Investment and capital project decisions
Is this project worth it: payback, net present value (NPV), and internal rate of return (IRR), compared with the cost of capital and the alternatives.
Key takeaways
- Compute payback, then NPV at the cost of capital, then compare the return with the alternatives and the risk, rather than approving any project that makes money on paper.
- Investment cases reward clean arithmetic and an explicit comparison with alternatives.
- The strong answer judges the project fully and in context. The weak one reacts to one undiscounted number.
What this case type is and when it shows up
An investment case asks whether to spend money on a project: a new machine, a new plant, a new system. It is judged on what goes in, what comes back, how fast, and how that compares with the risk and with other uses of the money.
The underlying theory, in plain language
Payback is how long it takes to earn back the cost. It is quick and easy to explain, but it ignores everything after the payback year and the time value of money.
Net present value (NPV) fixes both. Money in later years is worth less than money today, because today's money could be invested. Divide each future year's cash by (1 plus the discount rate) once for each year of waiting, add the results, and subtract the cost. The discount rate is usually the company's cost of capital, the return its investors and lenders expect. A positive NPV means the project earns more than the cost of capital and adds value.
Internal rate of return (IRR) is the discount rate at which NPV equals zero. If the IRR is above the cost of capital, the project adds value. In interviews, you can bracket it: try two rates and see where NPV changes sign. Return on investment (ROI) is the net gain divided by the cost; be clear whether you mean the net gain or the total cash back.
Always include the alternatives, including doing nothing. A project with a good return may still lose to a better use of the same money.
What the prompts sound like, from simple to hard
- Simple: should a Singapore warehouse buy a machine that saves money.
- Medium: build a new plant in India or upgrade the old one.
- Hard: pick among several projects with one budget.
Finding and narrowing the real problem
Key idea
Compute payback, then NPV at the cost of capital, then compare the return with the alternatives and the risk, rather than approving any project that makes money on paper.
Frameworks for this type, each as a thinking tool with its limit
- Payback: Cost divided by yearly cash, for a quick first check. Limit: Ignores the time value of money and any cash after payback.
- NPV and IRR: Discount future cash at the cost of capital; find the rate at which NPV is zero. Limit: Only as good as the cash forecasts and the discount rate.
- Compare with alternatives: Rank the project against other uses of the money and against doing nothing. Limit: Requires honest estimates for each alternative.
Methods for solving this type
- Estimate the spend and the yearly cash effect, after running costs
- Compute payback
- Compute NPV at the cost of capital
- Bracket the IRR
- Compare with alternatives and recommend
The math patterns it relies on
- Payback = cost / yearly cash
- Present value = cash / (1 + rate) for each year of waiting
- NPV = sum of present values minus cost
- IRR: the rate at which NPV is zero
Worked cases
Worked case
A sorting machine for a Singapore warehouse
The prompt
A Singapore logistics company can buy a warehouse sorting machine for SGD 240,000. It would cut costs by SGD 80,000 a year for six years, with no value at the end. The company's cost of capital is 10 percent a year. The table below compares the machine with the other use of the same budget. Is it worth buying?
Interviewer-led: the interviewer shows the two options and asks for payback, then NPV, then the IRR, and then which option to fund.
Clarifying questions, with the interviewer's answers
- Are the savings after running costs such as maintenance and power?Answer: Yes, they are net savings.
- What else could the money be used for?Answer: A software upgrade with an expected return of about 15 percent a year.
- Does the machine have any value at the end?Answer: No.
A hypothesis to say out loud: A three-year payback on a six-year machine looks healthy. My hypothesis is that it clears the 10 percent cost of capital comfortably, and that the real question is whether it beats the 15 percent software alternative.
The structure
- Payback, NPV, and IRR versus the alternatives
- Payback
- Key: NPV at the 10 percent cost of capital
- IRR versus the 15 percent alternative
The exhibit
| Option | Upfront cost (SGD) | Yearly benefit | Life (years) |
|---|---|---|---|
| Sorting machine | 240,000 | SGD 80,000 of net savings a year, no value at the end | 6 |
| Software upgrade | 240,000 | About 15 percent return a year | Not stated |
Working it through
1. Payback
SGD 240,000 against SGD 80,000 saved a year.
