Question

You are running a small manufacturing process that has projected cash flows of -$13,000 in year one, $4,000 in year 2, $5000 in year 3, -$3,000 in year 4, $6,000 in year 5, and $7,000 in year 6, what is the interest rate that gives a net present value of zero. For information, In year four, you were required to make some upgrades to the process and that forced the negative $3,000. (Hint: Take the cash flow at the end of the year) (Give answer to one decimal place. That is, xx.x%)

Answer 1

Cashflow table

NPV @ 10%

Year	1	2	3	4	5	6
Cashflows	(13,000.0)	4,000.0	5,000.0	(3,000.0)	6,000.0	7,000.0
PV factor @ 10% ---> 1/ (1+10%)^nth year	0.9091	0.8264	0.7513	0.6830	0.6209	0.5645
PV of cashflows ---> Cashflows x PV factor	(11,818.2)	3,305.8	3,756.6	(2,049.0)	3,725.5	3,951.3
NPV ---> Sum of PV of cashflows	872.0

NPV @ 15%

Year	1	2	3	4	5	6
Cashflows	(13,000.0)	4,000.0	5,000.0	(3,000.0)	6,000.0	7,000.0
PV factor @ 15% ---> 1/ (1+15%)^nth year	0.8696	0.7561	0.6575	0.5718	0.4972	0.4323
PV of cashflows ---> Cashflows x PV factor	(11,304.3)	3,024.6	3,287.6	(1,715.3)	2,983.1	3,026.3
NPV ---> Sum of PV of cashflows	(698.1)

NPV at lower discount rate	871.98
Lower discount rate	10.00%
Value at higher discount rate	(698.10)
Higher discount rate	15.00%
Step 1 : Higher discount rate - Lower discount rate	5.00%
Step2 : NPV at lower discount rate x step1	43.60
Step3 : NPV at lower discount rate - NPV at higher discount rate	1,570.08
Step4 : Step2 / Step 3	2.78%
Step 5 : Lower discount rate + step4 ---> IRR	12.8%

This way of computing the IRR would give an approximate rate. Excel function ---> "IRR" can be used to arrive at accurate IRR.

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