Finance Exam II Review BVI and BVII

Define the Coupon Rate

% of par value paid in coupon payments each year (expressed as APR)

Describe Interest Rate Risk and Bond Prices

- Effect of time on bond prices is predictable, but unpredictable changes in rates also affect prices - Bonds with different characteristics will respond differently to changes in interest rates - Investors view long-term bonds to be riskier than short-term bonds

Define Basis points

-A measurement unit for rates of return (alternative to %) -100 basis points = 1% (i.e. 1 basis point = 0.01%)

Describe Interest Rate Risk

-Applicable on on Bonds -Due to changes in YTM, if bonds sold prior to maturity @ a lower price

Define Treasury Securities

-Government-issued debt securities (bills, notes & bonds) -Safest security (usually)

Describe Default risk (credit Risk)

-Only present in corporate bonds Covered by credit rating agencies Risk issuer won't make payments as specified in contract -Default = not paying full amount -Default = not paying @ appropriate time •Bond rating agencies assess default risk of borrowers (Moody's, S&P, Fitch)

Define Credit Spread

-The difference between a bond's YTM and the YTM of treasury securities with the same maturity

Here are 4 values of a $100 bond with a 30 year maturity. Each one has a given present value of the graph on slide 22 from top to bottom. Describe what type of bond each one is. 1. N = 30, I/Y=5%, FV = 100, PMT = 10, PV (from calculator) = -176.9 2. N = 30, I/Y=5%, FV = 100, PMT = 5, PV (from calculator) = -100 3. N = 30, I/Y=5%, FV = 100, PMT = 3, PV (from calculator) = -69.3 4. N = 30, I/Y=5%, FV = 100, PMT = 0, PV (from calculator) = -23.1

1. (at premium) 2.(at par) 3. discount 4. discount (zero coupon) If the coupon rate is greater than par value the bond is a premium. Cr= PV then Par cr< par than discount. lower discount = lower payments.

Suppose you purchase a 30-year, zero-coupon bond with a yield to maturity of 6%. You hold the bond for 5 years before selling it. A.If YTM 6% when sell, annualized return on investment? B.If YTM 7% when sell, annualized return on investment? C.If YTM 5% when sell, annualized return on investment? D. Even if a bond has no chance of default, is your investment risk free if you plan to sell it before it matures? Please explain.

1. set as Face value of $100 A. 6.00%; i.e., because YTM is the same at purchase and sale. B. 1. Find Purchase Price: N= 30 I/Y=6 PMT=0 FV=100 PV0=??-17.411 2. Find Sell Price N=25 I/Y=7 PMT=0 FV=100 PV5=??-18.425 3. Find IRR N= 5 I/Y=?? =1.13% PMT=0 FV=18.425 PV=-17.411 because YTM rises, IRR < initial YTM. C. 1. We know Purchase Price 17.411 2. 2. Find Sell Price N=25 I/Y=5 PMT=0 FV=100 PV5=??-29.530 3. Find IRR N= 5 I/Y=?? =11.144% PMT=0 FV= 29.530 PV=-17.411 because YTM falls, IRR > initial YTM. D.Even without default, if you sell prior to maturity, you are exposed to the risk that the YTM may change.

Describe Time Effects and its implications What are Bond CF at maturity. What happens to the buyer if sold @ Maturity What is the Price at Maturity

@ maturity: only bond CF are (i) par repayment (ii) final coupon -If sold @ maturity, buyer not entitled to coupon -Price @ maturity = par -*Premium bond has built-in capital loss* -*Discount bond has built-in capital gain*

TF: Downward yield curves almost always precede recessions: A. True B. False

A (True) In the U.S., almost always a recession is preceded by an inverted yield curve! The only exception - July 1990 recession

Suppose you purchase a 10-year bond with 6% annual coupons. You hold the bond for 4 years, and sell it immediately after receiving fourth coupon. If YTM=5% when you bought & sold bond, what are the prices @ which you bought & sold at, per $100 face value? What is the effective yield? A. 5% B. 6% C. 7% D. None of the above

A. 1., we compute the initial price of the bond by N=10 I/Y= 5 PMT=6 FV=1 P0=107.72 2. we compute the price at which the bond is sold, which is the present value of the bond's cash flows when only six years remain until maturity: N=6 I/Y=5 PMT=6 FV=100 PV=-105.08 Therefore, the bond was sold for a price of $105.08. The cash flows from the investment are therefore as shown in the following timeline: Time 0: -107.72 Time 1: 6 Time 2: 6 Time 3: 6 Time 4: 6 + 105.08 We can calculate the I/Y with this cash flow stream using the TVM N=4 PMT=6 FV=105.08 PV=-107.72 I/Y = ??= 5% Note that this is to be expected, even if we did not do any calculations! As a rule of thumb, if the YTM at the time of purchase and the time of sale are the same, let us say 5%, then the YTM will be equal to them!

