Question

Angela's LandBuyers has a new commercial real estate development proposal. The project will cost $500,000 today and produce positive cash inflows of $150,000 for each of the next six years. In year six, the project also requires an environmental revitalization cost of $50,000. Based on these initial figures, Angela's has calculated that the project produces a positive NPV and has an IRR greater than the required return of 15%. Prior to making a final decision about the project, the town's oversight board decides that the environmental revitalization needs to occur in year three rather than year six. All else equal, with the change in revitalization cost from year six to year three, what will happen to NPV and IRR of the project?

Answer 1

A) When environmental revitalization occurs in year six

Statement showing NPV

Year	Cash flow	PVIF @ 15%	PV
	A	B	C = A x B
0	-500000	1	-500000
1	150000	0.8696	130435
2	150000	0.7561	113422
3	150000	0.6575	98627
4	150000	0.5718	85763
5	150000	0.4972	74577
6	100000	0.4323	43233
NPV	46056

Thus NPV = 46056$

IRR is rate at which NPV is 0

Assume rate = 18%

Statement showing NPV

Year	Cash flow	PVIF @ 18%	PV
	A	B	C = A x B
0	-500000	1.0000	-500000
1	150000	0.8475	127119
2	150000	0.7182	107728
3	150000	0.6086	91295
4	150000	0.5158	77368
5	150000	0.4371	65566
6	100000	0.3704	37043
NPV	6119

Now assume r = 19%

Year	Cash flow	PVIF @ 19%	PV
	A	B	C = A x B
0	-500000	1.0000	-500000
1	150000	0.8403	126050
2	150000	0.7062	105925
3	150000	0.5934	89012
4	150000	0.4987	74800
5	150000	0.4190	62857
6	100000	0.3521	35214
NPV	-6141

Now using interpolation we can find IRR

Rate	NPV
18%	6119
19%	-6141
1%	12259
?	6119

=6119/12259

=0.50%

Thus IRR = 18%+0.50% = 18.50%

B) When environmental revitalization occurs in year three

Statement showing NPV

Year	Cash flow	PVIF @ 15%	PV
	A	B	C = A x B
0	-500000	1.0000	-500000
1	150000	0.8696	130435
2	150000	0.7561	113422
3	100000	0.6575	65752
4	150000	0.5718	85763
5	150000	0.4972	74577
6	150000	0.4323	64849
NPV	34797

Thus NPV = $34797

Now IRR

Assume r = 17%

Statement showing NPV

Year	Cash flow	PVIF @ 17%	PV
	A	B	C = A x B
0	-500000	1.0000	-500000
1	150000	0.8547	128205
2	150000	0.7305	109577
3	100000	0.6244	62437
4	150000	0.5337	80048
5	150000	0.4561	68417
6	150000	0.3898	58476
NPV	7159

Assume r = 18%

Statement showing NPV

Year	Cash flow	PVIF @ 18%	PV
	A	B	C = A x B
0	-500000	1.0000	-500000
1	150000	0.8475	127119
2	150000	0.7182	107728
3	100000	0.6086	60863
4	150000	0.5158	77368
5	150000	0.4371	65566
6	150000	0.3704	55565
NPV	-5791

Now using interpolation we can find IRR

Rate	NPV
17%	7159
18%	-5791
1%	12950
?	7159

=7159/12950

=0.55

Thus IRR = 17+0.55 = 17.55%

Comparative statement

	When environmental revitalization occurs in year Six	When environmental revitalization occurs in year three	Change
NPV	46056	34797	11259
IRR	18.50%	17.55%	0.95%

Thus if environmental revitalization occurs in year three , then NPV will decrease by $11259 and IRR will be reduced by 0.95%