Question

NPV profile of a project. Given the following cash flow of Project​ L-2, draw the NPV profile. Hint​: Be sure to use a discount rate of zero for one intercept ​(y​-axis) and solve for the IRR for the other intercept ​(x​-axis).

Year 0   -$250,000
Year 1   $49,000
Year 2   $80,000
Year 3   $114,000
Year 4   $139,000

What is the NPV of Project​ L-2 where zero is the discount​ rate?

What is the IRR of Project​ L-2?

Which of the graphs below best fits the NPV profile of the​ project?

Answer 1

(a)-Net Present Value (NPV) of Project L-2 where zero is the discount rate

If the Discount Rate is Zero, the NPV of the Project is the sum of the Future cash flows deducted by Initial Investment

Net Present Value (NPV) = Sum of future cash flow – initial Investment

= [$49,000 + $80,000 + $114,000 + $139,000] - $250,000

= $382,000 - $250,000

= $132,000

“Hence, the Net Present Value (NPV) of the Project L-2 at Zero Discount rate = $132,000”

(b)-Internal Rate of Return (IRR) of Project​ L-2

Step – 1, Firstly calculate NPV at a guessed discount Rate, Say 16% (R1)

Year	Annual Cash Flow ($)	Present Value factor at 16%	Present Value of Cash Flow ($)
1	49,000	0.86207	42,241
2	80,000	0.74316	59,453
3	1,14,000	0.64066	73,035
4	1,39,000	0.55229	76,768
TOTAL			251,498

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

= $251,498 - $250,000

= $1,498

Step – 2, NPV at 16% is positive, Calculate the NPV again at a higher discount rate, Say 17% (R2)

Year	Annual Cash Flow ($)	Present Value factor at 17%	Present Value of Cash Flow ($)
1	49,000	0.85470	41,880
2	80,000	0.73051	58,441
3	1,14,000	0.62437	71,178
4	1,39,000	0.53365	74,177
TOTAL			245,677

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

= $245,677 - $250,000

= -$4,323 (Negative NPV)

Therefore IRR = R1 + NPV1(R2-R1)

                                   NPV1-NPV2

= 0.16 + [$1,498 x (0.17 – 0.16)]

              $1,498 – (-$4,323)

= 0.16 + [$14.98 / $5,821]

= 0.16 + 0.0026

= 0.1626 or

= 16.26%

“Hence, the Internal Rate of Return (IRR) of Project L-2 would be 16.26%”

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.