# People.stern.nyu.edu

## Coupon Bonds and Zeroes

**coupons** every six months and par value at maturity. • The quoted coupon rate is annualized. That is, if the quoted coupon rate is c, and bond maturity is time T, then for each $1 of par value, the bond cash flows are: that pays **off** $1 in t years. • I.e., d t is the price of a t-year zero as a fraction of par

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URL: http://people.stern.nyu.edu/jcarpen0/courses/b403333/01zero.pdf

### 01 Coupon Bonds and Zeroes

bonds pay **coupons** every six months and par value at maturity. • The quoted coupon rate is annualized. That is, if the quoted coupon rate is c, and bond maturity is time T, then each $1 par value (quantity) of the bonds pays out cash flows • For N par value, the bond cash flows are Coupon Bonds c/2 c/2 1 + c/2 0.5 years 1 year T years

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### Bonds and the Term Structure of Interest Rates: Pricing

Stripping is the process of spinning **off** each coupon and principal repayment as a separate zero. Prior to mid-1970’s there was little perceived need for zeros because interest rates were relatively stable. Prior to 1982, zeros were fashioned by investment banks (e.g. TIGRs – Treasury Investment Growth

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### Money Market and Debt Instruments

so it has N=7 more **coupons** to pay. Thus, can use the above formula to get the price: Quoted (see WSJ) Coupon Rate = 6%, so C = 0.5 × 6% × 100 = $3 per 1/2 year Ask Yield = 4.69%, so YTM = 4.69% / 2 = 2.345% per 1/2 year Calculating the present value of the 7 period annuity and the par value at maturity, we get the quoted price

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### Notes on Bonds: Liquidity at all Costs in the Great Recession

were well **off**-the-run during the time when the yield spread widened most notably. This yield spread documented in Figure 1 does not necessarily represent an arbitrage opportunity, since the note has a lower coupon than the bond and thus a longer duration. But with an upward sloping yield curve, as was the case during 2008, the difference in **coupons**

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### Mortgage -Backed Securities

l Z -class: last to be paid **off** l Floating/inverse floating CMOs l Planned Amortization Class bonds (PACs) and TACs stripped, the **coupons** and principal are separated out and sold as individual zero-coupon instruments n Investment banks create Strips when the total can be sold for more than the

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### Debt Instruments and Markets

Treasury notes and bonds in trust and sold **off** the individual **coupons** and principal pieces as zeroes (TIGRs, CATs, BEARs, TRs, etc.). In 1985, the Treasury created the STRIPS Program which allows dealers to strip and reconstitute Treasury notes and bonds with …

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### DEBT INSTRUMENTS AND MARKETS

Debt Instruments and Markets Professor Carpenter Zeroes and Coupon Bonds 3 Let dt denote the t-year discount factor, the price today of an asset which pays **off** $1 in t years, …or the price of a t-year zero as a fraction of par value. Because of the "time value of money," a dollar today is

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### A note of caution: Opportunities are not options…

claims are paid **off**. cumulated nominal value of these **coupons** to the face value of the debt. Maturity of the Debt • Face value weighted duration of bonds outstanding (or) • If not available, use weighted maturity . 79 Valuing Equity as an option -Eurotunnel in early

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### Caps, Floors, and Collars

The cap pays **off** when interest rates go up. Therefore, it is a bearish position in the bond market. Indeed, its interest rate delta is negative. Time 0.5 6.004% $0.470 4.721% $0.021 35 0.06004 0.04721 0.470 0.021 = − − − ir∆ = − Modeling a Capped Floater • Consider an investor holding a 2-year floater with an embedded 6% cap. The

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### CHAPTER 2 HIGH DIVIDEND STOCKS: BONDS WITH PRICE …

guaranteed income stream in the form of **coupons**. The trade **off** is that bonds have limited potential for price appreciation. A bond’s price may increase, as interest rates go down, but most of the money you make on your investment must come from the **coupons** you receive over the bond’s life.

