Internal Rate of Return (IRR)
DISCOUNT RATE @ 24%
IRR is the discount rate that generates zero NPV.
Increasing the discount rate will lower the NPV.
To generate negative NPV, we have to increase the discount rate.
Let this discount rate or cost of capital to be 24%.
Using discount rate of 24%, the values are as follow:
Initial Investment 160,000
Cash flows of constant 55,000 for year 1 to year 5.
Given that the discount rate or required rate of return is 24%
Total Present Value 150,996.15 #
Total Investment (160,000)
Net Present Value -9,003.85
CALCULATION
IRR
= DISCOUNT RATE for positive NPV + [DISCOUNT RATE DIFFERENCE x (Positive NPV / (Positive NPV - Negative NPV)]
= [18% + (24% - 18%) {11,994/(11,994-(-9,003.85)}] x 100%
= 18% + 3.4%
= 21.4%
As the cost of capital for this project is 21.4% and the firm will only receive 18% for each dollar invested, the company should not accept this project.
# Note: The total present value can be calculated thus
CF1/[(1+r)^1] + CF2/[(1+r)^2] + CF3/[(1+r)^3] + .... CF3/[(1+r)^n]
- is the discount rate that generates a zero net present value for a series of future cash flows
- it equates the present value of the future net cash flows from an investment project with the initial cash outflow of the project
- it is calculated by employing trial and error method
- a higher cost of capital lowers the value of NPV and vice versa
- it takes into account the concept of time value of money
- project with IRR more than the required rate of return is considered as acceptable and profitable.
IRR > Required rate of return, accept the project
IRR < Required rate of return, reject the project
IRR = DISCOUNT RATE for positive NPV + [DISCOUNT RATE DIFFERENCE x (Positive NPV / (Positive NPV - Negative NPV)]
Example:
DISCOUNT RATE @ 18%
Initial Investment 160,000
Cash flows of constant 55,000 for year 1 to year 5.
Given that the discount rate or required rate of return is 18%.
Total Present Value 171,994.41 #
Total Investment (160,000)
Net Present Value 11,994.41
Example:
DISCOUNT RATE @ 18%
Initial Investment 160,000
Cash flows of constant 55,000 for year 1 to year 5.
Given that the discount rate or required rate of return is 18%.
Total Present Value 171,994.41 #
Total Investment (160,000)
Net Present Value 11,994.41
DISCOUNT RATE @ 24%
IRR is the discount rate that generates zero NPV.
Increasing the discount rate will lower the NPV.
To generate negative NPV, we have to increase the discount rate.
Let this discount rate or cost of capital to be 24%.
Using discount rate of 24%, the values are as follow:
Initial Investment 160,000
Cash flows of constant 55,000 for year 1 to year 5.
Given that the discount rate or required rate of return is 24%
Total Present Value 150,996.15 #
Total Investment (160,000)
Net Present Value -9,003.85
CALCULATION
IRR
= DISCOUNT RATE for positive NPV + [DISCOUNT RATE DIFFERENCE x (Positive NPV / (Positive NPV - Negative NPV)]
= [18% + (24% - 18%) {11,994/(11,994-(-9,003.85)}] x 100%
= 18% + 3.4%
= 21.4%
As the cost of capital for this project is 21.4% and the firm will only receive 18% for each dollar invested, the company should not accept this project.
# Note: The total present value can be calculated thus
CF1/[(1+r)^1] + CF2/[(1+r)^2] + CF3/[(1+r)^3] + .... CF3/[(1+r)^n]
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