FIN 300 Exam 2

Calculate the price of a six-year $1000 face-value bond with a 7% annual coupon rate and a yield-to-maturity of 6% with semi-annual coupon payments.

$1,049

One of the basic relationships in interest rate theory is that, other things held constant, for a given change in the required rate of return, the the time to maturity, the the change in price.

-Longer; greater -Shorter; smaller

Types of bonds

-Mortgage bonds -Debentures -Subordinated debentures -Investment-grade bonds -Junk bonds

You would like to have $500,000 put away in 20 years for your retirement. You plan to put away $14,000 each year (end of year). What is the minimum interest rate that you would need to receive $500,000?

5.72%

If the yield-to-maturity of a bond is less than the coupon rate, the bond will sell at:

A premium

A bond sold at par with a coupon rate of 7% will have a YTM:

Equal to 7%

There is an increase in expected inflation. All else equal, bond prices will

Fall

Assuming the same positive discount rate and the same number of years over which they will be received, a $1,200 annuity with annual payments has a larger present value than a $100 annuity with monthly payments.

False

As the discount rate decreases, the present value of a positive cash flow to be received at a particular time in the future:

Gets larger

An upward sloping yield curve:

Has higher long term rates than short term rates

Compound interest can best be described as:

Interest on interest and interest on original principal

The spread between treasuries and corporate bonds:

Is usually positive

When we consider the time value of money, a dollar received in the future:

Is worth less than a dollar received today

A 12-year bond pays an annual coupon of 8.5 percent. The bond has a yield to maturity of 9.5 percent and a par value of $1,000. What is the bond's current yield?

N: 12 I: 9.5 *PV: 930.1616 PMT: 8.5 x 1000= 85 FV: 1000

You have just borrowed $10,000 and will be required to make monthly payments of $227.53 for the next five years in order to fully repay the loan. What is the implicit interest rate on this loan?

Less than 2%

A portfolio earns on average 10%. If the standard deviation of the same stocks was 5%, what is the probability that you will lose money on this portfolio?

M= 10%-5%= 5% M= 5%-5%= 0 2 deviations= 95%

Semiannual bonds

Multiply years by 2: number of periods = 2N Divide nominal rate by 2= periodic rate (I/YR)= rd/2 Divide annual coupon by 2: PMT= annual coupon/2

A bond has a coupon rate of 8.5%, matures in 10 years at a value of $1,000 and has a current market price of $832. What is the current yield?

N: 10 I: PV: 832 PMT: 8.5% x1000= 85 FV: 1000 *Current yield: 85/832= 0.1022

Suppose Ford Motor Company have 10 years remaining to maturity. Interest is paid annually; the bonds have a $1,000 par value; and the coupon interest rate is 12 percent. Compute the yield to maturity for the bonds if the current market price is $910.

N: 10 I: PV: 910 PMT: 12% x 1000= 120 FV: 1000 *Current yield: 120/ 910= 0.1319

Bond Terminology

Par value: face amount of the bond, which is paid at maturity (assume $1000) (fv) Coupon interest rate: stated interest rate (generally fixed) paid by the issuer. Multiply by par value to get dollar payment of interest. (pmt) Maturity date: years until the bond must be repaid (pv) Issue date: when the bond was issued (I) Yield to maturity: rate of return earned on a bond held until maturity (also called the "promised yield") (N)

YTC is used for n, not for YTM, and the premium is the FV

Then YTCeff=(1+I/Y)2-1 YTC =premium bonds YTM =par and discount bonds

A yield curve plots yield against time

True

The Boogie Board Inc firm has a beta of 2.3. If the Risk Free return is 3.5% and in general people earn 7% for putting their money into stocks, how much is the CAPM required rate of return for BBI?

(Return of market -RF)= mrp RF + B(mrp) 3.5 +2.3(7%)= 19.6

Which of the following statements is most incorrect?

-All else equal, if a bond's yield to maturity increases, its current yield will fall. -If a bond's yield to maturity exceeds the coupon rate, the bond will sell at a premium over par.

What is the value of an Orion bond that has a 10 percent annual coupon, pays interest semiannually, and has 10 years to maturity, if the annual required rate of return is 12 percent?