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### Aswath Damodaran Stern School of Business, New York

In corporate finance and valuation, we start **off** with the presumption that the riskfree rate For example, assume that **coupons** are annual and that you are provided with the following information on one-year and two-year coupon bonds: Price of a 2%, 1-year coupon bond = 1000 Price of a …

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### Problem Set I: Foundations of Finance Solutions

Problem Set I: Foundations of Finance Solutions 5 Example: Consider the WSJ quotes Rate Bid Asked Ask Yld. 41/ 2 99:27 99:28 4.57 51/ 4 101:06 101:08 4.59 For the 41/ 2 Coupon Rate note, Ask Yield > Coupon Rate and indeed Price<Par. For 51/ 4 Coupon Rate, Ask Yield <Coupon Rate and indeed Price>Par. This shows that the result in this problem is not a pure mathematical exercise, but it is

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### CHAPTER 7 RISKLESS RATES AND RISK PREMIUMS

Most risk and return models in finance start **off** with an asset that is defined as risk free and use the expected return on that asset as the risk free rate. The expected since the **coupons** on the bond will be reinvested at rates that cannot be predicted today. The risk free rate for a five-year time horizon has to

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### CHAPTER 4 RISK MEASUREMENT AND HURDLE RATES IN …

Most risk and return models in finance start **off** with an asset that is defined as risk-free and use the expected return on that asset as the risk-free rate. The expected returns 4.2 2 on risky investments are then measured relative to the risk-free rate, with the risk creating an expected risk premium that is added on to the risk-free rate.

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### GETTING&TO&THE&OPTIMAL:& …

to pay **off** debt" 3. Renegotiate with lenders" Does the ﬁrm have good "projects?" ROE > Cost of Equity" ROC > Cost of Capital" Yes" Take good projects with" new equity or with retained" earnings." No" 1. Pay **off** debt with retained" earnings." 2. Reduce or eliminate dividends." 3. Issue new equity and pay **off** "debt." Yes" No. Large mkt cap

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### THE$RIGHT$FINANCING$

17. The Trade **off** 18. Cost of Capital Approach 19. Cost of Capital: Follow up 20. Cost of Capital: Wrap up 21. Alternative Approaches 22. Moving to the optimal Financing Type 23. The Right Financing Dividend Policy 24. Trends & Measures 25. The trade **off** 26. Assessment 27. Action & Follow up 28. The End Game Valuation 29. First steps 30. Cash

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### A Framework for Getting to the Optimal

¨In addition, there may be a trade **off** between mismatching debt and getting greater tax benefits. Overlay tax preferences Deductibility of cash flows for tax purposes Differences in tax rates across different locales If tax advantages are large enough, you might override results of previous step Zero **Coupons**

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### Coupons in context: discounting prices or decreasing proﬁts

36 **coupons** are both offered in coupon booklets along with 37 other competitors’ coupon offerings, and in print adver-38 tisements where competitors’ prices and products are less 39 salient. We develop a contextual framework to show how the 40 presence of prices of the company’s other products, and the ∗ Tel.: +1-510-6431899; fax: 1-510

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### SESSION 6: THE TIME VALUE OF MONEY

3 Discounting and Compounding ¨ The mechanism for factoring in these elements is the discount rate. The discount rate is a rate at which present and future cash flows are traded **off**. It incorporates (1) Preference for current consumption (Greater .Higher Discount Rate)

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### Chapter 7

Preferred stock has perpetual life, and the **coupons** are set forever. I am valuing the preferred stock portion, using the preferred dividend rate on straight preferred. Value of Conversion Portion = $105 - $66.67 = $38.33 7-5 The convertible bond is a 10-year bond with a …

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### NEW YORK UNIVERSITY STERN SCHOOL OF BUSINESS

Consider the following characteristics of a 1-year semi-annual 8% Brady bond with the consequences of default meaning that the bond never gets paid **off**: (I) guaranteed principal, and (II) 10% probability of default each period. Assume the discount factors for 6-months and 1-year are respectively .95 and .90. What is the value of the Brady bond?

