A company that makes clutch disks for race cars has the annual net cash flows shown for one department.

Question

Answer 1

(a) Descartes’ rule of signs: 2 sign changes; up to two i* values

Norstrom’s criterion: series starts negative; 1 sign change; one positive root



(b) 0 = -65 + 30(P/F,i*,1) + 84(P/F,i*,2) – 10(P/F,i*,3) – 12(P/F,i*,4)



Solve for i* by trial and error or spreadsheet



i* = 28.6% per year (spreadsheet)



A negative root of -56.0% is discarded. It can be displayed using = IRR(B1:B5,-50%)



(c) Apply net-investment procedure steps because the investment rate ii = 15% is not

equal to i* rate of 28.6% per year.



Hand solution:



Step 1: F0 = -65 F0 < 0; use i?

F1 = -65(1 + i?) + 30 F1 < 0; use i?

F2 = F1(1 + i?) + 84 F2 > 0; use ii (F2 must be > 0, because last two terms are negative)

F3 = F2(1 + 0.15) -10 F3 > 0; use ii (F3 must be > 0, because last term is

negative)

F4 = F3(1 + 0.15) –12



Step 2: Set F4 = 0 and solve for i? by trial and error.

F1 = -65 – 65i? + 30



F2 = (-65 – 65i? + 30)(1 + i?) + 84

= -65 - 65i? + 30 – 65i? – 65i?2 + 30i? +84

= -65i?2 –100i? + 49



F3 = (-65i?2 –100i?+ 49)(1.15) – 10

= -74.8 i?2 –115i? + 56.4 – 10

= -74.8 i?2 –115i? + 46.4



F4 = (-74.8 i?2 –115i? + 46.4)(1.15) –12

= -86 i?2 –132.3i? + 53.3 – 12

= -86 i?2 –132.3i? + 41.3

Solve by quadratic equation, trial and error, or spreadsheet



i? = 26.6% per year (spreadsheet)



Spreadsheet solution: Using the format and functions of Figure 7-13, i? = 26.62%.