Question21 MIRR: A project has cash flows {−2,000 at t = 0; +900 at t = 1, 2, 3}. With a financeand reinvestment rate of 10%, the MIRR is ≈ ?Select one alternative: 10.0% 16.6% 14.2% 12.5% ResetMaximum marks: 4 Flag question undefined单项选择题
A
10.0%
B
16.6%
C
14.2%
D
12.5%

Question

Question21 MIRR: A project has cash flows {−2,000 at t = 0; +900 at t = 1, 2, 3}. With a financeand reinvestment rate of 10%, the MIRR is ≈ ?Select one alternative: 10.0% 16.6% 14.2% 12.5% ResetMaximum marks: 4 Flag question undefined单项选择题

A

10.0%

B

16.6%

C

14.2%

D

12.5%

BlackTom AI · Accepted Answer

MIRR treats negative and positive cash flows differently: you finance (or discount) outflows at the finance rate and reinvest inflows at the reinvestment rate, then find the single rate that grows the invested capital to the terminal value. With equal finance and reinvestment rates the standard MIRR formula applies.

1. Relevant concepts
- Modified Internal Rate of Return (MIRR) = (FV of positive cash flows at end / PV of negative cash flows at start)^(1/n) − 1.
- Here n = project life in years = 3. Finance rate = reinvestment rate = 10%.

2. Step-by-step reasoning and intermediate calculations
- Initial outflow at t = 0: 2,000 (PV of negatives = 2,000).
- Positive cash flows: 900 at t=1, 900 at t=2, 900 at t=3. Compound each to t=3 at 10%:

- t=1 cash flow to t=3: 900 × (1.10)^(3−1) = 900 × (1.10)^2 = 900 × 1.21 = 1,089
  - t=2 cash flow to t=3: 900 × (1.10)^(3−2) = 900 × 1.10 = 990
  - t=3 cash flow to t=3: 900 × (1.10)^0 = 900

- Sum the terminal values: FV = 1,089 + 990 + 900 = 2,979.

- Apply MIRR formula:
  MIRR = (FV / PV_negatives)^(1/n) − 1
  = (2,979 / 2,000)^(1/3) − 1
  = (1.4895)^(1/3) − 1
  ≈ 1.1423 − 1
  ≈ 0.1423 = 14.23%

3. Why this answer is correct
- The calculation explicitly compounds each positive cash flow to the same terminal date using the given 10% reinvestment rate, compares that terminal sum to the initial investment, and finds the annualized rate that equates them over 3 years. The numeric cube root yields ≈14.2%.

4. Why other choices are incorrect
- 10.0% would imply no net growth beyond reinvestment matching financing exactly (not the case: inflows compound to a terminal value larger than 2,000).
- 12.5% and 16.6% do not satisfy (2,979/2,000)^(1/3) − 1; 12.5% is too low and 16.6% too high compared with the computed 14.23%.