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Business Strategy and Accounting Basics

A company is considering investing in a new production line. A large investment (¥1 billion) is expected to bring revenue of ¥2.5 billion if demand is high (probability 0.6) and ¥800 million if demand is low (probability 0.4). A small investment (¥400 million) brings revenue of ¥700 million if demand is low; if demand is high, it brings ¥1.2 billion as is, but an additional investment of ¥500 million at that point raises revenue to ¥2.2 billion. If the policy that maximizes the expected profit (revenue minus investment) is adopted, which is that expected value?

  1. A¥820 million
  2. B¥900 million
  3. C¥1.2 billion
Show answer and explanation

Answer: B. ¥900 million

Working in units of ¥100 million, the expected profit of the large investment is 0.6 × 25 + 0.4 × 8 − 10 = 8.2, that is, ¥820 million. For the small investment, investing more when demand is high gives 22 − 5 = 17, which is more than the 12 without it, so the additional investment is chosen, and the expected value is 0.6 × 17 + 0.4 × 7 − 4 = 9.0, that is, ¥900 million. In a decision tree, the best choice is decided starting from the later decisions, and expected values are then compared working backward. Therefore the best policy is to start with the small investment and invest more if demand is high, with an expected value of ¥900 million.

  • A. This is the expected value of the large investment. The policy of a small investment followed by an additional investment when demand is high has a larger expected value.
  • B. Correct. It is the expected value of the small investment with an additional investment when demand is high.
  • C. This forgets to subtract the additional ¥500 million from the revenue of ¥2.2 billion in the small-investment-plus-expansion case.
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