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Internal Rate of Return (IRR)

Prerequisites

Before studying this chapter, make sure you understand:

1. Definition

The Internal Rate of Return (IRR) is the discount rate that makes the Net Present Value (NPV) of a project equal to Zero.

It represents the actual percentage return earned by the invested money.

Decision Rule:

  • Accept: If IRR > Cost of Capital (K)
  • Reject: If IRR < Cost of Capital (K)
  • Indifferent: If IRR = Cost of Capital (K)

2. Why "Internal"?

It is called "Internal" because it depends only on the cash flows of the project itself, not on external rates like bank interest rates.

3. Calculation Method (Interpolation)

Since there is no direct formula to find IRR for uneven cash flows, we use a Trial and Error approach with Interpolation.

Concept: We need to find a rate where NPV is 0.

  1. Try a "Lower Rate" (gives Positive NPV).
  2. Try a "Higher Rate" (gives Negative NPV).
  3. The actual IRR lies somewhere in between.

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4. Numerical Problem

Problem: Initial Investment: ₹1,00,000. Cash Inflows:

  • Year 1: ₹30,000
  • Year 2: ₹30,000
  • Year 3: ₹40,000
  • Year 4: ₹45,000

Find IRR.

Solution:

Trial 1: Let's try 15% Discount Rate

  • PV Factors @ 15%: 0.870, 0.756, 0.658, 0.572
  • Total PV = (30k×0.87) + (30k×0.756) + (40k×0.658) + (45k×0.572)
  • Total PV = 26,100 + 22,680 + 26,320 + 25,740 = ₹1,00,840
  • NPV @ 15% = 1,00,840 - 1,00,000 = +840
  • (Positive NPV means rate is too low. We need higher rate to reduce PV)

Trial 2: Let's try 16% Discount Rate

  • PV Factors @ 16%: 0.862, 0.743, 0.641, 0.552
  • Total PV = (30k×0.862) + (30k×0.743) + (40k×0.641) + (45k×0.552)
  • Total PV = 25,860 + 22,290 + 25,640 + 24,840 = ₹98,630
  • NPV @ 16% = 98,630 - 1,00,000 = -1,370
  • (Negative NPV means rate is too high)

Interpolation Formula: IRR is between 15% and 16%.

IRR = 15 + [ 840 / (840 - (-1370)) ] × (16 - 15)
IRR = 15 + [ 840 / (840 + 1370) ] × 1
IRR = 15 + [ 840 / 2210 ]
IRR = 15 + 0.38
IRR = 15.38%

Answer: IRR is 15.38%.

5. NPV vs IRR Comparison

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Exam Pattern Questions and Answers

Question 1: "Define Internal Rate of Return." (2 Marks) Answer: Internal Rate of Return (IRR) is that discount rate which equates the present value of cash inflows with the initial investment, resulting in a Net Present Value (NPV) of zero.

Question 2: "Calculate IRR if Investment is ₹100 and Year 1 inflow is ₹110." (2 Marks) Solution: We need rate 'r' where: 100 = 110 / (1+r) 1+r = 1.10 r = 0.10 or 10% Answer: IRR is 10%.

Quiz Time! 🎯

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