]Time Value of Money Review:
1. Future Values General Formula: It is for SINGLE cash ffow, and it calculates the FV of a
single amount, the PV. `
a. FV = PV(1 + i) n
b. FV = future value
c. PV = present value, or original amount invested at the beginning of the first
period
d. i= period interest rate, expressed as a decimal
e. n = number of periods
f. Differences if semi-annually or not.
2. Ex. of FV of a single amount.
a. Jane Farber places $800 in a savings account paying 6% interest compounded
annually. She wants to know how much money will be in the account at the end
of five years. (800=PV, 6%=i, 5=n)
i. FV5 = $800 X (1 + 0.06)5 = $800 X (1.338) = $1,070.40
b. IF compounded quarterly.
i. FV=$800*(1+.015)^20 =1077.48
3. PV of a single amount:
a. Present value is the current dollar value of a future amount of money.
b. Calculating the present value of future cash ffow to determine its worth is
commonly called discount cash ffow valuation.
c. The discount rate is often also referred to as the opportunity cost, the discount
rate, the required return, or the cost of capital.
d. How much do I have to invest today to have some amount in the future?
i. FV = PV(1 + i) n
ii. Rearrange the above formula we have 𝑃𝑉 = 𝐹𝑉/ (1+𝑖) 𝑛
iii. 1/ (1+𝑖) 𝑛 is called Present value interest factor
e. EX. How much will $5,000 to be received in 10 years be worth today if the
interest rate is 7%?
i. PV = FV (1/(1+i)^n ) = 5000 (1/(1.07)^10) = 5000 (.5083) = $2,541.50
4. Ordinary Annuities:
a. An annuity is a series of fixed payments for a specified number of periods. The
cash payments or receipts are constant. It is repeated and lasts for a significant
amount of periods.
b. If payments are made at the end of each period, the annuity is referred to as
ordinary annuity
c. FORMULA: PMT= [(1 – 1/(1+i)^n )/ i]
i. PMT = annuity payment deposited or received at the end of each period.
ii. i = discount rate (or interest rate) on a per period basis.
iii. n = number of periods for which the annuity will last.
d. EX. Your grandmother has offered to give you $1,000 per year for the next 3
years at the end of each year. What is the present value of this 3-year, $1,000
annuity discounted back to the present at 5 percent?
i. Draw a trendline:
ii. PV=1000[(1-(1/(1+.05)^3))/.05] = 2723.25.
iii. Or Pv= 1000/1.05 + 1000/1.05^2 + 1000/1.05^3
iv. Or use Financial calculator
5. Perpetuities: Basically same amount of money continuous forever.
a. A perpetuity is an annuity that continues forever or has no maturity. For
example, a dividend stream on a share of preferred stock. There are two basic
types of perpetuities:
i. Growing perpetuity in which cash ffows grow at a constant rate, g, from
period to period. So it increases by a constant rate, your 100 grows by 5%
every year.
ii. Level perpetuity in which the payments are constant from period to
period. Same payment forever, so 1000 every year.
b. PV of a Level Perpetuity
i. PV = PMT/i
c. PV of Growing Perpetuity
i. PV = PMT (yr 1) / (i-g)
1. PMT1 = PMT0*(1+g)
ii. The Constant Dividend Growth model = P0 = D1/(R-g)
d. Ex. What is the present value of a perpetuity stream of cash ffows that pays $500
at the end of year one but grows at a rate of 4% per year indefinitely? The rate of
interest used to discount the cash ffows is 8%. (PMT1=500, R=8%, i = 4%)
i. 𝑃𝑉 = $500 /(8% − 4%) = $12,500
Chapter 1: The Investment Environment:
1. What is Investment?
a. What is Finance? Finance is the study of (financial) resource allocation over
time and under uncertainty.
b. • An INVESTMENT is the current commitment of money or other resources in
the expectation of reaping future benefits.
i. For example • shares of stock • Insurance premium.
2. Why Invest?
a. Have your money work for you.
i. Your money earns money
ii. Buy something with your money that could increase in value
b. Have a chance to own (parts of) companies.
i. When you buy stock, you are actually buying the ownership of a
company
c. To buff your future risk in consumption
i. Human capital, retirement, education
ii. Insurance
3. What can we invest in?
a. Assets: Real and/or Financial
i. Real assets: land, building, machines, and knowledge that can be used to
produce goods and services.
ii. Financial assets: stock, bonds, and so on.
