Question

ABC, Inc., is considering the purchase of a digital camera for the maintenance of design specifications by feeding digital pictures directly into an engineering workstation where computer-aided design files can be superimposed over the digital pictures. Differences between the two images can be noted, and corrections, as appropriate, can then be made by design engineers. The capital investment requirement is $350,000 and the estimated market value of the system after a six-year study period is $120,000. Annual revenues attributable to the new camera system will be $130,000, whereas additional annual expenses will be $25,000. You have been asked by management to determine the IRR of this project and to make a recommendation. The corporation’s MARR is 20% per year.

1. Solve first by using linear interpolation
2. and then by using a spreadsheet.

Answer 1

a. by interpolation

Let IRR be i%, then

-350000 + (130000-25000)*(P/A,i%,6) + 120000* (P/F,i%,6) = 0

105000*(P/A,i%,6) + 120000* (P/F,i%,6) = 350000

Dividing by 10000

10.5*(P/A,i%,6) + 12* (P/F,i%,6) = 35

using trail and error method

When i = 24%, value of 10.5*(P/A,i%,6) + 12* (P/F,i%,6) = 10.5*3.020471 + 12*0.275087 = 35.01599

When i = 25%, value of 10.5*(P/A,i%,6) + 12* (P/F,i%,6) = 10.5*2.951424 + 12*0.262144 = 34.13568

using interpolation

i = 24% + (35.01599 - 35) /(35.01599 - 34.13568)*(25%-24%)

i = 24% + 0.018164% = 24.0182% ~ 24.02%

As IRR > MARR, project should be selected

b.

By spreadsheet

Year	Investment	Revenue	Cost	Salvage value	Net cash Flow
0	-350000				-350000
1		130000	-25000		105000
2		130000	-25000		105000
3		130000	-25000		105000
4		130000	-25000		105000
5		130000	-25000		105000
6		130000	-25000	120000	225000
				IRR	24.02%

As IRR > MARR, project should be selected

Showing formula in excel

Year	Investment	Revenue	Cost	Salvage value	Net cash Flow
0	-350000				=U33+V33+W33+X33
1		130000	-25000		=U34+V34+W34+X34
2		130000	-25000		=U35+V35+W35+X35
3		130000	-25000		=U36+V36+W36+X36
4		130000	-25000		=U37+V37+W37+X37
5		130000	-25000		=U38+V38+W38+X38
6		130000	-25000	120000	=U39+V39+W39+X39
				IRR	=IRR(Y33:Y39)