The sum of the future cash flows from an investment converted to present value using a discount rate, minus the amount invested. If it is greater than zero, the investment is judged worthwhile at that discount rate.
Japanese name: 正味現在価値(NPV)
Net present value (NPV) appears in 1 practice question across 1 topic, including Business Strategy and Accounting Basics.
¥1 million today is worth more than ¥1 million a year from now, because invested it would grow by the interest. This idea is called the time value of money, and future amounts are converted to present value by dividing by (1 + r) raised to the number of years, using a discount rate r. For example, at a 5% discount rate, ¥1.05 million one year from now has a present value of ¥1 million. The discount rate used is the cost of raising funds (the cost of capital) or the minimum return required of an investment.
Net present value is the sum of the present values of each year's cash flows minus the initial investment. If NPV is greater than zero, the investment yields a return above the discount rate and is worthwhile, and when comparing alternatives, the one with the larger NPV is better. Simply adding up cash flows without discounting overvalues effects in the distant future.
The internal rate of return (IRR) is the discount rate at which NPV becomes exactly zero, and it represents the investment's return. The payback period shows how many years it takes to recover the investment; it is easy to understand but ignores cash flows after payback. When investments of different sizes are compared, NPV and IRR can rank them differently, so they are used according to purpose.
Answer: A. about ¥890,000
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.
In general, it is based on the cost of capital, the average cost of raising funds through borrowing and from shareholders, and a higher discount rate is used for riskier investments. A higher discount rate makes the present value of distant cash flows smaller, so investments that take longer to pay back have smaller NPVs.
ROI (return on investment) is the profit from an investment divided by the amount invested, and it often ignores the time value of money. NPV discounts future cash flows and evaluates them as an amount of money, so it reflects differences in when the benefits are received.
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.
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