PV hay FV ?

Việc sử dụng PV để chiết khấu dòng tiền, so sánh tính hiệu quả của các dự án môt cách khách quan nhất có thể. Hôm rồi có xem 4 bài giảng trên Khanacademy về PV, thấy cũng hay, nhưng mà nếu chưa học về cái này chắc mình cũng không hiểu chú Sal nói gì nhiều lắm.

Xem comment trên Utube mới thấy một câu hỏi hay. Liệu ta có thể sử dụng FV thay cho PV không ? Nghe sơ qua thấy đơn giản, cái dự án nào tốt hơn thì bản chất tốt hơn, đâu quan trọng chuyện tương lai hay quá khứ…nhưng mà bạn đó còn dẫn thêm một phép tính nhìn thì hợp lí nhưng lại đi ngược với suy nghĩ ban đầu của mình, tiếc là không thấy chú Sal xuất hiện trả lời.

Trên trang chủ có debate với 9 comment, not bad l0l.

Đây là câu thắc mắc :

Khan claims that with the last discount rate (5%for2y,1%for1y) you would be best off going with the 3rd option because the PV of the 3rd option =$101.25 where PV of the 1st option =$100. We can apply all the same variables and find that the two year future value (FV) of the 3rd option =$20*1.05^2+$50*1.01+$35=$107.55, but the FV of the 1st option =$110.25. If we look at PV then the 3rd option is better but if we look at the FV then the 1st option is better. Shouldn’t we decide based off the FV?

HankyUSA

Một câu trả lời hay và khá hoàn hảo :

HankyUSA, this is a great question, but your (and the rest of the responders’) logic is slightly off. Think about what you are really saying in your example:

I will invest $20 at a 5% interest rate STARTING NOW
I will invest $50 at a 1% interest rate STARTING NOW
I will invest $35 at a 0% interest rate STARTING NOW

Do you see the error? You are assuming a timeline that starts all of your investments at the current time. But of course that isn’t true. You won’t have access to the $50 for a whole year and the $35 for a whole two years. Therefore you can’t use addition to simply sum $20, $50*1.01, and $35*(1.02^2) because $50 isn’t the present value it’s the FUTURE VALUE in one year’s time. Similarly, $35 is what the value WILL BE in 2 years time. This conundrum is the entire reason for using the discounting method.

The correct logic is to ask the question: How much money would I need today to have $50 in a year at a 1% interest rate. That is exactly the formula Sal gave ($50/1.01). And the same goes for $35 in two years at 2%.

Another way to think about it is that the present value as Sal calculated is $101.25. Using the FV interest calculation given in a previous video we have (1.05)^2 multiplied by $101.25 (the present value of the investment) which gives us $111.63. Clearly more than the $110.25 in option 1. Hope this helps.

JJ MacCammon

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