A 10-year zero coupon bond has par value of $1,000 and YTM of 6%. Assuming annual compounding, what is its price? A.$558.39 B.$1,790.85 C.$943.40 D.$1,000.00

A. N = 10 I/Y = 6 PV=? PMT = 0 FV = 1000

suppose a​ seven-year, $1,000 bond with an 8.0% coupon rate and semiannual coupons is trading with a yield to maturity of 6.75 % a. Is this bond currently trading at a​ discount, at​ par, or at a​ premium? Explain. b. If the yield to maturity of the bond rises to 7.00% ​(APR with semiannual​ compounding), what price will the bond trade​ for?

A. Because the yield to maturity is less than the coupon​ rate, the bond is trading at a premium. B. N=14 I/Y=3.5 PMT=40 PV?? FV=1,000 P=1054.60

Give the number of public firms for each: AAA AA A BBB BB B CCC CC C,D

AAA-6 AA-19 A-177 BBB-431 Junk bonds: BB- 331 B321 CCC-12 CC-1 C,D-5

Describe Bond Ratings.

All the way from AAA to D AAA has the lowest risk CCC (Caa for Moddy's) /CC(Ca for Moody's)/ C have the highest risk. D is in Default. BBB (or Baa) has medium risk BB/B have high risk. Invest in BBB and up. Lower r for the higher rated a bond is

*You purchase 5-year bond with annual 6% coupons today, when YTM is 7%. You sell bond 3 years later, just after receiving 3rd annual coupon. Par is $100.* If YTM=9% when you sell, what is your annual rate of return? A.2.00% B.5.87% C.-1.23% D.-0.41% What is your return if YTM is 7% when you sell bond?

B. At the time of sale, the bond has N=2 years remaining, YTM is 9%, and coupon is $6. Therefore: First find PV0 N=5 I/Y=7% PMT=6 FV=100 PV0=??-- 95.8998 Then find Sell Value: N=2 I/Y= 9 PMT=6 FV=100 PV3= 94.722 Then Find the Annual Rate of Return= N=3 I/Y=?? PMt=6 PV=-95.8998 FV=94.722 I/Y= 5.87% If YTM= 7% then PV0=??-- 95.8998 find Sell Value N=2 I/Y= 7 PMT=6 FV=100 PV3= ???- 98.192 Then Find the Annual Rate of Return= N=3 I/Y=?? = 7% PMt=6 PV=-95.8998 FV=98.192 Note that the effective return on the bond purchase and sale is r=7%, which is exactly the YTM = 7% at the time when it was purchased. Why? Because the YTM at the time of purchase is the same as the YTM at the time of sale.

*Your firm has credit rating of A. You notice that credit spread for 10-year maturity A-rated debt is 90 basis points (0.90%). Your firm's 10-year debt has coupon rate 5%. New 10-year treasury notes are being issued @ par w/ coupon rate 4.5%.* What is YTM of your firm's debt? A.9.50% B.5.40% C.5.90% D.0.05%

B. Is the correct answer. 4.50% + 0.90% = 5.40% How do we get that? The quote is presented to us as the default spread: what is this? The difference between the risk-free and risky debts' interest rates. From now on, risk free interest rate is rF. The risky debt's interest rate will be called rD. rF=Coupon Rate=4.5% rBOUND= default premium (.9) + rF = 5.40

Zero coupon bonds always trade at a discount!!! Why?

Because for them, coupon rate, which is zero, is less than YTM!

Bond with face value $1000 has maturity of 10 years & pays semi-annual coupons of 4%. Discount rate applicable to bond is 6%. At what price should this bond sell? A.$852.80 B.$541.20 C.$851.23 D.$914.70

C is the correct answer. N = 20 = 10 years * 2 I/Y = 3 = 6% / 2 PMT = 20 = 4% * 1000 / 2 FV = 1000 So PV = -851.23 Notice that the semi-annual coupon rate of 4% translates into a payment every six-month period of 4% * 1000 / 2 = 20

Which of the following statements is true of bond prices? A. A fall in bond prices causes interest rates to fall. B. A fall in interest rates causes a fall in bond prices. C. A rise in interest rates causes bond prices to fall. D. Bond prices and interest rates are not connected.

