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Best of P and Q for 5-year study period

Short answer

Calculate present worth over the 5-year study: PW(P) = Rs. 289,203, PW(Q) = Rs. 335,120. Incremental IRR of P over Q is about -2.1% below 10% MARR. Project Q is best.

Select the best project. Required study period is 5 years.

Project PProject Q
Initial Investment (Rs.)5,00,0003,50,000
Annual net revenue (Rs.)2,00,0001,75,000
Salvage value (Rs.)50,00035,000
Useful life (Years)65
MARR10%10%

Study period = 5 years, MARR = 10%.

Assumptions

  • Project Q has a life equal to the study period (5 years): salvage Rs. 35,000 is received at year 5.
  • Project P has a life of 6 years but is needed for 5 years only. It is sold at the end of year 5; as no other market value is given, take the stated salvage (Rs. 50,000) as the year-5 market value.

Cash-flow diagram (Rs., '000)

P:  200   200   200   200   200+50
     |     |     |     |      |
 0 --1-----2-----3-----4------5--> year
 v 500
Q:  175   175   175   175   175+35
     |     |     |     |      |
 0 --1-----2-----3-----4------5--> year
 v 350

Present worth

(P/A, 10%, 5) = 3.7908, (P/F, 10%, 5) = 0.6209

PW(P) = -500,000 + 200,000(3.7908) + 50,000(0.6209) = -500,000 + 758,157 + 31,046 = Rs. 289,203

PW(Q) = -350,000 + 175,000(3.7908) + 35,000(0.6209) = -350,000 + 663,388 + 21,732 = Rs. 335,120

Check by incremental IRR (P over Q)

Extra investment 150,000, extra net revenue 25,000 per year, extra salvage 15,000 at year 5. PW of increment at 10% = -150,000 + 25,000(3.7908) + 15,000(0.6209) = -45,917 < 0 Incremental IRR ≈ -2.1% < 10%, so the extra investment in P is not justified.

ProjectIRRPW at 10%
P30.1%289,203
Q42.1%335,120

Answer: Select Project Q (higher PW, Rs. 335,120, and the extra investment in P earns less than MARR).

✓ Answer checked by Claude Opus 5.5 (high effort)

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