Payback (years):240,000 ÷ 80,000 = 32. Savings before discounting
SGD 80,000 a year for six years, twice the cost. This is a 2 times cash multiple (a 100 percent net gain), but it ignores the time value of money.
Undiscounted savings (SGD):80,000 × 6 = 480,0003. Present value at 10 percent
Divide each year's saving by 1.1 once per year of waiting (1.21 is 1.1 x 1.1, and so on).
Present value of savings (SGD):80,000 ÷ 1.1 + 80,000 ÷ 1.21 + 80,000 ÷ 1.331 + 80,000 ÷ 1.4641 + 80,000 ÷ 1.61051 + 80,000 ÷ 1.771561 = 348,4214. NPV
Present value of savings minus the cost.
NPV at 10 percent (SGD):348,420.86 - 240,000 = 108,4215. Bracket the IRR: try 24 percent
At 24 percent the savings are still worth slightly more than the SGD 240,000 cost.
Present value at 24 percent (SGD):80,000 ÷ 1.24 + 80,000 ÷ (1.24 × 1.24) + 80,000 ÷ (1.24 × 1.24 × 1.24) + 80,000 ÷ (1.24 × 1.24 × 1.24 × 1.24) + 80,000 ÷ (1.24 × 1.24 × 1.24 × 1.24 × 1.24) + 80,000 ÷ (1.24 × 1.24 × 1.24 × 1.24 × 1.24 × 1.24) = 241,6386. Bracket the IRR: try 25 percent
At 25 percent they are worth slightly less than the cost, so the IRR is about 24 percent.
Present value at 25 percent (SGD):80,000 ÷ 1.25 + 80,000 ÷ (1.25 × 1.25) + 80,000 ÷ (1.25 × 1.25 × 1.25) + 80,000 ÷ (1.25 × 1.25 × 1.25 × 1.25) + 80,000 ÷ (1.25 × 1.25 × 1.25 × 1.25 × 1.25) + 80,000 ÷ (1.25 × 1.25 × 1.25 × 1.25 × 1.25 × 1.25) = 236,114
What the exhibit shows
Both options use the same budget, so the machine must beat the software upgrade's 15 percent, not only the 10 percent cost of capital.
The recommendation
I recommend buying the machine. First, it pays back in three years, and its savings are worth about SGD 348,000 in today's money against a cost of SGD 240,000, an NPV of about SGD 108,000 at the 10 percent cost of capital. Second, its IRR is about 24 percent, above both the cost of capital and the 15 percent software alternative. Third, savings could fall by about 30 percent before the NPV reaches zero. Confirm the savings at a reference site before signing.
Risks: Savings may be lower if volumes fall; Maintenance costs may rise in later years.
Next steps: Visit a reference site using the same machine; Negotiate a performance guarantee with the supplier.
A strong candidate
Computed payback, NPV, and a bracketed IRR, and compared the return with both the cost of capital and the alternative.
A weak candidate
Said yes because it "saves 80,000 a year" and "doubles the money," without discounting or comparing.
Worked case
Electric or diesel vans for a UK parcel company
The prompt
A UK parcel company must replace 100 delivery vans this year. Should it buy electric vans instead of diesel ones?
Candidate-led: you set up the comparison, ask for costs, and choose the measures; the interviewer answers and then tests your answer with a change.
Clarifying questions, with the interviewer's answers
- Are we comparing a new electric van with a new diesel van, or with keeping the old vans?Answer: With a new diesel van; the old vans must be replaced this year anyway.
- What cost of capital should I use?Answer: 8 percent a year.
- How long do the vans last?Answer: About six years for both types, with little value at the end.
A hypothesis to say out loud: Electric vans cost more to buy but less to run. My hypothesis is that the running-cost saving pays back the extra price within the van's life, and that the answer is most sensitive to the price of electricity.
The structure
- Extra upfront cost versus running-cost savings, in today's money
- Extra upfront cost per van, including charging
- Yearly saving per van: fuel and maintenance
- Key: Payback and NPV at 8 percent
- Sensitivity: electricity price
Working it through
1. Extra upfront cost
Candidate: "What do the two vans cost?" Interviewer: "Electric GBP 45,000, diesel GBP 30,000, plus about GBP 3,000 per van for depot chargers."
