costs of expenses for the lifetime of the
machine (15 years), now (at time=0). The present value of this investment costs $556,137.96.
Then, to calculate the amount it will cost per year, we implement the Capital Recovery equation,
which returns a value of $114,223.80. This value represents the amount of money this
investment will cost per year, at ac economic growth rate of 10% per year. Therefore, the
investment must earn for the company a minimum of this value $114,223.80 per year in order to
pay for itself, any income greater than this value is profit (if the only expenses are those
mentioned in the problem).
The chart of values below shows the expenses per year and the Present Value equivalents at time
= 0.
Year
Expenses
PV(t=0)
0
$250,000
$250,000.00
1
$20,000
$18,181.82
2
$23,000
$19,008.26
3
$26,000
$19,534.18
4
$29,000
$19,807.39
5
$52,000
$32,287.91
6
$35,000
$19,756.59
7
$38,000
$19,500.01
8
$41,000
$19,126.80
9
$44,000
$18,660.30
10
$77,000
$29,686.83
11
$50,000
$17,524.69
12
$53,000
$16,887.43
13
$56,000
$16,221.21
14
$59,000
$15,536.54
15
$102,000
$24,417.99