48. Types of bonds, calculation of present value of discount and coupon bonds. Types of bond yield.

By profitability: coupon, discount (zero-coupon)

By issuer: State, municipal, corporate, bank (pledged assets)

By term: ST, LT, MidTerm

PV=principal/(1+d)^n

PV = Disc. CF + principal/(1+d)^n

TYPES OF BOND YIELD:

Coupon Rate (ex: 9% of par value)

Current Rate (current income / current cost)

YTM – most important – как IRR в NPV.

There are a lot of different types of bonds, they can be classified into traditional bonds – the basic types that have been around for years – and contemporary bonds – newer, more innovative types of bonds that have been developed and/or become popular in recent years.

Traditional types of bonds:

Debentures – Unsecured bonds that only creditworthy firms can issue. Convertible bonds are normally debentures. Claims are the same as those of any general creditor. May have other unsecured bonds subordinated to them

Subordinated debentures – Claims are not satisfied until those of the creditors holding certain (senior) debts have been fully satisfied. Claim is that of a general creditor but not as good as a senior debt claim.

Income bonds – Payment of interest is required only when earnings are available from which to make such payment. Commonly issued in reorganization of a failed or failing firm. Claim is that of general creditor. Not in default when interest payments are missed, since the are contingent only on earnings being available.

Mortgage bonds – Secured by real estate or buildings. Can be open-end (other bonds issued against collateral), limited open-end (a specified amount of additional bonds can be issued against collateral), or closed-end; may contain an after-acquired clause (property subsequently acquired become part of mortgage collateral). Claim is on proceeds from sale of mortgaged assets; if not fully satisfied, the lender become a general creditor. The first-mortgage claim must be fully satisfied before distribution of proceeds to second-mortgage holders, and so on. A number of mortgages can be issued against the same collateral.

Collateral trust bonds – Secured by stock and/or bonds that are owed by the issuer. Collateral values is generally 25 to 35 percent greater than bond value. Claim is on proceeds from stock and/or bond collateral; if not fully satisfied, the holder becomes a general creditor.

Equipment trust certificates – Used to finance “rolling stock” – airplanes, trucks, boats, railroad cars. A mechanism whereby a trustee buys such an asset with funds raised through the sale of trust certificates and then leases it to the firm, which, after making the final scheduled lease payment, receives title to the asset. A type of leasing. Claim is on proceeds from the sale of the asset; if proceeds do not satisfy outstanding debt, trust certificate holders become general creditors.

Contemporary types of bonds.

Zero (or low) coupon bonds – Issued with no or very low coupon rate and sold at large discount from par.

Junk bonds – Used by rapidly growing firms to obtain growth capital, most often as a way to finance mergers and takeovers of other firms.

Floating rate bonds – popular when future inflation and interest rates are uncertain.

Extendable notes – short maturities, typically one to five years, which can be redeemed or renewed for a similar period at option of their holders.

Putable bonds – bonds that can be redeemed at par at the opinion of their holder either at specific dates or when firm is being acquired, acquiring another firm, or issuing a large amount of additional bonds

Present value calculation of discount bond:

P_db=C*(1/1+tc)*100% P_db—price of sale of bond with discount; C—nominal price of bond; t—

amount of years after which bonds will be paid out; c—reinvestment rate %; P_p—present price

P_p-P_bd=Present value of discount bond

PV = FV/(1 + R)^t PV-Present Value; FV-Future Value; R-Interest (Discount) Rate; t-Number of periods before the money is received

Present value calculation of coupon bond:

P+a=C(t)/(1+t)^t

in which: C (t) = cash flow in respect of the loan in year (t) y = yield to maturity p = clean price a = accrued interest since the last coupon date¹ N = number of years remaining to maturity

There are three bond yield measures commonly quoted by dealers. They are:

Current Yield: it relates the annual coupon interest to the market price.

Current yield=Annual dollar coupon interest / Price

Yield to Maturity: is the interest rate that will make the present value of the cash flows equal to the price.

P=C/(1+y)¹+C/(1+y)²+C/(1+y)³+…+C/(1+y)ⁿ+M/(1+y)ⁿ P—price of he bonds; C—semiannaul coupon interest; M—maturity value; n—number of periods (number of years x 2)

Yield to call: for bond that may be called prior to the started maturity date.

P=C/(1+y)¹+C/(1+y)²+C/(1+y)³+…+C/(1+y)^n*+M*/(1+y)^n* M*—call price; n*—number of periods until first call date (number of years x 2)

49. Present value of shares: dividend discount model.

There exist 2 approaches towards the analysis of shares – technical and fundamental.

Here we speak only about fundamental approach, which is based on the dividend discount model (or Discounted Cash Flow model). It is easier to analyze bonds as the exact cash-flows are known.

Analyzing shares we try to predict what dividend pay-out in the coming years will be. There could be 3 cases:

1. Constant dividends

2. Constant growth at the rate g

3. Firstly – supernormal growth rate, then constant growth rate

Gordon’s equation:

We have to find out the present value of future dividends

PV = Do(1+g)/(1+d) + Do(1+g)^2/(1+d)^2 + infinitywhere g is the growth rate and d is the discount rate

In case when g < d then PV =Do(1+g) / (d-g)

Hence, we receive the current value of share and compare it with market price.

PV > Market Price, the security is underpriced

PV < Market Price, the security is overpriced