ENGINEERING ECONOMICS
LECTURE 6 PART 2
‫صافى القيمة الحالية‪2- Net present value (NPV) :‬‬
‫‪Net present value (NPV) is the difference between the present‬‬
‫‪value of cash inflows and the present value of cash outflows over a‬‬
‫‪period of time.‬‬
‫صافي القيمة الحالية ‪ :NPV‬هو الفرق بين القيمة الحالية للتدفقات النقدية والقيمة الحالية‬
‫للتدفقات النقدية الخارجة على مدى فترة زمنية‪.‬‬
‫التدفقات النقدية‬
‫الخارجة‬
‫التدفقات النقدية‬
‫الداخلة‬
‫‪cash inflows – cash out flows‬‬
‫صافى القيم‬
‫الحالية‬
‫= ‪NPV‬‬
Example 1:
A project with a 3-year life and a cost of 100,000 generates revenue
of 25,000 in year 1, 45,000 in year 2, and 65, 000 in year 3. If the
discount rate is 8%, what is the NPV of the project?
solution
year
Cash flow
DCF @8% ‫معامل الخصم‬
Present Value
0
1
(100,000)
25,000
1.0
0.9259
(100,000)
23,148.15
2
3
NPV
45,000
65,000
0.8573
0.7938
13,327.50
38,580.25
51,599.10
Net Present value (NPV) = 23,148.15+ 38,580.25+ 51,599.10 -100,000 = 13,327.50
NPV > zero
NPV is positive then project should be accepted.
Example2:
A project with a 4-year life and a cost of 225,000 generates revenue
of 48,000 in year 1, 67,000 in year 2, 95, 000 in year 3 and 110,000
in year 4. If the discount rate is 15%, Can be
accepted the project?
solution
DCF @15% ‫معامل الخصم‬
year
Cash flow
0
(225,000.00)
1.00
1
48,000.00
0.8696
2
67,000.00
0.7561
3
95,000.00
0.6575
4
110,000.00
0.5718
Present Value
(225,000.00)
41,739.13
50,661.63
62,464.04
62,892.86
(7,242.34)
NPV
Net Present value (NPV) = 41,739.13+ 50,661.63+ 62,464.04+ 62,892.8 -225,000.00 = - 7,242.34
NPV < zero
NPV is negative then project should be not accepted.
3- Internal Rate of Return (IRR):‫معدل العائد الداخلى‬
Internal Rate of Return is the interest rate that makes the Net Present Value Zero.
STEPS OF CALCULATION OF IRR
Step 1: Select 2 discount rates for the calculation of NPVs
You can start by selecting any 2 discount rates on a random basis that will be
used to calculate the net present values in Step 2.
It is important not to select discount rates that are ridiculously distant from the
IRR (e.g. 10% and 90%) as it could undermine accuracy.
Step 2: Calculate NPVs of the investment using the 2 discount rates
You shall now calculate the net present values of the investment on the basis of
each discount rate selected in Step 1.
Step 3: Calculate the IRR
Using the 2 discount rates from Step 1 and 2 calculate net present values . Then
you shall calculate the IRR
Step 4: Interpretation
Example:
if you want to invest 350,000 in a Hardware business. The cash inflows during the first,
second and third years are expected to be 125,000, 150,000 and 170,000 respectively.
Cost of capital is 11%
Calculate the IRR for the proposed investment and interpret your answer.
solution
Step 1 : Select 2 discount rates
R1 = 10% and R2 = 15%
Step 4 : Interpretation
The investment should be accepted because the cost of capital (11 %) is lower than the IRR of 12.44%