Calculate the measures used to judge whether introducing a system or investing in equipment is worth its cost. Future money is treated as worth less than money today, so it is discounted to its present value and compared with the investment. You can check net present value (NPV), internal rate of return (IRR) and how many years it takes to recover the cost (payback period) at the same time.
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Result
Net present value (NPV)
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Internal rate of return (IRR)
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Profitability index (PI)
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Payback period (undiscounted)
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Discounted payback period
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Cash flows are discounted as if received at the end of each year. Within the payback year, the cash flow is assumed to arrive evenly and the period is interpolated linearly. IRR is calculated when all cash flows are 0 or more.
See it as a graph
Other inputs stay at their current values while the chosen input varies from 1/4 to 4 times its current value. The red dot is the current value.
The time value of money and present value
¥1 million today is worth more than ¥1 million a year from now, because money received now can be invested to earn interest or used for other investments. Future cash flows are therefore discounted at a discount rate and converted to their value today (present value) for comparison. At a discount rate r, C received t years from now has a present value of C ÷ (1 + r)ᵗ. At a 5% discount rate, 105 received in one year is worth the same as 100 today.
Net present value (NPV)
Net present value (NPV) is the sum of the present values of future cash flows minus the initial investment. If NPV is positive, the investment earns more than the return demanded by the discount rate and is worth making; if negative, it does not pay off. In the example “Investment 1,000; 3 years of 300, 400, 500; discount rate 5%”, the present values total about 1,080.4 and NPV is a positive 80.4 or so. A simple sum would be 1,200, which shows how discounting reduces the value.
Internal rate of return (IRR) and payback period
The internal rate of return (IRR) is the discount rate at which NPV is exactly zero, and it shows the annual percentage return the investment generates. If IRR exceeds the cost of raising funds (the cost of capital) or the return the company requires, the investment is judged worthwhile. The payback period is the number of years until cumulative cash flows reach the initial investment. It is simple and easy to understand but ignores cash flows after payback and the time value of money. The discounted payback period uses cumulative present values instead.
Evaluating IT investments
When introducing an information system, effects such as reduced staff time or higher sales are estimated as cash flows and compared with the costs of introduction and operation. Some effects, such as shorter working hours, are easy to express in money, while others, such as higher customer satisfaction, are not, so qualitative effects are considered alongside the financial measures. When comparing several options, IRR and the profitability index are also used because they are easy to compare across projects of different sizes.
Converting the future savings to present value gives 4 × (0.952 + 0.907 + 0.864) = 4 × 2.723 = ¥10.892 million. Subtracting the investment of ¥10 million gives a net present value of about ¥890,000, which is greater than zero, so the investment is judged worthwhile at a 5% discount rate. Simply adding the savings without discounting, ¥12 million, and subtracting the investment gives ¥2 million (20% of the investment), but considering the time value of money, ¥4 million in the future is worth less than ¥4 million today.
FAQ
How do I choose the discount rate?
It is common to use the cost of raising funds through loans or equity (the cost of capital) or the minimum return the company requires from the investment (the hurdle rate). Riskier investments use higher discount rates.
Can NPV and IRR give different answers?
When comparing options that differ in size or in the timing of cash flows, the option with the larger NPV and the one with the higher IRR can differ. If the goal is to increase the company's value as much as possible, NPV is the basic criterion.
Can I decide on the payback period alone?
The payback period is easy to understand and useful when you want to recover funds quickly, but it ignores cash flows after payback and the time value of money. It is best used together with NPV and IRR.
How does this appear on exams?
The strategy area of IT certification exams such as Japan's Fundamental and Applied Information Technology Engineer Examinations includes questions that compare investment options by net present value calculated from a discount rate and yearly cash flows, and questions that ask for the payback period.