本文封面源于网络，侵删。
这个系列文章流产了，因为我已经考完了！！！
写在前面
《公司财务》是BUAA经济管理学院的一门必修课，每个经管学院的学生都要学习，更加硬核的是这门课采用全英文的形式教学和考核，我觉得有必要整理一下，方便以后复习和学弟学妹的学习。
与离散数学一样，为了防止以后忘记，先写一个中英文对照表…
中英文对照表
Discounted Cash Flow Valuation
Valuation: The One-Period Case
Time allows you the opportunity to postpone consumption and earn interest
Future Value
The total amount due at the end of the investment is called the Future Value (FV).
$$
FV = C_0 \times (1+r)
$$
Where $C_0$ is cash flow today (time zero), and $r$ is the appropriate interest rate.
Present Value
The amount that a borrower would need to set aside today to be able to meet the promised payment in one year is called the Present Value (PV).
$$
PV = \frac{C_1}{1+r}
$$
Where $C_1$ is cash flow at Period 1, and $r$ is the appropriate interest rate.
The Multiperiod Case
Future Value
The general formula for the future value of an investment over many periods can be written as :
$$
FV = C_0 \times (1+r)^T
$$
Where C_0 is cash flow at date 0, r is the appropriate interest rate, and T is the number of periods over which the cash is invested.
Present Value
$$
PV = \frac{C_T}{(1+r)^T}
$$
Number of Periods
$$
T = \frac{ln(\frac{FV}{PV})}{ln(1+r)}
$$
Double your money
the “Rule-of-72” :
Years to Double = $\frac{72}{i}$
Rate
$$
r = \sqrt[n]\frac{FV}{PV} -1
$$
Compounding Periods
Compounding an investment $m$ times a year for $T$ years provides for value of wealth:
$$
FV = C_0\times (1+\frac r m)^{m\times T}
$$
Effective Annual Rate (EAR)
The EAR of interest is the annual rate that would give us the same end-of-investment after $T$ years.
$$
EAR = (1+\frac rm)^m-1
$$
The actual rate of interest earned after adjusting the nominal rate for factors such as the number of compounding periods per year.
Continuous Compounding
The general formula for the future value of an investment compounded continuously over many periods can be written as:
$$
FV = C_0 \times e^{rT}
$$
Where $C_0$ is cash flow at date 0, $r$ is the stated annual interest rate, $T$ is the number of years, and $e$ is a transcendental number approximately equal to 2.718.
Simplifications
Perpetuity
A constant stream of cash flows that lasts forever.
$$
PV = \frac C r
$$
Where $C$ is constant cash flow, and $r$ is the stated annual interest rate.
Growing Perpetuity
A growing stream of cash flows that lasts forever.
$$
PV = \frac{C_1}{r-g} = \frac{C_0(1+g)}{r-g}
$$
Where $C_i$ is cash flow at date $i$, $r$ is the stated annual interest rate, and $g$ is the growth rate.
We also called this Gordon formula.
Annuity
A constant stream of cash flows with a fixed maturity.
$$
PV = \frac C r [1-\frac{1}{(1+r)^T}]\
FV = \frac C r [(1+r)^T-1]
$$
Where $C$ is constant cash flow, $r$ is the stated annual interest rate, and $T$ is the number of years.
Care about deferred annuity.
Growing Annuity
A growing stream of cash flows with a fixed maturity.
$$
PV = \frac{C_1}{r-g}[1-(\frac{1+g}{1-r})^T]
$$
Where $C_i$ is cash flow at date $i$, $r$ is the stated annual interest rate, $g$ is the growth rate, and $T$ is the number of years.
Loan Amortization
Pure Discount Loans
The simplest form of loan.
Treasury bills.
Interest-Only Loans
cash flows :
Year 1~n-1 : Interest payment
Year n : Interest + principle
Amortized Loans
With Fixed Principal Payment
Interest + principle
利息 = 尚未归还的本金*利率
每期支付的本金相同但利息不同
With Fixed Payment
每期支付的金额相同
Steps:
- Calculate the payment per period
- Determine the interest in Period t
- Compute principal payment in Period t
- Determine ending balance in Period t
- Start again at Step 2 and repeat.
