Question

You have 3 projects with the following cash​ flows:

Year    0       1   2      3         4
Project 1   -$149   $19   $42   $61      $79
Project 2   -827      0   0   7,002   -6,508
Project 3   18          39   62   81      -247

a. For which of these projects is the IRR rule​ reliable?_______.

b. Estimate the IRR for each project​ (to the nearest 1 %​).________.

c. What is the NPV of each project if the cost of capital is 5 %? 20 %? 50 %​?________.

a. For which of these projects is the IRR rule​ reliable?  ​(Select from the​ drop-down menus.)

The IRR rule is reliable for▼project 1 project 2 project 3. Unless all of the ▼positive negative cash flows of the project precede the ▼negative

positive​ones, the IRR rule may give the wrong answer and should not be used.​ Furthermore, there may be multiple IRRs or the IRR may not exist.

Answer 1

a.

IRR rule is reliable for Project 1. Unless all of the negative cash flow of the project precedes positive ones.

b.

Computation of IRRs using excel:

	A	B	C	D
1	Year	Project 1	Project 2	Project 3
2	0	($149)	($827)	$18
3	1	$19	$0	$39
4	2	$42	$0	$62
5	3	$61	$7,002	$81
6	4	$79	($6,508)	($247)
7	IRR	10.70%	10.65%	11.01%

If excel sheet look like above table,

Insert formula “=IRR(B2:B6)” in Cell B7 to get IRR of project 1 as 10.70 %

Insert formula “=IRR(C2:C6)” in Cell C7 to get IRR of project 2 as 10.65 %

Insert formula “=IRR(D2:D6)” in Cell D7 to get IRR of project 3 as 11.01 %

c.

Computation of NPV @ 5 %:

Year	Computation of PV factor	PV Factor @ 5 % (F)	Cash Flow Project 1 C1	PV Project 1 (=C1 x F)	Cash Flow Project 2 C2	PV Project 2 (=C2 x F)	Cash Flow Project 3 C3	PV Project 3 (=C3 x F)
0	1/(1+0.05)^0	1	($149)	($149.00)	($827)	($827.00)	$18	$18.0000
1	1/(1+0.05)^1	0.952380952	$19	$18.09524	$0	$0.0000	$39	$37.1429
2	1/(1+0.05)^2	0.907029478	$42	$38.09524	$0	$0.0000	$62	$56.2358
3	1/(1+0.05)^3	0.863837599	$61	$52.69409	$7,002	$6,048.5909	$81	$69.9708
4	1/(1+0.05)^4	0.822702475	$79	$64.99350	($6,508)	($5,354.1477)	($247)	($203.2075)
			NPV	$24.87807	NPV	($132.55684)	NPV	($21.85798)

NPV of Project 1, 2 and 3 at discount rate of 5 % is $24.88, -$ 132.56, -$21.86 respectively.

Computation of NPV @ 20 %:

Year	Computation of PV factor	PV Factor @ 20 % (F)	Cash Flow Project 1 C1	PV Project 1 (=C1 x F)	Cash Flow Project 2 C2	PV Project 2 (=C2 x F)	Cash Flow Project 3 C3	PV Project 3 (=C3 x F)
0	1/(1+0.20)^0	1	($149)	($149.00000)	($827)	($827.0000)	$18	$18.0000
1	1/(1+0.20)^1	0.833333333	$19	$15.83333	$0	$0.0000	$39	$32.5000
2	1/(1+0.20)^2	0.694444444	$42	$29.16667	$0	$0.0000	$62	$43.0556
3	1/(1+0.20)^3	0.578703704	$61	$35.30093	$7,002	$4,052.0833	$81	$46.8750
4	1/(1+0.20)^4	0.482253086	$79	$38.09799	($6,508)	($3,138.5031)	($247)	($119.1165)
			NPV	($30.60108)	NPV	$86.58025	NPV	$21.31404

NPV of Project 1, 2 and 3 at discount rate of 20 % is -$30.60, $ 86.58, -$21.31 respectively.

Computation of NPV @ 50 %:

Year	Computation of PV factor	PV Factor @ 50 % (F)	Cash Flow Project 1 C1	PV Project 1 (=C1 x F)	Cash Flow Project 2 C2	PV Project 2 (=C2 x F)	Cash Flow Project 3 C3	PV Project 3 (=C3 x F)
0	1/(1+0.50)^0	1	($149)	($149.00000)	($827)	($827.0000)	$18	$18.0000
1	1/(1+0.50)^1	0.666666667	$19	$12.66667	$0	$0.0000	$39	$26.0000
2	1/(1+0.50)^2	0.444444444	$42	$18.66667	$0	$0.0000	$62	$27.5556
3	1/(1+0.50)^3	0.296296296	$61	$18.07407	$7,002	$2,074.6667	$81	$24.0000
4	1/(1+0.50)^4	0.197530864	$79	$15.60494	($6,508)	($1,285.5309)	($247)	($48.7901)
			NPV	($83.98765)	NPV	($37.86420)	NPV	$46.76543

NPV of Project 1, 2 and 3 at discount rate of 50 % is - $83.99, -$ 37.86, -$46.77 respectively.