C. A rise in interest rates causes bond prices to fall. When bond prices fall, the interest rates increase.

*Which of these bonds has the greatest interest rate risk if they are otherwise identical?* A. A 20-year 8% coupon bond B. A 5-year zero coupon bond C. A 20-year zero coupon bond D. A 5-year 6% coupon bond

C. Is the correct answer. EXAM QUESTION This is the correct answer because the interest rate risk (i.e., the exposure of the value of the bond to changes in the underlying interest rate) are most prominent for bonds that pay LOW coupons, and bonds that have LONG maturity!!! To derive the answers note the following. 1.Bond in C is risker than bond in B. 2.Bond in A is riskier than bond in D. 3.The above two imply that the correct answer is either A or C. 4.Compare A & C: clearly bond in C is riskier than bond in A, because A pays coupon, C does not, and C and A both have the same maturity.

Bond with face value of $1000 has maturity of 10 years & pays annual coupons of 5%. Discount rate applicable to bond is 6%. At what price should this bond sell? A. $872.40 B. $912.50 C. $926.40 D. $1000

Calculations: set in the financial calculator the following - N = 10 I/Y = 6% PMT = 50 (5% of the face value of 1,000) PV = ? FV = 1000 Calculating PV, we obtain $926.40.

What is the yield to maturity of a one-year, risk-free, zero-coupon bond with a $10,000 face value and a price of $9,400 when released? A. 3.191% B. 6.000% C. 6.383% D. 0.009%

Correct answer is C. With the calculator: N=1, FV=10000, PV=-9400, PMT=0, so I/Y=?

*A 6% coupon bond with semi-annual coupon payments and 10 years to maturity has a par value of $1,000 & market price of $975. YTM?* A.6.19% B.5.66% C.3.17% D.6.34%

Correct answer is D. N = 20 PV= - 975 FV=1000 PMT=30 I/Y = ? (need x2 - why?) YTM is always presented as APR in contracts and therefore in the answer to the question.

Treasury= 5.2 (Yield %) AAA Corporation 5.4 BBB Corp 6.8 B Corp =7.2 The above table shows the yields to maturity on three-year, zero-coupon securities. What is price per $100 of face value of three-year, zero-coupon corporate bond w/ BBB rating? A. $99.06 B. $115.57 C. $82.55 D. $66.04

Correct: B Explanation: The credit spread is the difference in YTM between Treasury and BBB corporate bond of the same maturity and coupon structure. Therefore: 7.2% - 5.2% = 2%.

Treasury= 5.2 (Yield %) AAA Corporation 5.4 BBB Corp 6.6 B Corp =6.9 The above table shows the yields to maturity on three-year, zero-coupon securities. What is price per $100 of face value of three-year, zero-coupon corporate bond w/ BBB rating? A. $99.06 B. $115.57 C. $82.55 D. $66.04

Correct: C N = 3 PMT = 0 I/Y = 6.6% FV = 100 so PV = -82.55

How do we calculate Coupon Rates?

Coupon Percentage * Face Value / # of coupon payments per year

Consider 3-year bond with 6.5% coupon rate & $1,000 par value. -Suppose coupons paid semi-annually -Coupon payment?

Coupon rate is a feature of bond contract...Unless specified in contract, it is constant throughout life of bond The coupon payment is 3.25% = 6.5%/2, per six months, or 32.50$ for a $1000 par value.

Define Issue Date

Date when bond issued.

How will bond price change if YTM increases?

Decrease. Example: Suppose that a bond has N = 7, F=1000, C=8% & semi-annual compounding, YTM = 7% (note both C rate and YTM are noted in APR format - need to first present them as semi-annuals) Is this bond traded: A. at par B. at premium C. at discount The answer is premium. Since YTM<coupon. The actual price of this bond will be 1054.60.

What are the 3 different type of risk for corporate bonds?

Default Risk (Credit Risk) Interest Rate Risk Investment Risk (rollover risk

AAA bonds have a higher interest rate than BBB bonds. A.True B.False

False

Tf: Premium bonds are bad investments and discount bonds are good investments

False

TF: At maturity, the only cash flow from a bond is the repayment of its entire par value. A. True B. False

False At maturity we anticipate both the last coupon payment and the principal repayment.

TF: At maturity, the only cash flow from a bond is the repayment of its entire par value.

False At maturity, the cash flows consist of the final coupon payment as well as the repayment of the par value

The credit spread of a bond shrinks if it is perceived that the probability of the issuer defaulting increases. A.True B.False

False Explanation: Note that when the probability of default increases, the credit spread has to increase to allow for greater compensation to the investor buying it.

Describe Interset Rate risk: Varies with certain bond characteristics list them What if a bond is held to maturity?

