Judging an investment: payback, ROI, and present value
Payback, return on investment, net present value, and the perpetuity shortcut cases often use.
Key takeaways
- Perpetuity shortcut: a cash flow that continues every year with no end is worth the yearly amount divided by the discount rate.
- Payback period: how long until the investment earns back its cost. Spend INR 10 lakh on a machine that saves INR 2.5 lakh a year, and the payback is 4 years.
- Return on investment (ROI): the gain compared with the cost. Put in 1,000, get 1,200 back, and the ROI is 20 percent.
- Net present value (NPV): the value today of all future cash, minus what you invest today.
Many cases end with an investment question: should the client spend money now to earn or save money later? Three tools cover most cases.
The three tools
- Payback period: how long until the investment earns back its cost. Spend INR 10 lakh on a machine that saves INR 2.5 lakh a year, and the payback is 4 years.
- Return on investment (ROI): the gain compared with the cost. Put in 1,000, get 1,200 back, and the ROI is 20 percent. Simple ROI ignores when the money arrives.
- Net present value (NPV): the value today of all future cash, minus what you invest today. Money in the future is worth less than money today, because money today can be invested and earn a return. So each future amount is divided by (1 + r) once for every year you wait, where r is the yearly discount rate. If NPV is above zero, the investment creates value.
Example: at a 10 percent discount rate, 110 received one year from now is worth 110 divided by 1.1, which is 100 today. You rarely need to discount many years by hand in a case. You do often need one shortcut: the perpetuity.
Key idea
Perpetuity shortcut: a cash flow that continues every year with no end is worth the yearly amount divided by the discount rate. If the yearly amount also grows at rate g, it is worth the first year's amount divided by (r minus g). This works only when r is larger than g, and it assumes the first amount arrives one year from now.
Worked case
Is a cost-saving project worth it?
The prompt
A logistics firm in Dubai can spend AED 15 million now on new software that saves AED 2 million every year, with no planned end date. The discount rate is 8 percent. Should it invest?
The structure
- NPV = value today of the savings minus the investment
- Value of savings = yearly saving divided by the discount rate
- Subtract the AED 15 million investment
Working it through
1. Value the savings today
The saving continues with no end date, so use the perpetuity shortcut: 2 divided by 0.08.
Value of savings (AED millions):2 ÷ 0.08 = 252. Subtract the investment
The savings are worth 25 million today. The project costs 15 million today.
NPV (AED millions):25 - 15 = 103. Check the payback too
A simple payback check: 15 million divided by 2 million a year.
Payback (years):15 ÷ 2 = 7.5
The recommendation
The firm should invest, because the savings are worth about AED 25 million today against a cost of AED 15 million, an NPV of about AED 10 million at the 8 percent discount rate. The main weakness is time: payback takes about 7.5 years, which means much of the value depends on savings lasting well beyond that. The risk is that the software becomes outdated and the AED 2 million of yearly savings stop early. As a next step, confirm the savings with the operations team and check how long similar systems stay in use.
Risks: The savings may not last forever, for example if the software becomes outdated; A higher discount rate would reduce the value.
A contract pays EUR 3 million a year with no end date. The discount rate is 10 percent. What is it worth today, in EUR millions?
Two projects each cost 100 and each return 150 in total. Project A returns it in year 1, project B in year 5. Which is worth more today?
Sources for this lesson (1)
- Recognized public explanations of case-interview concepts and frameworks
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