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Business Strategy and Accounting Basics

Introducing a business system with an investment of ¥10 million is expected to save ¥4 million in costs at the end of each of the next three years. With a discount rate of 5% per year, and present value factors (1 ÷ 1.05ⁿ) of 0.952, 0.907 and 0.864 for one, two and three years ahead, which is closest to the net present value (NPV) of this investment?

  1. Aabout ¥890,000
  2. Babout ¥1.43 million
  3. C¥2 million
Show answer and explanation

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.

  • A. Correct. Each year's savings are discounted by the present value factor, summed, and the investment is subtracted.
  • B. This discounts all three years of savings by the one-year factor only (12 ÷ 1.05 − 10, in ¥ million). The savings in years 2 and 3 must be discounted for two and three years respectively.
  • C. This simply subtracts the investment from the undiscounted total savings of ¥12 million.
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