Interest Rate Risk: Price moves indirectly with interest rates (YTM) 1.Longer-term bonds have greater interest rate risk 2.Lower-coupon bonds have greater interest rate risk •If bond held to maturity, interest rate risk is irrelevant Interest rate risk is increasing in the maturity of the bond and decreasing in the coupon rate of the bond.

What are the two Parties of a bond? Define Them

Issuer = party borrowing money (bond is liability) Investor/bondholder = party loaning money (bond is asset)

When does re-investment risk matter?

It matters when interest rates are declining @ the re-investment time, and you are the investor. Reinvestment risk affects the yield-to-maturity of a bond, which is calculated on the premise that all future coupon payments will be reinvested at the interest rate in effect when the bond was first purchased (and therefore, when valued, these coupons can be discounted with the same YTM that is prevalent at the time of the issuance/ purchase of that bond). Simply put, the reinvestment risk can also be viewed as the risk that future coupons from a bond will not be reinvested at the prevailing interest rate when the bond was initially purchased.

What measures are taken when deciding what category a bond falls under

Operating Income/ Sales (%) (Higher the better) FCFF/ Sales(%) (higher the better) EBITDA/(Interest +Dividneds) varies Total Liabilities/Net worth (%)(lower the better, negative is the worst) EBITA/ Total Assets(%) higher the better Total Debt/ Market Cap(%) lower the better Historical default rate (lower the better)

*•YTM < coupon rate →*

P > F Sells at Premium

Reinvestment Risk Example: Consider Royal Crown Co bond with a 10% yield to maturity (YTM). In order for an investor to actually receive the expected yield to maturity, she must reinvest the coupon payments she receives at a 10% rate. This is not always possible. If the investor could only reinvest at 5% (say, because market returns fell after the bonds were issued), the investor's actual return on the bond investment would be lower than expected.

Remember that issuers usually call bonds when interest rates fall, leaving the investor to reinvest the proceeds at a lower rate. So if Royal Crown Co bonds are callable, & rates fall from 10% to 3%, Royal Crow Co will probably call the 10% bonds and issue new bonds with a lower coupon. The holders of the 10% bonds would receive their principal back (and probably a small call premium), but they would then have to find other investments, none of which would probably pay as well as the Royal Crown Co bonds.

TF: Most Bonds have a deferred call & a declining call premium.

T

TF: Yield Curves for BBB and AA are higher than the U.S> treasury Yield Curve

T

TF: The bond with the smaller coupon payments is more sensitive to changes in interest rates.

T Because its coupons are smaller relative to its par value, a larger fraction of its cash flows are received later. later cash flows are affected more greatly by changes in interest rates, so compared to the 12% coupon bond, the effect of the interest change is greater for the cash flows of the 4% bond.

Define Face (Par) Value

The amount of the debt to repaid at some future date (maturity) -Aka "Par value", typically $1,000

Define an Underlying Asset

The asset underlying the option is the firm's bond.

A perpetual cash flow pays $10 every year, forever, starting in 10 years. The discount rate is 10%. What is the present value today? A. $10/0.10 B. $10/0.10 but discounted for 9 years, [$10/0.10]*[1/1.109] C. $10/0.10 but discounted for 10 years, [$10/0.10]*[1/1.1010] D. None of the above

The correct answer is B, because we have PV(as of year 9) of the perpetual to be 10/.1, i.e., as a of year 9.

You make monthly payments on your car loan. It has a quoted APR of 5% (monthly compounding). What percentage of the outstanding principal do you pay in interest each month? A. 5% B. 0.417% C. 0.40% D. None of the above

The correct answer is B. Because we have APR is annual, and we need to reflect it by month. So 5%/12 = 0.417%.

*A company releases a five-year bond with a face value of $1000 and coupons paid semiannually. If market interest rates imply a YTM of 6%, what should be the coupon rate offered if the bond is to trade at par?* A. 3% B. 5% C. 6% D. 7%

The correct answer is C. Here you do not need to make any calculations. Instead, it is necessary to realize that the coupon will be traded at par as long as YTM = Coupon rate.

Describe Re-Investmetn Risk

The facts that yield curves are not flat implies that a strategy of short-term investment will likely have different returns than a strategy of long term investment The re-investment risk exists also for the U.S. treasuries! Why? Because the yield curve is not flat!

Describe Reinvestment Risk

The risk that CFs will have to be reinvested in future @ lower rates, reducing income. EX: •You won $500,000 lottery. Will invest money & live off interest. -Buy 1-year bond, YTM = 10%. -You will have to re-invest every year, & YTM may decrease @ re-investment to, e.g., YTM = 5%. Reinvestment risk is the chance that an investor will not be able to reinvest cash flows from an investment @ a rate equal to the investment's current rate of return.

