Skip to content

Latest commit

 

History

History
119 lines (106 loc) · 5.64 KB

time_value_of_money.md

File metadata and controls

119 lines (106 loc) · 5.64 KB
Raw

Background

I took CFA level 1 and this is the most fundamental of the material. I document it here for my own refresher.

WARNING: This is my mental model with my own language. Proceed with care.

Example: there is no such thing as distortion field in finance literature (AFAIK), nor financial instrument == tunnel to send money between past, present and future.

Cash Flow Diagram

  • x-axis: time
  • Arrow up: money put into the account
  • Arrow down: money taken out of the account

Examples:

  • Put money $100.00 to a bank account, and take out $120.00 in 5 years:

    Wallet
======
                             120      pv: -100
                             ^        fv: 120
                             |        n : 5
    o----1----2----3----4----5
    |
    v
    100

Bank Account
============ (Note this is the reverse of Wallet account)

    100                                pv: 120
    ^                                  fv: -120
    |                                  n : 5
    o----1----2----3----4----5
                             |
                             v
                             120

  • Put money $100.00 to bank account, per year, for 5 years, starting today; receive $518.74 at year 5

    Wallet
============
                          518.74       pv : 0
                          ^            pmt: -100 (beginning of period, TODO: CHECK this)
                          |            n  : 5
 0----1----2----3----4----5            fv : 518.74
 |    |    |    |    |
 v    v    v    v    v
 100  100  100  100  100

  • Put money $10,000.00 now and receive $100 for eternity

    Wallet
======
     100  100  100  100  100  100  100  100  100             pv : -10,000
     ^    ^    ^    ^    ^    ^    ^    ^    ^               pmt: 100
     |    |    |    |    |    |    |    |    |               n  : infinity
0----1----2----3----4----5----6----7----8----9---- ...       fv : :shrug:
|
v
10,000.00

  • Get money today for 1,000. Pay 202 per month for 5 months.

    Wallet
======
1,000                                  pv : 1,000
 ^                                     pmt: -202
 |                                     n  : 5
 0----1----2----3----4----5            fv : 0
      |    |    |    |    |
      v    v    v    v    v
      202  202  202  202  202

Time Value of Money

Rate

  • Moving money from present to future or vice-versa involve a "distortion field" called "rate"

    • depending on context, rate can be inflation, interest, rate of return, etc.

  • This is Time Value of Money

  • Examples:

    • Current money (n=0) of $100 is "equivalent" with $102 in 1 year (n=1) under "distortion field"/rate of 2%

    • Same money (n=0) of $100 is "equivalent" with $108 in 1 year (n=1) under "distortion field"/rate of 8%

    • The following are tables of this "equivalence"

      n rate=2% rate=3% rate=5% rate=8%
      0 100.00 100.00 100.00 100.00
      1 102.00 103.00 105.00 108.00
      2 104.04 106.09 110.25 116.64
      3 106.12 109.27 115.76 125.97
      5 110.41 115.93 127.63 146.93
      8 117.17 126.68 147.75 185.09
      10 121.90 134.39 162.89 215.89
      15 134.59 155.80 207.89 317.22
      20 148.59 180.61 265.33 466.10

  • Financial instruments are like tunnels (with distortion field) to send money between present and future.

    • You have loads of money now that you don't need: send it through a tunnel to receive it in the future, be it in form of cash, savings, stocks, equity, bonds, gold, foreign currency, etc.
    • You need a lot of money to pay for a big expense now and decide that future you will send your future money to now: find a tunnel that can channel your future money: loan, mortgage, etc.
    • There are many tunnels to choose from, with different characteristics (reliability, ability to take out your money mid-flight, guaranteed/constant/variable/pegged-to-something distortion field, etc.)
    • If you are in financial industry, you can create new kind of tunnels with desired characteristics.

  • Anecdotal story

    • If You give me 100, I will give back 120.
      • This statement is missing at least two critical information to decide:
        • WHEN the 120 will be returned. If it is immediate, with no risk, that is a "too good to be true", if it is in 100 years, meh.
        • WHAT risk is this 120?