Question 8.P.8: Compute the ROR for the following cash flows:...

Descartes’ rule tells us to expect no more than three positive values for i * . Adding and subtracting $31 000 from CF_2, we obtain

0 = -$50 000 + $30 000(P/A, i*%, 3) – $31 000(P/F, i*%, 2)

As a first approximation, neglect the last term on the right:

(A/P, i*%, 3) = \frac{\$30  000}{\$50  000} = 0.60000

From the tables in Appendix A, we see that:

Hence, for the approximate equation, 30% < i* <40%. Restoring the neglected term should pull i* closer to 30% ; hence, try i = 30% :

NPV = -$50 000 + $30 000(0.55063)^{-1} – $31 000(1.6900)^{-1} = -$13 860.15

Under the previous approximation, NPV = -$31000(P/F, i*%, 2) = -$18000, and under the present approximation, NPV = -$I3 860.15; we conclude that i* < 30%. Try i = 8%:

NPV = -$50 000 + $30 000(0.38803)^{-1} – $31 000(1.1664)^{-1} = +$736.11

Hence, i* >8%. Try i = 10%:

NPV = -$50 000 + $30 000(0.40211)^{-1} – $31 000(1.2100)^{-1} = -$1013.38

Hence, 8% < i* < 10%. Try i = 9%:

NPV = -$50 000 + $30 000(0.39505)^{-1} – $31 000(1.1881)^{-1} = -$152.33

Hence, 8% < i* < 9%. By linear interpolation,

i* ≈ 8% + \frac{0  –  \$736.11}{-\$152.33  –  \$736.11} (9% – 8%) = 8.83%

It is not difficult to show that there are no other positive values-in fact, no other real values-of i* besides i * = 8.83%.