Question 2 OR
NPV, IRR and the ranking conflict of two mutually exclusive projects
15 marks
- Time to write
- About 30 minutes
From an older CBCS paper
Question
Question 2 OR · 15 marksDEF ltd is weighing two mutually exclusive projects. The after-tax cash flows of these projects are given below:
| Project I | Project II | |
|---|---|---|
| Initial Investment | ₹2,50,000 | ₹2,50,000 |
| Expected Cash flows at the end of | ||
| Year 1 | ₹ 80,000 | 0 |
| Year 2 | ₹ 80,000 | 0 |
| Year 3 | ₹ 80,000 | 0 |
| Year 4 | ₹ 80,000 | 0 |
| Year 5 | ₹ 80,000 | ₹ 500,000 |
The required rate of return on these projects is 9%.
What is the net present value of each project?
What is the internal rate of return of each project?
What has given rise to the ranking conflict?
Which project should be accepted? Why?
Reworded from the university paper: names and figures differ, the task is the same. The original paper belongs to the University of Delhi. See DU's question bank.
Before you write
Read off the question and its marks
Read from the question
- What is the…?What…?Which…?4 asks, each with its own marks below. Answer all 4. Where it asks why, give reasons, not a description.
- net present valueCash flows year by year in one table, then discount, then a one-line decision.
What the paper leaves open
Project II's year-5 amount is printed in Western grouping (₹ 500,000 here); every amount is read as rupees received at the end of the year shown. The "ranking conflict" in (iii) is read as the NPV and IRR rankings disagreeing.
Write it in this order
A step that gives the answer away stays hidden: tap it to see it.
- Read the data; note exactly what is asked 2 min
- 1 NPV of each project 4 marks 7 min
- 2 IRR of each project 5 marks 9 min
- 3 Cause of the ranking conflict: timing, reinvestment assumption, crossover rate 3 marks 5 min
- 4 Project to accept, with reasons 3 marks 5 min
- Check: arithmetic, units (₹, %), final answer underlined 2 min
Try it first. About 30 minutes for 15 marks. Write it out, then open the solution.
Solution
Hover or tap a marked figure, like 72,000, to see how it is made and where else it appears.
Data. Both projects cost ₹2,50,000 and run for 5 years. Project I returns ₹80,000 at the end of every year; Project II returns nothing until a single ₹5,00,000 at the end of year 5 (paper note). Required rate of return 9%. Standard 3-decimal table factors are used, as the question prints none: PVIFA(9%, 5 years) = 3.890 and PVIF(9%, year 5) = 0.650.
(i) Net present value. Each project's inflows are discounted at 9% and the initial investment is deducted.
| Particulars (₹) | Project I | Project II |
|---|---|---|
| Cash inflow | 80,000 a year (years 1–5) | 5,00,000 (year 5) |
| PV factor at 9% | 3.890 (annuity) | 0.650 |
| PV of inflows | 3,11,200 | 3,25,000 |
| Less: initial investment | 2,50,000 | 2,50,000 |
| NPV | 61,200 | 75,000 |
(ii) Internal rate of return. The IRR is the discount rate that makes a project's NPV zero.
- Project I (equal annual inflows). The annuity factor sought = 2,50,000 ÷ 80,000 = 3.125. In the 5-year annuity row it lies between 18% (3.127) and 19% (3.058): IRR = 18% + (3.127 − 3.125) ÷ (3.127 − 3.058) × 1% = 18% + 0.03% = 18.03%.
- Project II (one inflow). 2,50,000 = 5,00,000 ÷ (1 + r)^5, so (1 + r)^5 = 2 and r = 2^(1/5) − 1 = 14.87%. (Interpolating the 5th-year factors at 14%, 0.519, and 15%, 0.497, for the factor 0.500 gives about 14.86%.)
| Criterion | Project I | Project II | Higher |
|---|---|---|---|
| NPV (₹) | 61,200 | 75,000 | II |
| IRR | 18.03% | 14.87% | I |
(iii) What has given rise to the ranking conflict. The outlays are equal and the lives are equal, so neither a size difference nor a life difference explains it. The cause is the timing of the cash flows (time disparity): Project I gets its money back evenly from year 1, while Project II's whole return arrives at the end of year 5.
- Different reinvestment assumptions. NPV implicitly reinvests each intermediate inflow at the discount rate used, here 9%. The IRR method assumes they earn the project's own IRR, 18.03% for Project I, and that assumption favours projects whose cash comes early over those whose cash comes late.
- The crossover rate. A late-paying project loses value faster as the discount rate rises. The two NPV profiles cross at about 11.2%, the rate at which the incremental flows (II minus I: −₹80,000 in each of years 1–4 and +₹4,20,000 in year 5) have zero NPV. Below that rate NPV ranks Project II first; above it both methods rank Project I first. With the cost of capital at 9%, below the crossover, the two methods disagree.
| Discount rate | 0% | 9% | 11% | 12% | 15% |
|---|---|---|---|---|---|
| NPV of Project I (₹) | 1,50,000 | 61,200 | 45,680 | 38,400 | 18,160 |
| NPV of Project II (₹) | 2,50,000 | 75,000 | 46,500 | 33,500 | −1,500 |
(Table factors: 5-year annuity 3.696, 3.605 and 3.352, and year-5 factor 0.593, 0.567 and 0.497, at 11%, 12% and 15%.)
(iv) Which project should be accepted? Project II.
- The projects are mutually exclusive, so only one can be taken, and the NPV is the measure to rank them by: it is the project's contribution to the shareholders' wealth, so maximising it serves the firm's objective. Project II adds ₹75,000, which is ₹13,800 more than Project I. The highest-IRR project need not be the one that maximises wealth.
- The 9% reinvestment rate behind the NPV is the realistic one for this firm. Reinvested at 9%, Project I's five inflows grow to 80,000 × 5.985 (FVIFA 9%, 5 years) = ₹4,78,800 by the end of year 5, less than the ₹5,00,000 Project II delivers on the same outlay. Project I's 18.03% would be earned only if its inflows could be reinvested at 18.03%.
- The choice holds only while the required rate stays below the crossover rate of about 11.2%; at a higher required rate Project I would be preferred on both counts.
Where the 15 marks sit
| # | Component | Marks |
|---|---|---|
| 1 | NPV of each project | 4 |
| 2 | IRR of each project | 5 |
| 3 | Cause of the ranking conflict: timing, reinvestment assumption, crossover rate | 3 |
| 4 | Project to accept, with reasons | 3 |
| Total | 15 |
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