MACRO SUMMARY
CHAPTER 27: THE BASIC TOOLS OF FINANCE
1. Present & Future Value: Measuring the time Value of Money
a. Present & Future Value:
. Present value the amount of money today needed to produce a future amount of money,
given prevailing interest rates
. Future value the amount of money in the future that an amount of money today will yield,
given prevailing interest rates
In general,
FV = PV(1 + r)N
Whereby. r: interest rate
N: period of time
Solved by PV,
PV = FV/(1 + r)N
Example 1: Deposit
Deposit $100 in the bank at 5% interest. What is the future value (FV) of this amount?
In one year, FV = $100(1 + 0.05) = $105.00
In two years, FV = $100(1 + 0.05) (1 + 0.05) =$100(1 + 0.05)2 = $110.25
In three years, FV = $100(1 + 0.05)(1 + 0.05)(1 + 0.05) = $100(1 + 0.05)3 = $115.76
Example 2: Investment decision
Suppose r = 0.06. Should General Motors spend $100 million to build a factory that will yield
$200 million in ten years?
Solution:
Find a present value of $200 million in 10 years:
PV = ($200 million)/(1.06)10 = $112 million
Since PV > cost of factory, GM should build it.
Alternatively, $100(1+6%)10 < $200, it’s worth for investment
b. Simple and Compound Interest:
. Compounding: the accumulation of a sum of money where the interest earned on the sum
earns additional interest
Because of compounding, small differences in interest rates lead to big differences over time.
. Simple Interest: C × i × N (whereby C is capital, i is rate and N is the period of time)
. Compound Interest: C(1+i)N (whereby C is capital, i is rate and N is the period of time)
Example 1: Buy $1000 worth of Microsoft stock, hold for 30 years.
If rate of return = 0.08, FV = $10,063
If rate of return = 0.10, FV = $17,450
Example 2: Suppose that a capital of 500$ earns 150$ of interest in 6 years
a. What was the interest rate if compound interest is used?
b. What if simple interest is used?
Solution:
a. Using compound interest:
500(1+i)6 = 500+150 = 650$
i = 0.0447 = 4,47%
b. Using simple interest:
500 × i × 6 = 150
i = 0,05 = 5%
Example 3: How long does it take to double your capital if you put it in an account paying
compound interest at the rate of 7,5%? What if the account pays simple interest?
a. Using compound interest:
PV(1+7,5)N = 2PV
(1,75)N = 2 7,5N = 2 log(1,75N) = log(2) N = log(2)/log(1,75)
N = 9,58
b. Using simple interest:
PV × 7,5% × N = PV
N = 1/7.5% = 13,33
The rule of 70:
If a variable grows at a rate of x percent per year, that variable will double in about 70/x years.
Example:
If interest rate is 5%, a deposit will double in about 14 years.
If interest rate is 7%, a deposit will double in about 10 years.
2. Managing Risk – Risk Aversion
a. Risk Aversion: dislike of certainly
» Utility: A person’s subjective measure of well – being/satisfaction
» Utility function:
. Every level of wealth provides a certain amount of utility
. Exhibits diminishing marginal utility
+ The more wealth a person has
+ The less utility he gets from an additional dollar
b. Managing risk with Insurance
How insurance works:
. A person facing a risk pays a fee to the insurance company, which in return accepts part or all
of the risk.
. Insurance allows risks to be pooled, and can make risk averse people better off:
E.g., it is easier for 10,000 people to each bear 1/10,000 of the risk of a house burning down than
for one person to bear the entire risk alone.
Two Problems in Insurance Markets:
1. Adverse Selection: A high – risk person benefits more from insurance, so is likely to
purchase it.
2. Moral Hazard: People with insurance have less incentives to avoid risky behaviour.
c. Reducing risk through Diversification
. Diversification reduces risk by replacing a single risk with a large number of smaller,
unrelated risks.
. A diversified portfolio contains assets whose returns are not strongly related:
+ Some assets will realize high returns, others low returns.
+ The high and low returns average out, so the portfolio is likely to earn an intermediate
return more consistently than any of the assets it contains.
+ Diversification can reduce firm-specific risk, which affects only a single company.
+ Diversification cannot reduce market risk, which affects all companies in the stock
market.
d. Trade-off between Risk and Return
Risk & Return: The more risk you taken, the more return you earn (kind of)
Example:
Suppose you are dividing your portfolio between two asset classes.
. A diversified group of risky stocks:
average return = 8%, standard dev. = 20%
. A safe asset:
return = 3%, standard dev. = 0%
The risk and return on the portfolio depend on the percentage of each asset class in the portfolio
3. Asset Valuation:
a. Fundamental Analysis:
When deciding whether to buy a company’s stock, you compare the price of the shares to the
value of the company.
+ If share price > value, the stock is overvalued.
+ If price < value, the stock is undervalued.
+ If price = value, the stock is fairly valued.
Value of a share
= PV of any dividends the stock will pay
+ PV of the price you get when you sell the share
Problem: When you buy the share, you don’t know what future dividends or prices will be.
» One way to value a stock: fundamental analysis, the study of a company’s accounting
statements and future prospects to determine its value
b. The efficient markets Hypothesis:
Efficient Markets Hypothesis (EMH): the theory that each asset price reflects all publicly
available information about the value of the asset
Implications of EMH:
+ Stock market is informationally efficient:
Each stock price reflects all available information about the value of the company.
+ Stock prices follow a random walk:
A stock price only changes in response to new information (“news”) about the company’s
value. News cannot be predicted, so stock price movements should be impossible to
predict.
+ It is impossible to systematically beat the market.
By the time the news reaches you, mutual fund managers will have already acted on it.
Index funds vs Managed funds:
c. Market Irrationality
Many believe that stock price movements are partly psychological:
+ J.M. Keynes: stock prices driven by “animal spirits,” “waves of pessimism and
optimism”
+ Alan Greenspan: 1990s stock market boom due to “irrational exuberance”
Bubbles occur when speculators buy overvalued assets expecting prices to rise further.
The importance of departures from rational pricing is not known.
