Term
what are the three reasons you would rather be paid today rather than 10 years later? 

Definition
utility: you can use the money immediately however you wish
risk: the risk of nonpaymentother 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



Term
what does "present value" mean with respect to the time value of money? 

Definition
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 


Term
what is the future value of your $100 in the bank (10% annual interest) at the end of 1 year? 2 years? 3 years? 

Definition
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 


Term
how do you calculate the interest on $100 that is 10% compounded semiannually for 2 years? 

Definition

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

You take the answer from #1 and add 1. Here the answer is 1.05

you figure out how many times you need to compound by this percentage. semiannually for 2 years = 4 times. (compounded every three months for 2 years would equal 8)

(1.05)^4 = 1.2155

multiply this by your starting amount. 100 x 1.215 = 121.55
FV = x(1 + [k/m])^mn
p.248 


Term
what is the "annual effective yield" ? 

Definition
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 


Term
what is the concept of present value? 

Definition
how much is some amount in the future worth today?
p.250 


Term
if you need to make a payment in 2 years from today of $121, how much would you need to save in the bank (bearing 10% interest compounded annually)? 

Definition
$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.25051 


Term
what is the difference between an "interest rate" and a "discount rate" ? 

Definition
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 


Term

Definition
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 


Term
how do you calculate the present value of a lump sum of $100 to be paid at the end of year 2, assuming a discount rate of 10% compounded semiannually? 

Definition
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



Term
what is the effect of the present value of a lump sum to be paid in the future if compounding occurs more frequently than annually? 

Definition
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.25455 


Term
what is the difference between "ordinary annuities" and "annuities due" ? 

Definition
"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 


Term
please explain the "rule of 72" 

Definition
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 8year 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 12year horizon:
72 = 6 x yrs
72/6 = 12
12 years is the payback period.
p. 25657 


Term
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 25year old person need today in order to retire as a millionaire at age 65 without saving another cent over that time? 

Definition
$31,250.

with a 9% interest rate, the money doubles in 8 years.

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 


Term
using the rule of 72:
a 25year 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? 

Definition
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 


Term
The U.S. Treasury instruments provide a riskfree rate of interest. How does this affect the value of the any other asset in the economy, like the value of businesses and shares of stock in them? 

Definition
when the riskfree 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 riskfree rates)
when the riskfree 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 riskfree rate)
p.258 


Term
is it better to be taxed 35% on your investment after each year for a total of 30 years, or to be taxed 35% once at the end of the 30 years? 

Definition
it is better to be taxed once at the end of 35%. The aftertax rate of return may only be a difference of 23%, but over a few decades this works out to be lots of dollars.
p.25859



Term

Definition
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 


Term
What is the value of a bond? 

Definition
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.26162 


Term
what is a "coupon" as it relates to bonds? 

Definition
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 


Term
what is "effective yield" as it pertains to bonds? 

Definition
"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 


Term
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? 

Definition

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.

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.

(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 


Term
is it better to invest in a bond or common stock? 

Definition
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 