TF: Zero coupon bonds always sell at a discount (before maturity)?

True

TF: the higher the Interest rate the higher the credit spread

True

TF: Bonds with a high risk of default generally offer high yields. A.True B.False

True Explanation: It is true that when a bond is more likely to not pay, it is necessary to offer higher yield to compensate the investor for buying it.

TF: callable securities (like callable bonds and redeemable preferred stock) carry extra reinvestment risk

True because if they are called away, the investor will not even collect all the expected interest payments, much less reinvest them effectively.

TF: The greater the coupon premium, the likelier that the bond will be traded at a premium

True.

Define Covenants

Various contractual commitments ('promises') issuer makes to bondholder.

A major determinants of bond prices is interest rates. Describe how in relation to callable bonds.

When interest rates fall, and the bond price rises, this makes repurchasing the bond at a fixed price more attractive.

Four zero-coupon bonds trading @ prices shown below per $100 face value. YTM for each bond? P 1 year = 96.62 P 2 year= 92.45 P 3 year = 87.63 P 4 year = 83.06

YTM1= 3.5% YTM2= 4% YTM3=4.5% YTM4= 4.75% Take the PV equation and solve for r PV= F/(1+r)^T -> r= (F/PV)^1/T -1 for each. or do calculator. N= T I/Y=YTM ? PV= Each given one PMT=o FV=100 You can see clearly here that when the YTM goes up, the PRICE on zero coupon bonds goes down.

Define Maturity

Years until bond must be repaid. Declines through time.

Your firm has taken out a $500,000 loan with 9.0% APR​ (compounded monthly) for some commercial property. As is common in commercial real​ estate, the loan is a 5​-year loan based on a 15​-year amortization. This means that your loan payments will be calculated as if you will take 15 years to pay off the​ loan, but you actually must do so in 5 years. To do​ this, you will make 59 equal payments based on the 15​-year amortization schedule and then make a final 60th payment to pay the remaining balance. ​(Note: Be careful not to round any intermediate steps less than six decimal​ places.) a. What will your monthly payments​ be? b. What will your final payment​ be?

a. N=180 I/Y= .75 (9/12) PMT=??? PV=500,000 FV=0 Pmt= 5071.333 b. N=121 (180-59) I/Y=.75 PMT= 5071.333 PV=?? FV=0 Final payment = 405,411.15

Suppose a​ ten-year, $ 1 000bond with an 8.0% coupon rate and semiannual coupons is trading for $1,034.74. a. What is the​ bond's yield to maturity​ (expressed as an APR with semiannual​ compounding)? b. If the​ bond's yield to maturity changes to 9.0 %9.0% ​APR, what will be the​ bond's price?

a. 7.5 N=20 I/Y=?? x2 PMT=40 PV=1034.74 FV=1000 B. N=20 I/Y= 9/2=4.5 PMT=40 PV?? FV=1,000 PV= 934.96

Risk- free securities are backed...

and issued by the U.S. Treasure. BVII covers other bonds.

Define *Yield-To_Maturity*

discount rate that sets PV(promised payments) = market price -Always express YTM as APR! -YTM same as bond "internal rate of return" (IRR) -IRR of purchasing & holding until maturity Solve for r "y" in the Price of a Bond. •Show r "y" as APR: if semi-annual compounding →YTM=2×y

Define a Default Premium

higher r to compensate bondholder for risk of default

Define callable bonds

issuer has the option of repurchasing at a specified price (the call price) at any time to maturity (sometimes callable bonds have call protection in the initial several years). The call price may be the bond's face value, but it may not just as well. Similar to a loan that can be repaid at face value at anytime prior to maturity.

With Zero-Coupon Yield Curve:

longer maturities carry a higher interest rate. We just saw that on the prior question

Describe zero coupon bonds reinvestment risk

zero coupon bonds have less reinvestment risk, since they have no interim coupon payments. However, one has to re-invest the proceeds from those as well, and when the time of re-investment comes, it could be difficult to secure the same rate of return as the one available when the investment was initially made.

Describe a Zero-Coupon Bond

•Bond pays no coupons: coupon rate = 0% •Single CF: par value repayment @ maturity Price= PV = (F/(1+r)^T)

If *YTM > coupon rate →*

•P < F •sells @ discount

*If YTM= Coupon Rate ->*

•P = Par Value (F)

Define Coupon Payments

•Periodic payments made while bond outstanding -Name came from physical coupons -Typically once every 6 months

Define a Bond

•security that obligates issuer to make specific payments to bondholder -Money being borrowed with promise to repay -Bond contract specifies details of repayment