Question

Robert purchased a new copy machine for his business. The copy machine was purchased for $10,000 and is expected to generate the following cash flows for the next four years: Year 1:$3000, Year 2:5000, Year 3: 3600, Year 4: 1500. Assume the copy machine can be sold for $1800 at the end of year 4. Robert’s required rate of return is 5%. What is the net present value and should the machine be purchased? What is the internal rate of return?

Answer 1

Net Present Value (NPV)

Year	Annual Cash Flow ($)	Present Value factor at 5%	Present Value of Cash Flow ($)
1	3,000	0.95238	2,857.14
2	5,000	0.90703	4,535.15
3	3,600	0.86384	3,109.82
4	3,300 [1,500 + 1,800]	0.82270	2,714.92
TOTAL			13,217.02

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

= $13,217.02 - $10,000

= $3,217.02

DECISION

“YES”. The Machine should be purchased, since the Net Present Value (NPV) of the Machine is Positive $3,217.02

Internal Rate of Return (IRR)

Step – 1, Firstly calculate NPV at a guessed discount Rate, Say 18%

Year	Annual Cash Flow ($)	Present Value factor at 18%	Present Value of Cash Flow ($)
1	3,000	0.84746	2,542.37
2	5,000	0.71818	3,590.92
3	3,600	0.60863	2,191.07
4	3,300 [1,500 + 1,800]	0.51579	1,702.10
TOTAL			10,026.47

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

= $10,026.47 - $10,000

= $26.47

Step – 2, NPV at 18% is positive, Calculate the NPV again at a higher discount rate, Say 19%

Year	Annual Cash Flow ($)	Present Value factor at 19%	Present Value of Cash Flow ($)
1	3,000	0.84034	2,521.01
2	5,000	0.70616	3,530.82
3	3,600	0.59342	2,136.30
4	3,300 [1,500 + 1,800]	0.49867	1,645.61
TOTAL			9,833.74

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

= $9,833.74 - $10,000

= -$166.26 (Negative NPV)

Therefore IRR = R1 + NPV1(R2-R1)

                                   NPV1-NPV2

= 0.18 + [$26.47 x (0.19 – 0.18)]

              $26.47 – (-$166.26)

= 0.18 + 0.0014

= 0.1814

= 18.14%

“Therefore, the Internal Rate of Return (IRR) = 18.14%”

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.