1. No more than sheets of paper or computer entries
2. They do not contribute directly to the productive capacity of the
economy
3. It is the reallocation of capital!! It is a tool for companies to gain
capital.
iii. While real assets generate net income to the economy, financial assets simply
define the allocation of income or wealth among investors.
4. Three types of Financial Assets:
a. Fixed income (Debt) = or debt securities promise either a fixed stream of
income or a stream of income determined by a specified formula.
b. Equity (Stock, common or preferred) = or common stock in a firm represents
an ownership share in the corporation.
c. Derivatives (Options) = Derivative securities are so named because their values
derive from the prices of other assets.
5. Players in the market:
a. Ones who need to buy these financial assets (eg. households)
b. Ones who need to sell these financial assets (eg. firms are net demanders of
capital).
c. Ones who can help these parties (eg. Financial intermediaries)
d. Government
i. Claims taxes
ii. Spends for common/public benefit
iii. Since World War II, the US. Government typically has run budget deficits.
6. 4 Financial Intermediaries:
a. Pool and Invest Funds:
i. Banks
ii. Investment companies like mutual funds
iii. Insurance companies
iv. Credit Unions
b. Investment Banking:
i. Firms that specialize in primary market transactions
ii. Sell newly issued securities to public in the primary market
1. Investors trade previously issued securities among themselves in
the secondary markets
c. Venture Capital:
i. Invest to finance new firm
d. Private Equity:
i. Invest in companies not trade on stock exchange.
7. Financial Market:
a. Players arrive at the financial market to trade (exchange) and realize resource
(re)allocation. Broad term– over the counter or phone or in a large place.
b. Financial assets and the markets in which they trade play several crucial roles in
developed economies.
i. Financial assets allow us to make the most of the economy’s real assets.
c. Financial markets are highly competitive.
8. Risk-Return Trade-Off:
a. Investments are associated with risks.
b. Actual or realized returns will almost always deviate from the expected return
anticipated at the start of the investment period.
c. If you want high expected returns, you will need to bear more risk. Otherwise,
the market will adjust the price to make it less “attractive”.
d. If returns are independent of risk, nobody want to hold risky assets. Then, the
market will adjust the price to compensate more (offer more return).
e. THERE MUST BE A TRADE-OFF!!
Chapter 2: Asset Classes
1. Asset Classes = 1) Common Stock 2) Derivative Securities 3) Fixed Income
Securities (Money Market and bond Market).
2. The Money Market: Fixed-income securities
a. The subsector of the fixed-income market
b. Securities are short-term, liquid, low risk, and often have large
denominations
c. Large denominations of these securities make them out of the reach of
individual investors
3. Money Market Mutual Funds: Allow individuals to access the money market by
pooling resources of many investors and purchase a wide variety of money
market securities.
a. Created by financial intermediaries.
b. Fidelity Report
4. Money Market Instruments:
a. Treasury Bills (KNOW THIS ONE)
b. CDS (Certificates of Deposit)
c. Commercial Paper
d. Banker’s Acceptances
e. Eurodollars
f. Repos and Reverses (KNOW THIS ONE)
g. Broker’s Funds
h. LIBOR (London Interbank Offer Rate).
5. Treasury Bills:
a. Short-term debt of U.S. government
b. Maturities of 4, 13, 26, or 52 weeks
c. Minimum denomination of $100 ($10,000 is more common)
d. Most important Characteristics: High liquidity, low-interest rate risk,
zero default risk, exempt from all state and local taxes.
e. Interest rate risk = if interest goes up and down, prices of stock go up or
down too. It can happen to the bond market too. But interest does not
really affect treasury bills.
f. KNOW THE DIFFERENCE BETWEEN BID AND ASK PRICE for
TREASURY BILLS.
i. Bid – is the price the investor can sell or the dealer can buy from
you.
ii. Ask – dealer sell to you or investor buy at this price
iii. The more discount the cheaper the price
6. Repos and Reverses:
a. Repurchase agreement (repos): Short-term borrowing – usually
overnight, typically within 14 days (shorter than treasury bills)
b. Repo: Dealer sells govt. securities to an investor with an agreement to
buy back those securities the next day at a slightly higher price. The
securities serve as a collateral.
c. The party on the other side ( the lender) is said to have a reverse repo.