Extra upfront cost per electric van (GBP):45,000 - 30,000 + 3,000 = 18,0002. Yearly saving
Candidate: "And running costs?" Interviewer: "Diesel costs about GBP 6,000 a year per van, electricity about GBP 2,000, and electric vans save about GBP 1,000 a year in maintenance."
Yearly saving per van (GBP):(6,000 - 2,000) + 1,000 = 5,0003. Payback
The extra cost divided by the yearly saving: inside the six-year life, but not by much.
Payback (years):18,000 ÷ 5,000 = 3.64. Savings in today's money
Discount six years of GBP 5,000 at 8 percent (1.1664 is 1.08 x 1.08, and so on). Six years of savings are worth about 4.62 years of savings today.
Present value of savings per van (GBP):5,000 ÷ 1.08 + 5,000 ÷ 1.1664 + 5,000 ÷ 1.259712 + 5,000 ÷ 1.360489 + 5,000 ÷ 1.469328 + 5,000 ÷ 1.586874 = 23,1145. NPV per van and for the fleet
Present value of savings minus the extra upfront cost, then times 100 vans.
Fleet NPV (GBP):100 × (5,000 × 4.62288 - 18,000) = 511,4406. Test: electricity price rises by half
Interviewer: "What if electricity prices rise 50 percent?" Candidate: "Electricity would cost GBP 3,000 a van, so the yearly saving falls to GBP 4,000, and the NPV per van almost disappears."
NPV per van if electricity rises 50 percent (GBP):4,000 × 4.62288 - 18,000 = 492
The recommendation
Buy electric vans, but in phases and with electricity costs fixed where possible. First, each electric van costs GBP 18,000 more including charging but saves about GBP 5,000 a year, a payback of 3.6 years within a six-year life. Second, at an 8 percent cost of capital each van adds about GBP 5,100 of value in today's money, about GBP 511,000 for the fleet. Third, the answer depends on electricity prices: if they rise by half, the value per van almost disappears, so agree a fixed-price electricity contract for the depot before committing the whole fleet. Start with the 40 vans on the shortest urban routes, where range is not a concern.
Risks: Electricity prices may rise more than expected; Battery life may be shorter than six years on long routes; Depot power supply may need an upgrade that costs more than GBP 3,000 a van.
Next steps: Get quotes for a fixed-price electricity contract; Ask the local power network whether the depot can take 100 chargers; Run 10 electric vans for three months and measure real running costs.
A strong candidate
Compared the right alternative (a new diesel van, not the old one), computed payback and NPV, and tested the one assumption that could flip the answer.
A weak candidate
Added six years of undiscounted savings, GBP 30,000 against GBP 18,000, and called it a clear win without discounting or testing electricity prices.
Prompt: "Should we buy this machine?"
Weaker answer
Says yes because it "saves 80,000 a year" and "doubles the money," without discounting, IRR, or alternatives.
Stronger answer
Finds a three-year payback, an NPV of about SGD 108,000 at 10 percent, and an IRR of about 24 percent, then shows it beats the 15 percent alternative as well as the 10 percent cost of capital.
Why the stronger answer wins: The strong answer judges the project fully and in context. The weak one reacts to one undiscounted number.
Common mistakes, traps, and curveballs
- Adding up future cash without discounting it
- Approving any project with a positive return, ignoring the alternatives
- Forgetting running costs such as maintenance and power
- Treating risky and safe returns as equal
- Mixing up a cash multiple (2 times) with a return (100 percent)
Investment cases reward clean arithmetic and an explicit comparison with alternatives. Interviewers may add a second project to force a real choice under one budget. Formats differ by office and change over time, so check the current process for your target office.
Practice
What is EUR 1,210 received in two years worth today, at 10 percent a year?
A solar installation for a factory in the UAE costs AED 900,000 and saves AED 150,000 a year in power. What is the payback, in years?
What is GBP 1,000 received in three years worth today, at 5 percent a year?
Two projects cost the same. A has an NPV of +50 and a payback of 5 years; B has an NPV of +20 and a payback of 2 years. Cash is not tight. Which adds more value?
A project's NPV is positive at an 8 percent discount rate and negative at 12 percent. What do you know about its IRR?
An electric van costs more than a diesel van. Which comparison is correct?
Discount future cash at the cost of capital: a project is worth doing if its NPV is positive and it beats the other uses of the money.
Sources for this lesson (1)
- Recognized public explanations of case-interview concepts and frameworks
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