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### Explaining the Rate Spread on Corporate Bonds

including **coupons**, ratings, and callability. A subset of the data in the Warga database is used in this study. First, all bonds that were matrix priced rather than trader priced are eliminated from the sample.5 Employing matrix prices might mean that all our analysis un-covers is the rule used to matrix-price bonds rather than the economic in-

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### When managing the debt, Governments deal with the trade

Note that longer-term debt issued at **coupons** of 15% and inflation close to 6% implied ex-ante real interest rates of about 9% and possibly much higher ex-post real interest rates if the government objective of lowering inflation to 4% in the medium run was achieved.

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### The Emerging Landscape for Retail E-Commerce

versioning, or through targeted non-transferable **coupons** that offer customized discounts **off** a high list price. The Mixed Evidence on Price Dispersion Comparing the price level and price dispersion of online retail markets to traditional retailers can indicate the extent to …

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### GETTING TO THE OPTIMAL: TIMING AND FINANCING CHOICES

¨In addition, there may be a trade **off** between mismatching debt and getting greater tax benefits. Overlay tax preferences Deductibility of cash flows for tax purposes Differences in tax rates across different locales If tax advantages are large enough, you might override results of previous step Zero **Coupons**. Title: cfpacket2spr20

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### Professor Paul Zarowin

Financial Reporting and Analysis - B10.2302/C10.0021 - Class Notes. Non-Current Liabilities: Bonds. The key feature of accounting for non-current liabilities, such as bonds (with or without **coupons**), is that their book values are always based on their original effective interest rate, i.e. the market yield in effect when they were first sold.

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### Option Pricing Applications in Valuation

Aswath Damodaran! 78! Application to valuation: A simple example! Assume that you have a ﬁrm whose assets are currently valued at $100 million and that the standard deviation in this asset value is 40%.! Further, assume that the face value of debt is $80 million (It …

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### CHAPTER 6 A SHAKY BASE: A “RISKY” RISKFREE RATE

even if it is issued by a default free entity, because the **coupons** every 6 months will have to be reinvested at uncertain rates. The solution is to strip the **coupons** from the bond and make it a zero-coupon bond. Thus, the riskfree rates for each period will be measured by using the rate on a zero-coupon default-free bond maturing in that period.

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### Designing the Perfect Debt

Aswath Damodaran 6 Ensuring that you have not crossed the line drawn by the tax **code** All of this design work is lost, however, if the security that you have designed does not deliver the tax beneﬁts. In addition, there may be a trade **off** between mismatching debt and getting greater tax beneﬁts.

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### Application Test: Getting to the Optimal

¨In addition, there may be a trade **off** between mismatching debt and getting greater tax benefits. Overlay tax preferences Deductibility of cash flows for tax purposes Differences in tax rates across different locales If tax advantages are large enough, you might override results of previous step Zero **Coupons**

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### CHAPTER 28: APPLICATION OF OPTION PRICING THEORY IN

small, callable bonds have high **coupons**. One of the benefits of early exercise is that these **coupons** can now be replaced with lower interest payments. 28-3 The conversion option in a convertible bond is linked to the underlying bond, i.e., if the conversion option is exercised the underlying bond ceases to exist. In contrast, a warrant

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### Investment Philosophy: The Secret Ingredient in Investment

There is a trade **off** between risk and return • To get investors to take more risk, you have to offer a higher expected returns **coupons**) and capital gains • The different tax rates on various portions of savings (pension versus non-pension) • Changing tax rates across time. Aswath Damodaran 11 The Tax Effect: Stock Returns before and after

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### Giddy/NYU Foundations of Finance Course

Maturities range from 7 to 15 years, and are quoted on a 30/365 day-count basis. Most government bonds are straight bonds with annual **coupons**, although some floating-rate notes have been issued. Foreign Bonds Bonds issued by nonresidents in a country's domestic capital market. Such bonds are subject to domestic regulations and are underwritten

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### Giddy/Financial Markets and Instruments

Between 1982 and 1986, a number of enterprising companies and funds purchased Treasuries, stripped **off** the ``coupon'' (an anachronism from the days when new bonds had **coupons** attached to them) and sold the **coupons** for income and the non-coupon portion (TIGeRs or Strips) as zeroes. Merrill Lynch was the first when it introduced TIGR's and

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### Professor Paul Zarowin

The accompanying three examples show N/R=s with (1) zero **coupons** (i.e., no periodic cash receipt), (2) **coupons** at less than r%, and (3) **coupons** at the effective rate of interest, r%. Troubled Debt Restructurings (chapter 8, pages 362-368) When a firm cannot meet the interest and/or principal payments on its debt, it may restructure the debt.

