Define IRR; find IRR and ERR of project

IRR

The internal rate of return (IRR) is the interest rate i* at which the PW (or FW, AW) of the net cash flow of a project is zero, i.e. PW of inflows = PW of outflows. A project is accepted if IRR ≥ MARR.

Numerical

Assumption: the table shows no cash flow at year 2, so it is taken as zero. Amounts are in the same unit as printed (say Rs thousand).

 Year :  0    1    2    3    4    5
 CF   : -50  -10   0   +30  +40  +50

IRR (trial and error): PW(i) = −50 − 10(P/F, i, 1) + 30(P/F, i, 3) + 40(P/F, i, 4) + 50(P/F, i, 5)

Interpolating between 18% and 20%: IRR = 18 + 2 × 2.271/(2.271 − (-1.588)) ≈ 19.2%.

IRR ≈ 19.16% > MARR 15%.

ERR (external rate of return) with ε = 15%, N = 5:

• PW of outflows at ε: 50 + 10 (P/F, 15%, 1) = 50 + 10 × 0.8696 = 58.696
• FW of inflows at ε (year 5): 30 (F/P, 15%, 2) + 40 (F/P, 15%, 1) + 50 = 30 × 1.3225 + 40 × 1.15 + 50 = 135.675
• (1 + ERR)^5 = 135.675 / 58.696 = 2.3115
• ERR = (2.3115)^(1/5) − 1 = 18.24%

Answer: IRR ≈ 19.2%, ERR ≈ 18.2%. Both exceed MARR = 15%, so the project is acceptable. ERR is lower than IRR because the inflows are reinvested at 15%, not at the IRR.