How to Calculate Internal Rate of Return (IRR) with Example & Decision Rule

How to Calculate Internal Rate of Return (IRR) with Example & Decision Rule

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Question:

A project has an initial cost of $1000 and generates the following cash flows over five years:

Year	Cash Flow ($)
1	200
2	300
3	300
4	400
5	500

Compute the Internal Rate of Return (IRR) for this project. If the opportunity cost of capital is 12%, should the project be accepted?

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Explanation & Steps to Compute IRR

Step	Description
Step 1	Assume K (discount rate) = 12% and compute the Net Present Value (NPV).
Step 2	If NPV < 0, the project is not financially viable at 12%.
Step 3	If NPV > 0, the project is viable, but we need to find the exact IRR by adjusting K until NPV ≈ 0.
Step 4	The discount rate at which NPV = 0 is the Internal Rate of Return (IRR).

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NPV Calculation at 12% Discount Rate

Year	Cash Flow (FV)	Discount Factor (1+K)^n	Present Value (PV)
1	200	1.12^1 = 1.12	178.57
2	300	1.12^2 = 1.2544	239.16
3	300	1.12^3 = 1.4049	213.53
4	400	1.12^4 = 1.5735	254.21
5	500	1.12^5 = 1.7623	283.71
Total PV of inflows	1169.18
Initial Investment	1000
NPV	+169.18		Positive

🔹 Since NPV > 0, the project is financially viable at 12%, but we need to determine the exact IRR.

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Finding IRR (Where NPV = 0)

Year	Cash Flow (FV)	Discount Factor (1+K)^n (K = 17.7%)	Present Value (PV)
1	200	1.177	169.92
2	300	1.3853	216.56
3	300	1.6305	183.99
4	400	1.9191	208.43
5	500	2.2588	221.35
Total PV of inflows	1000.25
Initial Investment	1000
NPV	≈ 0

🔹 IRR = 17.7%, since NPV becomes zero at this rate.

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Decision Rule

Condition	Decision
IRR > Discount Rate (12%)	✅ Accept the project
IRR < Discount Rate (12%)	❌ Reject the project

Since IRR (17.7%) > Cost of Capital (12%), the project should be accepted.

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