Profit and loss (in $1000 units) associated with the sale of a vision-guided machine tool loading system and the resulting NCF amounts are recorded. (a) Use sign-change rules to determine the possible number of i* values. (b) Find all i* values between 0 and 100%. (c) If the required MARR for the company is 15% per year, how small can the gradient be for years 3 through 6?
 FIGURE 1.png)
(a) One sign change in NCF and cumulative CF indicates only one i*.
(b) 0 = -5000 - 10,100(P/F,i*,1) + [4500(P/A,i*,5) + 2000(P/G,i*,5)](P/F,i*,1)
i* = 33.7% per year (spreadsheet)
(b) Use ROR equation with i* = 15% and solve for G. Alternatively, enter NCF values
onto a spreadsheet and use Goal Seek to find the lowest G value to make i* = 15%
0 = -5000 -10,100(P/F,15%,1) + [4500(P/A,15%,5) + G(P/G,15%,5)](P/F,15%,1)
= -5000 -10,100(0.8696) + [4500(3.3522) + G(5.7751)](0.8696)
5.022G = 665.131
G = $132.44
Spreadsheet: Goal Seek results in G = $132.72
It is possible to have a gradient as low as $133 and still realize a 15% return.
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