- 2072 Asoj · 6 marks
IRR with investment balance diagram
Short answer
IRR ≈ 20.9% is found by trial and error. The investment balance diagram shows the unrecovered investment remains negative throughout and reaches zero at year 5, confirming the project earns that rate on the outstanding balance.
Calculate IRR from the following cash flow and draw investment balance diagram.
| Year | 0 | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|---|
| Cash Flow | -800 | 250 | 300 | 400 | -150 | 600 |
Cash flow
Year : 0 1 2 3 4 5
CF : -800 +250 +300 +400 -150 +600
There are three sign changes (− + + + − +), so more than one IRR is possible in theory; only one is positive and meaningful here (checked by scanning PW over 0 to 300%).
IRR by trial and error
PW(i) = −800 + 250(P/F,i,1) + 300(P/F,i,2) + 400(P/F,i,3) − 150(P/F,i,4) + 600(P/F,i,5)
| i | PW(i) |
|---|---|
| 10% | 245.83 |
| 20% | 16.94 |
| 21% | -1.34 |
| 22% | -18.95 |
| 20.93% | 0.00 |
Interpolation between 20% and 21%: IRR = 20 + 1 × 16.94/(16.94 − (-1.34)) ≈ 20.93%.
IRR ≈ 20.93%
Investment balance diagram
Unrecovered investment at end of year t: B_t = B_(t−1)(1 + i) + CF_t, with i = 20.93%. The balance must reach exactly zero at year 5.
| Year | B_(t−1)(1+i) | CF | B_t |
|---|---|---|---|
| 1 | -967.4 | +250 | -717.4 |
| 2 | -867.5 | +300 | -567.5 |
| 3 | -686.3 | +400 | -286.3 |
| 4 | -346.2 | -150 | -496.2 |
| 5 | -600.0 | +600 | 0.0 |
Unrecovered balance (each # = about 40)
yr0: -800.0 |-####################
yr1: -717.4 |-##################
yr2: -567.5 |-##############
yr3: -286.3 |-#######
yr4: -496.2 |-############
yr5: 0.0 |0
The balance stays negative (investment not yet recovered) until the end of year 5, rising from −800 to −286.3 in year 3, falling back to −496.2 in year 4 because of the −150 outflow, and reaching 0 at year 5. This confirms the IRR of 20.93%: the project recovers the capital and earns exactly 20.93% on the unrecovered balance.
Answer: IRR ≈ 20.9% (accept if MARR is lower).
✓ Answer checked by Claude Opus 5.5 (high effort)
Related questions
- AW sensitivity to investment and net annual cash flow · Engineering Economics, chapter 6
- IRR with varying benefit and O&M; unrecovered balance · Engineering Economics, chapter 3
- IRR with unrecovered balance, graphical and tabular · Engineering Economics, chapter 3
- Socialistic economy and cash flow diagram · Engineering Economics, chapter 1
- IRR by trial and error; investment decision · Engineering Economics, chapter 3
- IRR choose best of four, 10-year study · Engineering Economics, chapter 4
- Laplace: 3x3 grid 400/800/600/1200 · Numerical Method, chapter 7 · asked 6×
- Corner stresses of 400 x 800 column (250 kN) · Concrete Technology and Masonry Structure, chapter 8 · asked 7×
- Three-point problem: A 800 m N, C 400 m W (500, 100, 300) · Engineering Geology I, chapter 5 · asked 4×
- Three-point problem: A 600 m N, C 400 m W (400, 100, 300) · Engineering Geology I, chapter 5 · asked 4×