Question

Butler International Limited is evaluating a project in Erewhon. The project will create the following cash flows:

  

Year	Cash Flow
0	–$	1,310,000
1		485,000
2		550,000
3		445,000
4		400,000

  

All cash flows will occur in Erewhon and are expressed in dollars. In an attempt to improve its economy, the Erewhonian government has declared that all cash flows created by a foreign company are “blocked” and must be reinvested with the government for one year. The reinvestment rate for these funds is 3 percent.

  

If the company uses a required return of 13 percent on this project, what are the NPV and IRR of the project? (Negative amounts should be indicated by a minus sign. Do not round intermediate calculations and round your final answers to 2 decimal places, e.g., 32.16. Enter your IRR answer as a percent.)

Answer 1

Net Present Value (NPV) of the Project

Year 1 cash flow = $0

Year 2 Cash Flow = $499,550 ($485,000 x 1.03)

Year 3 Cash Flow = $566,500 ($550,000 x 1.03)

Year 4 Cash Flow = $458,350 ($445,000 x 1.03)

Year 5 Cash Flow = $412,000 (400,000 x 1.03)

Year	Annual Cash Flow ($)	Present Value factor at 13%	Present Value of Cash Flow ($)
1	0	0.88496	0.00
2	4,99,550	0.78315	3,91,220.93
3	5,66,500	0.69305	3,92,612.92
4	4,58,350	0.61332	2,81,114.64
5	4,12,000	0.54276	2,23,617.09
TOTAL			12,88,565.58

Net Present Value (NPV) = Present Value of annual cash inflows – Initial Investment

= $12,88,565.58 - $13,10,000

= -$21,434.42 (Negative NPV)

“Therefore, the Net Present Value (NPV) of the Project = -$21,434.42 (Negative NPV)”

Internal Rate of Return (IRR) for the Project

Step – 1, Firstly calculate NPV at a guessed discount Rate, Say 12%

Year	Annual Cash Flow ($)	Present Value factor at 12%	Present Value of Cash Flow ($)
1	0	0.89286	0.00
2	4,99,550	0.79719	3,98,238.20
3	5,66,500	0.71178	4,03,223.51
4	4,58,350	0.63552	2,91,289.71
5	4,12,000	0.56743	2,33,779.86
TOTAL			13,26,531.29

Net Present Value (NPV) = Present Value of annual cash inflows – Initial Investment

= $13,26,531.29 - $13,10,000

= $16,531.29

Step – 2, NPV at 12% is positive, Calculate the NPV again at a higher discount rate, Say 13%

Year	Annual Cash Flow ($)	Present Value factor at 13%	Present Value of Cash Flow ($)
1	0	0.88496	0.00
2	4,99,550	0.78315	3,91,220.93
3	5,66,500	0.69305	3,92,612.92
4	4,58,350	0.61332	2,81,114.64
5	4,12,000	0.54276	2,23,617.09
TOTAL			12,88,565.58

Net Present Value (NPV) = Present Value of annual cash inflows – Initial Investment

= $12,88,565.58 - $13,10,000

= -$21,434.42 (Negative NPV)

Therefore IRR = R1 + NPV1(R2-R1)

                                   NPV1-NPV2

= 0.12 + [$16,531.21 x (0.13 – 0.12)]

              $16,531.21 – (-$21,434.42)

= 0.12 + 0.0044

= 0.1244

= 12.44%

“Therefore, the Internal Rate of Return (IRR) for the Project = 12.44%”

NOTE

The Formula for calculating the Present Value Factor is [1/(1 + r)ⁿ], Where “r” is the Discount/Interest Rate and “n” is the number of years.