Question

How many possible IRRs could you find for the following set of cash flows?

Time 0 1 2 3 4 Cash Flow –$ 15,000 $ 6,000 $ 10,000 $ 12,000 $ 1,000

Multiple Choice

2

1

3

Unable to determine unless we have the cost of capital.

Answer 1

There will be one IRR i.e Option 2) 1 IRR

We know that PV of Cash inflow is equal to the PV of the cash outflow.

So the rate at which PV of inflows is equal to PV of outflows is IRR.Since there are no negetive cash inflow in the middle of the project so there will be only 1 IRR.

Computation of IRR

Year	Cash flow	Disc @ 10%	DCF	Disc @ 20%	DCF	Disc @ 25%	DCF	Disc @ 30%	DCF	Disc @35%	DCF	Disc @ 36%	DCF
0	($15,000)	$1	($15,000)	$1	($15,000)	$1	($15,000)	$1	($15,000)	$1	($15,000)	1	($15,000)
1	$6,000	0.9091	$5,454.55	0.8333	$5,000	0.8	$4,800	0.769230769	$4,615.38	0.740740741	$4,444.44	0.735294118	$4,411.76
2	$10,000	0.8264	$8,264.46	0.6944	$6,944	0.64	$6,400	0.591715976	$5,917.16	0.548696845	$5,486.97	0.540657439	$5,406.57
3	$12,000	0.7513	$9,015.78	0.5787	$6,944	0.512	$6,144	0.455166136	$5,461.99	0.406442107	$4,877.31	0.397542235	$4,770.51
4	$1,000	0.6830	$683.01	0.4823	$482	0.4096	$410	0.350127797	$350.13	0.301068228	$301.07	0.292310467	$292.31
	NPV		$8,417.80		$4,371		$2,754		$1,344.67		$109.79		($119)

We know that at IRR , NPV should be 0.

From the table we can tell that IRR lies between 35% and 36%

Disc	NPV
35%	$109.79
36%	($119)

Change in Dis	Change in NPV
1	228.79( $ 109.79+$119)
X	109.79

We get X = 109.79*1/228.79

= 0.4978

Hence IRR is 35.4798%

So Cost of capital isnot necessary for determination of IRR.So option 4 is not correct.

Two IRR are present when the negetive cash flows occuring at the middle of the project or during the tenure of the project,apart from start of the project.Then there will be two IRR.

3 IRR is not possible.