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### SEARCH RESULT -- WSJ Interactive Edition

"Save 45%-60% when you take an additional 30% **off** permanently reduced merchandise. Markdown taken at register," the sign says. Confused, Ms. Latter asks a clerk to scan the item. There is a pause. "It's 30% **off**," she says, just before the lunch-hour rush. "I know," Ms. Latter says, "but can you scan it just to make sure?"

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### 12 Level and Slope Factors in Bond Returns--Evidence from

varying **coupons** and maturities, and thus have time-varying risk loadings. To get cleaner time series of returns, we construct the returns on implied zeroes with “constant” maturities, which are likelier **off** the diagonal. Σ can be decomposed as Σ = QΛQ’ where

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### Finding the Right Financing Mix: The Capital Structure

written in terms of the **coupons** (interest payments) on the bond (loan) and the face value of the bond to be – n Holding other factors constant, the duration of a bond will increase with the maturity of the bond, and decrease with the coupon rate on the bond. Duration of Bond = dP/dr = t*Coupon t (1+ r)t t=1 t=N ∑ + N*Face Value (1+ r)N

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### Investment Philosophies: An Overview

QThe trade **off** between Risk and Return • Most, if not all, investors are risk averse • To get them to take more risk, you have to offer higher expected returns • Conversely, if investors want higher expected returns, they have to be willing to take more risk. Q- Ways of evaluating risk

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### Giddy: A Day in the Life

CSFB was quoting the paper at 100 1/8 bid before the Treasury market backed **off**, when the price moved to 99 7/8 bid, still very comfortably inside the 1 3/8 per cent full underwriting fees. Traders opined that the terms were very generous, and speculated that Holderbank might even have been able to borrow the funds more cheaply by going direct

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### Prof. Ian Giddy: Telecoms Debt

Analysis of existing telecom bonds with step-up **coupons** shows that the value of the option is worth 5-15 basis points. This value is not usually taken **off** the issue price - it becomes apparent during the trading of bonds in the secondary market.

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### Design the perfect financing instrument

¨ In addition, there may be a trade **off** between mismatching debt and getting greater tax benefits. Overlay tax preferences Deductibility of cash flows for tax purposes Differences in tax rates across different locales If tax advantages are large enough, you might override results of previous step Zero **Coupons**

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### Giddy/ABS Mortgage-Backed Securities/ 1

l Z-class: last to be paid **off** l Floating/inverse floating CMOs l Planned Amortization Class bonds (PACs) and TACs stripped, the **coupons** and principal are separated out and sold as individual zero-coupon instruments n Investment banks create Strips when the total can be sold for more than the

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### Summary of Foundations of Financial Markets

Some securities have intermediate cash flows, for example bonds that pay **coupons** or stocks that pay securities, in which case the trading strategy must have the …

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### Struggling Groupon Ousts Its Quirky CEO

its online **coupons**, and has restated its financial results more than once. To rev up growth, the company has tried shifting its business into new areas including discounted online goods, software for small businesses and electronic payments. Few of those efforts are quickly paying **off**. Groupon has reported just one quarter of profits since its

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### Giddy: International bond market case study

Credit Suisse First Boston was the lead manager of a €150m three-year bond for Holderbank Inc., the Swiss cement concern. The bonds offered a 6 1/8 per cent coupon, and were snapped up by eager Swiss investors. CSFB was quoting the paper at 100 1/8 bid before the European governments market backed **off**, when the price moved to 99 7/8 bid

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