utility: you can use the money immediately however you wish

risk: the risk of non-payment--other party may breach, go bankrupt, or you might forget

opportunity cost: the opportunity to invest (note: brotherton says that opportunity cost and utility are essentially the same)

p.245

present value tells us what the right to receive a certain sum at some point in the future is worth to us today.

present value allows us to determine the rate of return we will receive on our investment if we anticipate receiving a particular sum of money in the future.

p.245

p.246

FV = [the amount of your money] x (1 + rate)^#of years

1 year:

FV = 100 x (1.1)^1

     = 110

2 years:

FV = 100 x (1.1)^2

    = 121

3 years:

FV = 100 x (1.1)^3

    = 132

1. you divide the interest by 2 (since you are compoundin it twice a year.. if it was compounded every three months, you would divide the interest by 4). Here the answer is 0.05
2. You take the answer from #1 and add 1.  Here the answer is 1.05
3. you figure out how many times you need to compound by this percentage.  semi-annually for 2 years = 4 times. (compounded every three months for 2 years would equal 8)
4. (1.05)^4 = 1.2155
5. multiply this by your starting amount. 100 x 1.215 = 121.55

FV = x(1 + [k/m])^mn

p.248

the annual effective yeild is the actual rate given the compounding of interest. E.g. the credit card company tells you that the interest is 18% BUT it's actually closer to 19.56% annual interest since the 18% interest is compounded monthly.

AEY = (1 + k/m)^m - 1

how much is some amount in the future worth today?

p.250

$100.

PV = x / [(1+k)^n]

instead of multiplying x by the future value factor, we divide x by the future value factor to determine present value

PV = 121 / [(1 + 0.1)^2]

PV = 121 / (1.21)

PV = 121 / 1.21

PV = 100

p.250-51

they are they same rate. the rate is called "interest rate" when calculating a future value, while "discount rate" is for calculating a present value.

p.251

the payment of a constant sum at fixed intervals over a period of years is called an annuity.  for example, being paid $10 at the end of each year for the next 5 years.

p.253

instead of multiplying x by (1 + k/m)^mn, divide x by (1 + k/m)^mn.

PV = 100 / [(1 + k/m)^mn]

PV = 100 / [(1 + 0.1 / 2) ^ 2*2]

PV = 100 / (1.05^4)

PV =  100 / (1.2155)

PV = 82.64

p. 255

the present value will be lower.

(think.. this is the opposite effect of future value... when your money is compounded more frequently than annually, you get more interest, and the value is higher)

p.254-55

"ordinary annuities" are paid at the end of the period, while "annuities due" are paid at the beginnging of the period.  Thus, for identical annuities, annuities due will be discounted for one less period compared to ordinary annuities.

p.256

the rule of 72 helps you gauge how long it takes a given amount of money to double at varying compounded interest rates.

72 / interest rate (without decimals) = number of years it takes to double the amount

e.g. for a sum to double over an 8-year period requires a 9% annual return:

72 = rate x 8

72/8 = 9

9% is the rate.

e.g. a 6% annual return requires a 12-year horizon:

72 = 6 x yrs

72/6 = 12

12 years is the payback period.

p. 256-57

using the rule of 72:

if the available average annal rate is of return on money from now until 40 years from now is 9%, then how much money does a 25-year old person need today in order to retire as a millionaire at age 65 without saving another cent over that time?

$31,250.

1. with a 9% interest rate, the money doubles in 8 years.
2. start w/ 1,000,000 at 65 --> 65 - 8 = 57 she will have have 500,000 --> 49 yr old: 250,000 --> 41: 125,000 --> 33:  62,500 --> 25: $31, 250

p. 257

using the rule of 72:

a 25-year old reasonably expects a 6% annual rate of return.  She starts with $31,250.  She does not save a cent more through out the years.

1) how much will she have when she is 61 years old?

2) what age will she be to have 100,000?

72 = rate * yr

72/6 = 12 years

1)

25 yr: $31,250

37 yr: $62,500

49 yr: $125,000

61 yr: $250,000

answer: $250,000

2)

61 yr: $250,000

73 yr: $500,000

85 yr: $1,000,000

answer: she would be 85 years old

when the risk-free rate is high, then the value of riskier assets are low. (because there is no reason you would put your money in something with risk when you can get great risk-free rates)

when the risk-free rate is low, then things like average stock prices go up because it makes it relatively easy for investors to get a risk premium (returns above the risk-free rate)

p.258

it is better to be taxed once at the end of 35%.  The after-tax rate of return may only be a difference of 2-3%, but over a few decades this works out to be lots of dollars.

p.258-59

bonds can be thought of as IOUs, with an issuer promising to repay the borrowed amount (principal) along with periodic payments of interest.  Bonds are issues by corporations, governemental agencies, and other entities.

p.261

the value of a bond (same thing as everything else) is the present value of its future cash flows, which consists of

(1) periodic interest payments promised to be made

PLUS

(2) the principal to be repaid at maturity

p.261-62

the coupon is essentially the rate of interest that will be paid for the bond. (because in the past you would clip a coupon and turn it into the issuer to get your interest payment)

the coupon on a bond is expressed as a percentage of the bond's face amount or par value.  so a bond with a 10% coupon and a face amount of $1,000 promises to pay $100/year.

p.262

"effective yield" or "market value" is the return to bondholders.

as the market value of the bond changes with changes in the interests rates of that time period, the yield to bondholders changes as well.

for bonds selling at a discount (when the bond sells for less than face value), the effective yield is higher than the coupon. for bonds trading at a premium (when the bond sells fro more than face value), the effective yield is lower than the coupon.

p.262

A bond with a face value of $100,000, due in 5 years, with a 9% premium ($9,000 per year).  However, the interest rate in the market is now closer to 11%. 

 What is the value of the bond?

1. determine the present value of the principal:  the $100,000 you will get in 5 years, with a discount value of 11%, is worth $59,350 today. 
2. determine the present value of the stream of interest payments you will be receving:  the $9,000 you will be receving every year, with a discount value of 11%, is worth in total $33,264. 
3. (1) + (2) = value of the bond today: 59,350 + 33,264 =  $92,614.  This means that the bond should sell at a discount.

p.263

it depends.  equity securities (aka stocks) are riskier than bonds, but at the same time, the discount rate (aka "cost of equity") will greater.

calculating the value of equity securities requires estimating cash flows and discount rate.

p.263