Jun 202 min read

💫BAFS必知: 9成人都錯的Net Present Value (凈現值) 計算題

很多同學在做BAFS Personal financial management (個人理財) Ch 1的 Net Present Value (凈現值) 計算題時都會忽略了Cash flow (現金流)發生的時間點!

例如在 BAFS DSE中, 題目問你:

Hana Company paid $100,000 to buy a second-hand yacht on 1 January 2024. It is expected that she'll receive $80,000 for hiring out the yacht at the end of 2024 and the start of 2025. In addition, the disposal value of the yacht is estimated to be $40,000 after 2-year use. The cost of capital is 5%. Calculate the net present value of the yacht.

Hana公司於2024年1月1日支付10萬美元購買了一艘二手遊艇。她預計將在 2024 年底和 2025 年初出租這艘遊艇獲得 $80,000 的收入。此外，使用2年後，該遊艇的變賣價值預計為$40,000。資金成本為5%。計算遊艇的淨現值。

❌☹️Common mistake answer❌:

❌Workings:

Year 0 (now): Cash outflow of $100,000

Year 1 (the end of 1st year / 2024.12.31)Cash inflow of $80,000

Year 2 (the end of 2nd year / 2025.12.31): Cash inflow of $80,000 + $40,000 = $120,000 *☹️❌👉🏻大部分人的錯誤是把2025年年頭收到的款項當作為年尾處理! 因為很多考生看見題目說Hana是"2025年收款"就當作是"Year 2"處理!! 但這是很嚴重的謬誤!! 因我們所指的"year 2"是指第2年的年尾 ("year 1"則是指第1年的年尾)!

❌Wrong final answer:

💫🤩滿分計算示例 by Miss Hana💫:

Workings:

Year 0 (now): Cash outflow of $100,000 Year 1 (the end of 1st year / 2024.12.31) or (the start of 2nd year / 2025.1.1): Cash inflow of $80,000 + $80,000 = Cash inflow of $160,000 *🤩👉🏻注意因為Hana是在2025年初收到$80,000，因此將和第一年年尾時間點是一樣！ Year 2 (the end of 2nd year / 2025.12.31): Cash inflow of $40,000