FIN 4424 CH. 5,6,7,8

Continuous Compounding

EAR = e^(q) - 1 The e is a special function on the calculator normally denoted by e^(x)

Common Stock

Equity without priority for dividends or in bankruptcy.

Future Value Interest Factor

(1+r)^t

Term structure upward

- LT rates are higher than ST rates -

Term structure downward

- ST rates are higher than LT rates

Term structure "humped"

- rates increase at first, but then begin to decline as we look at longer- and longer-term rates

Term structure

- relationship between time to maturity and yields, all else equal - tells us what nominal interest rates are on default-free, pure discount bonds of all maturities. These rates are, in essence, "pure" interest rates because they involve no risk of default and a single, lump sum future payment. - tells us the pure time value of money for different lengths of time.

Discount Cash Flow

- valuation method used to estimate the attractiveness of an investment opportunity - used to evaluate the potential of an investment using future cash projections and to discount them to arrive at a present value

Present Value Interest Factor [PVIF(r,t)] Discount Factor (Rate)

1/(1+r)^t

Zero Coupon Bond

A bond that pays no coupons at all must be offered at a price that is much lower than its stated value - coupon rate = 0% - The entire yield-to-maturity comes from the difference between the purchase price and the par value - Cannot sell for more than par value - Sometimes called zeroes, deep discount bonds, or original issue discount bonds (OIDs) - Treasury Bills and principal-only Treasury strips are good examples of zeroes

Growing Annuity

A growing stream of cash flows with a fixed maturity Formula slide 44

bond prices and interest rates always move in opposite directions. When interest rates rise, a bond's value, like any other present value, will decline. Similarly, when interest rates fall, bond values rise. Even if we are considering a bond that is riskless in the sense that the borrower is certain to make all the payments, there is still risk in owning a bond

As interest rates increase, present values decrease So, as interest rates increase, bond prices decrease and vice versa

reason that bonds with lower coupons have greater interest rate risk is essentially the same is because the value of a bond depends on the present value of its coupons and the present value of the face amount. If two bonds with different coupon rates have the same maturity, then the value of the one with the lower coupon is proportionately more dependent on the face amount to be received at maturity. As a result, all other things being equal, its value will fluctuate more as interest rates change. Put another way, the bond with the higher coupon has a larger cash flow early in its life, so its value is less sensitive to changes in the discount rate

As interest rates increase, the price of the bond goes down with any bond

Perpetuity - infinite series of equal payments

C/r

Municipal Securtities

Debt of state and local governments Varying degrees of default risk, rated similar to corporate debt Interest received is tax-exempt at the federal level

Present Value Formula

FV* [1/(1+r)^t]

Treasury Securities

Federal government debt T-bills - pure discount bonds with original maturity of one year or less T-notes - coupon debt with original maturity between one and ten years T-bonds - coupon debt with original maturity greater than ten years

Present value info

Finding out how much we would need to invest today in order to get the amount we are looking to get in the future Putting down money to grow to the amount you need in the future

Bond Prices: Relationship Between Coupon and Yield

If YTM = coupon rate, then par value = bond price If YTM > coupon rate, then par value > bond price Why? The discount provides yield above coupon rate Price below par value, called a discount bond If YTM < coupon rate, then par value < bond price Why? Higher coupon rate causes value above par Price above par value, called a premium bond

Bond Value Formula

PV of Coupons + PV of the par value; PV of annuity + PV of lump sum C * [1-1/(1+r)^t]/r + F/(1+r)^t

Future Value

PV(1+r)^t

Annuity Formula

PV: C {[1-1/(1+r)^t]/r} FV: C {[(1+r)^t-1]/r}

The provisions of an indenture document

The basic terms of the bonds. The total amount of bonds issued. A description of property used as security. The repayment arrangements. The call provisions. Details of the protective covenants.

Interest Rate Risk

The risk that arises for bond owners from fluctuating interest rates ---- Interest rate risk a bond has depends on how sensitive its price is to interest rate changes. This sensitivity directly depends on two things: the time to maturity and the coupon rate. - All other things being equal, the longer the time to maturity, the greater the interest rate risk. - All other things being equal, the lower the coupon rate, the greater the interest rate risk. - it increases at a decreasing rate. In other words, if we compared a 10-year bond to a 1-year bond, we would see that the 10-year bond has much greater interest rate risk because it has a longer maturity.

Government Bonds

Treasury Securities Municipal Securtities

Example APR

What is the APR if the semiannual rate is .5%? .5(2) = 1% What is the monthly rate if the APR is 12% with monthly compounding? 12 / 12 = 1%

EAR Formula

[1 + (Quoted rate/m)]m − 1

Discount Bond

bond sells for less than face value

Premium Bond

bond sells for more than its face value

Current Yield

bond's annual coupon divided by its price - When the current yield is too low, the reason is because it considers only the coupon portion of your return; it doesn't consider the built-in gain from the price discount. For a premium bond, the reverse is true, meaning that current yield would be higher because it ignores the built-in loss.

Bid-Ask Spread

difference between the bid and asked price

YTM (yield)

interest rate required in the market on a bond

Amortized loan

lender may require the borrower to repay parts of the loan amount over time

APR

period rate times the number of periods per year m [ (1+EAR)^(1/m) - 1 ]

Bid Price

price a dealer is willing to pay for a security

Ask Price

price a dealer is willing to take for a security

Pure discount loan

the borrower receives money today and repays a single lump sum at some time in the future

EAR

the rate you will actually earn

Interest Only Loan

type of loan repayment plan calls for the borrower to pay interest each period and to repay the entire principal (the original loan amount) at some point in the future - if there is just one period, a pure discount loan and an interest-only loan are the same thing. - With a pure discount or interest-only loan, the principal is repaid all at once.

Indenture

written agreement between the corporation (the borrower) and its creditors. A.K.A. the deed of trust.