货币的时间价值
Adollar in our pocket today is worth more than a dollar in our pocket tomorrow (vedio).The primary reason is that we can invest money we have today and earn somereturn on it, where the return might be the dividends, interest or growths ofinvestment in stock market or real estate. The second reason is that we prefercurrent consumption over future consumption, so we have to give up some future rewardto meet our current consumption need. The third reason is that with inflation,we can purchase less in the future with the same money we have today. In factif we have higher inflation in the future, the value of dollars in our pocketsgoes down. Finally, future cash flows involve risk that we might not get thecash we expect.
货币的时间价值是基于一个普遍的认知假设：即比起明天的一块钱，人们更愿意拥有今天的一块钱。四个原因：1 今天的钱可以用来投资获取收益，比如分红、利息、股票或地产收益； 2 比起明天消费来，人们更愿意今天就买想要的东西，所以就适当牺牲一些远期可能的收益； 3 考虑到通货膨胀，今天的一块钱明天拿去花就没办法买到和今天一样数量的东西了； 4 未来的现金流入是带风险的，人们没办法保证预期的收入一定会发生。
两个时间点上的钱的数量是无法用来相加或是相比较的，必须要统一至一个时间点上。
Discounting:the process by which future cash flows are adjusted to some equivalent amount today.
贴现：把未来现金流计算至今天的实际价值 - 现值
Discount rate: the interest rate used to capture inflation, risk, and preference forcurrent consumption.
折扣率： 计算现值用的利率
Compouding:earning returns on original investment plus previous returns. a powerful concept
复利： 原始本金加上当前收益之后的回报计算
“The most powerful force in the universe is compound interest”– AlbertEinstein
宇宙中一个最具能量的动力就是复利 - -爱因斯坦 （据说是他说的）
Present value: Value of an expected future cash flow in today’s dollars
现值PV：预期未来现金流入的当前价值计算
Future value: value in the future of an amount invested today
期值FV：今天投入资金的未来价值计算
Five types of cash flow: 现金流的五种形式
1 single cash flows or lump sums 未来的单笔现金流入
PV of single future cash flow = CFt / (1+i)t
现值 = 流入资金 / (1 + 利率) ^t次方
t为利息计算的时间周期的次数，比如以年计息，五年后收入10000元，t为5
2 annuities: a constant cash flow that occurs at regular intervals during a fixed period;eg. home loan
年金：持续的按一定周期比率发生的现金流，如房屋按揭贷款
PV of annuity = receipt * [1-(1/(1+i))t]/i –(Annuity discount factor)
年金的现值 = 每期现金流 * [1-(1/(1+利率))^t次方] / 利率
例如：以澳洲房产为例，30年的房贷，每月固定还款3500元，年利率为5%
因为按月还款，实际利率 = （1+.05/12)^12次方 - 1 = 5.116% 每年
则所有还款数的现值 （按年算） = 3500*12 / .05116 * [1 - 1/1.05116^30次方] = 637,192.51
而该套房产的实际贷款额为576,000，少于未来还款数的现值，这就说明银行收取的实际利率应当大于5.1%，测算数值约为6%/年，可能的原因为银行提取利率的复利周期更短，比如按天计算。
eg:a mortgage, 30 years, borrowed 300000, 4.5% interest rate,
monthlyinterest rate = 4.5% / 12 = 0.00375
FV of annuity = Amount of annuity * [(1+i)t-1]/i –(Annuity future value factor)
年金的期值 = 每期现金流 * [(1+利率)^t次方-1]/利率
eg:when 25-year old, saving 2000 each year, 65-year retirement, 7% interest rate
FV =2000 * [(1+0.07)^40-1]/0.07 = 399,270
3 Growing annuities: investment providing cash flows that are expected to grow over time
增长式年金：每期的现金流以一定比率不断增长，如不断增长的租金收入
eg:surgical robot investment – initial investment $2-3M, robot performs 400 procedures each year, expected to generate 500,000 in profits in first year,profit will grow by 5% each year, robot will last 5 years before it needs to bereplaced, assume the discount rate is 10%
PVof a growing annuity = (Annuity * (1+g)) * [1-(1+g)t / (1+i)t/(1-g)]
=500000*(1+.05) *[1-(1+.05)5 / (1+.10)5/(1-.05)]
4 perpetuities:annuity of a constant cash inflow or outflow that lasts forever
永续年金：持续地永远发生的现金流，如英国政府80年代发行的用续国债，受益人将永远按年度获得分红，并且过世后可指定继承人；
eg:council bond issued by British government in 80s, never matures
PV of perpetuity = Amount of constant annuity / i
永续年金的现值 = 每期现金流 / 利率
例如：澳洲价值为790,000的公寓房产，年租金回报为5%，每期现金流 = 790000*.05 = 39500
假设同样的资金同期银行存款利息为3%，该房屋租金收入的现值 = 39500 / .03 = 1,316,666
假设同样的资金用于投资年回报率为10%的项目，该租金收入的现值 = 39500 / .1 = 395,000
注意，这里计算的是可能发生的租金收入的现值，没有考虑房屋的本身价值
5 growing perpetuities: a cash flow that is expected to grow at a constant rate forever;often help us to estimate the price of stocks of certain companies or the rent of properties
增长式用续年金：预期以一定比例增长的永久现金流，通常可以用来预估股票价格或者房产租金收益
PV of growing perpetuity = CF1 / (i-g) next year’s cash flow divided by the difference between the discount rate i and the expected perpetuity growth rate g
增长式用续年金现值 = 第一个时间周期的现金流 / (折现率 - 预期增长率）
eg:100,000 property, growth rate 5% (interest rate), discount rate 8% (earning rate)
PV =105000 / (.08-.05) = $3.5M