公司财务精品教学（徐江旻）Session2 NPV.pdfVIP

Net Present Value Jiangmin Xu Today’s Class • Future value – Compounding • Present value and net present value (NPV) – Discounting – Special cases (perpetuity, annuity, etc.) – Examples Reminder • Course public email: – Go to – Sign in with the following credentials • ID: gsm2014cf@126.com • Password: gsm2014 – All the course materials and announcements are in the email account’s inbox • First homework due next Tuesday (September 30) in class – Hand your homework to the TAs before the class starts. They will grade it and return it to you later • Registration and exam arrangement Time Value of Money • $1 in the future is worth less than $1 today – Why? • Get $1 in the future, forgo its use between now and then, perhaps by investing it – Put it in a bank and earn some interest • Two identical cash flows, the one that occurs earlier in time is more valuable Future Value • The value at some future date 1 (for example in one year), of an investment made at date 0 (= now) • For example, assume you have $100 and the constant risk-free interest rate is 5% per year – In one year, you will have 100 ×(1+0.05) = $105 5 – In 5 years, have 100× (1+ 0.05) $127.63 – In 50 years, have 100× (1+ 0.05)50 $1146.74 !! Compounding • More generally, if there are T years, and you earn the same interest rate r in each year with an initial investment C0 , you will end up with a future value FV C (1+ r)T T 0 • Compounding interest on interest – $1 over 2 periods: (1+ r)2 1+ r