7. The Bond Market – A bond is a fixed-income security with the maturity of 1-30
years for which the issuer promises to pay the holder periodic interest and
repay the principle at maturity.
a. – Treasury Notes and Bonds
b. – Inffation-Protected Treasury Bonds
c. – Federal Agency Debt
d. – International Bonds
e. – Municipal Bonds
f. – Corporate Bonds
g. – Mortgages and Mortgage
h. -Backed Securities
8. Treasury notes and bonds:
a. Maturities:
i. Notes – Up to 10 years
ii. Bonds – From 10 to 30 yrs.
b. Par Value – $1000
c. Coupon Payments: Interest paid semiannually
d. Characteristics
i. High Liquidity
ii. Interest Rate Risk
iii. Zero Default risk
iv. Exemption from state and local taxes
9. Inffation-Protected Treasury Bonds:
a. • In the US, Treasury Inffation-Protected Securities (TIPS) Provide
inffation protection
b. The principal is adjusted proportionally to changes in CPI
10. Federal Agency Debt:
a. In addition to federal, state, and local government, a number of federal
agencies issue debt as well.
b. These agencies are formed to channel credit to a particular sector of the
economy that Congress believes might not receive adequate credit
through normal private resources. Kinda government-backed securities.
• E.g., Fannie Mae, Freddie Mac
11. International Bonds:
a. Eurobonds: A bond denominated in a currency other than that of the
country in which it is issued.
i. Example: A dollar-denominated bond sold in Britain would be
called a Eurodollar bond.
b. Yankee Bonds: A dollar-denominated bond sold in the US by a non-US
issuer.
12. Municipal Bonds –
a. Issued by state and local governments
b. Interest is exempt from federal income tax and sometimes from state
and local tax
c. Types:
i. General Obligation bonds: Backed by taxing power of issuer.
ii. Revenue bonds: backed by project’s revenues or by the municipal
agency operating the project. Ex. building a highway and tolls
back the bonds.
d. To choose between taxable and tax-exempt bonds, compare after-tax
returns on each bond.
i. 𝑅𝑎𝑓𝑡𝑒𝑟𝑡𝑎𝑥 = 𝑅𝑡𝑎𝑥𝑎𝑏𝑙𝑒(1 − 𝑡𝑎𝑥 𝑟𝑎𝑡𝑒)
e. Thus, if your marginal rate for federal tax is 28% and state taxes is 12%, a
municipal bond that offers you a yield of 6% is approximately equivalent
to a taxable bond which offers you a yield of ___________.
i. ETY = 6%/ (1-.40) = 10%
13. Corporate Bonds:
a. Issued by private firms like Apple
b. Typically issued with face values of $1000, and semi-annual interest
payments.
c. Subject to larger default risk than gov. Securities
14. Equity Markets: Common Stock:
a. Residual claim
b. Limited liability
c. The liquidity of common stocks vary greatly
15. Residual Claim: Debt vs. Equity:
a. Creditors generally receive the first claim on the firm’s cash ffow.
b. Shareholder’s equity is the residual difference between assets and
liabilities.
c. Equity is riskier than Debt.
d. Debt magnifies the gains/losses to shareholders.
e. Ex. Assets = 100. Debt =75 and Equity =25.
i. How much debt holders lose if the firm value decreases by $10?
By $20? By $30?
1. Decrease by $10, the firm is not losing any money. Because
Equity is still covering the debt.
2. Decrease by $20, still not losing money.
3. Decrease $30, you lose $5mil, and you can’t cover the
entirety of $75 mil debt with $70 mil assets.
ii. How much shareholders lose if the firm value decreases by $10?
1. 10/25 = 40% of their investment
2. If they gained $10 mil, only the equity holder will be
gaining it and it would be a 40% gain.
16. Preferred Stock:
a. In-between debt and equity.
b. Similar to a bond: fixed dividends; no voting power