N: 10 x2 = 20 I: 12%/ 2= 6 *PV: 885.30 PMT: 10% x 1000= 100/2=50 FV: 1000

Joe Kernan Corporation has bonds on the market with 10.5 years to maturity, a YTM of 8.5 percent, and a current price of $1,090. The bonds make semiannual interest payments. What must the coupon rate be on Kernan's bonds?

N: 10.5 x 2=21 I: 8.5/2 =4.25 PV: 1090 *PMT: 49.0638 FV: 1000

Palmer Products has outstanding bonds with an annual 8 percent coupon. The bonds have a par value of $1,000 and a price of $865. The bonds will mature in 11 years. What is the yield to maturity on the bonds?

N: 11 *I: 10.09% (10.0868) PV: -865 PMT: 1000 x 8%= $80 FV: $1000

Consider a bond with a face value of $1,000, currently selling for $1,349.96, and maturing in 11 years. If this bond pays coupons semiannually and its yield to maturity is 4.03%, what is the coupon rate?

N: 11 I: 4.03% PV: $1,349.96 PMT: 80.31 FV: $1000 * Coupon rate: 80.31/1000=0.0803

What should be the price of a bond with 12 years to maturity and a 10% coupon rate if the required rate of return on the bond is 8 percent?

N: 12 I: 8% *PV: 1150.7216 PMT: 10 x 1000= 100 FV: 1000

A 12-year bond pays an annual coupon of 8.5 percent. The bond has a yield to maturity of 9.5 percent and a par value of $1,000. What is the bond's current yield?

N: 12 I: 9.5 PV: 930.16 (find first) PMT: 1000 x 8.5= 85 FV: $1000 *Current yield: 85/930.16= 9.14%

What is the yield to maturity of a TVA bond that has a 9 1/2 percent coupon, pays interest semiannually, has 12 years to maturity, and sells for $871.50?

N: 12 x 2= 24 *I: 5.7504 PV: 871.50 PMT: 9.5% x 1000= 95/2= 47.5 FV: 1000

Suppose Ford Motor Company sold an issue of bonds with a 12-year maturity, a $1,000 par value, a 12% coupon rate. Two years after the bonds were issued, the going rate of interest on bonds such as these had risen to 14 percent. At what price would the bonds sell?

N: 12-2= 10 I: 14% *PV: 895.6777 PMT: 12% x1000= 120 FV: 1000

A corporate bond has a face value of $1,000, and pays a $50 coupon every six months (that is, the bond has a 10 percent semiannual coupon). The bond matures in 12 years and sells at a price of $1,080. What is the bond's nominal yield to maturity?

N: 12x 2= 24 *I: 4.45 x 2= 8.90% PV: 1080 PMT: $50 FV: $1000

Mustaine Enterprises has bonds on the market making annual payments, with 13 years to maturity, and selling for $850. At this price, the bonds yield 7.4 percent (YTM). What is the coupon rate on these bonds?

N: 13 I: 7.4 PV: 850 *PMT: 55.6433 FV: 1000

Krogers in Conway, Arkansas, wants you to make sure they don't run out of toilet paper over Toad Suck weekend in May. If the average number of packages you sell is 600 per week, with a variance of 5250 per week, how many should you make sure you order to be pretty certain that you won't run out?

var= 5250 S.D.=5250= 72.46 units

Due to a number of lawsuits related to toxic wastes, a major chemical manufacturer has recently experienced a market reevaluation. The firm has a bond issue outstanding with 15 years to maturity and a coupon rate of 8 percent, with interest paid semiannually. The required nominal rate on this debt has now risen to 16 percent. What is the current value of this bond?

N: 15 x 2= 30 I: 16%/ 2= 8% *PV: $550 PMT: 1000 x 8%= 80, 80/2= 40 FV: $1000

Due to a number of lawsuits related to toxic wastes, a major chemical manufacturer has recently experienced a market reevaluation. The firm has a bond issue outstanding with 15 years to maturity and a coupon rate of 8 percent, with interest being paid semiannually. The required rate of return on these bonds has now risen to 16 percent. What is the current value of this bond?

N: 15x 2= 30 I: 16%/2= 8 *PV: 549.6887 PMT: 8% x 1000= 80/2=40 FV: 1000

The price of a bond is $736.68, it has 16 years to maturity, a $1,000 face value, and pays an annual coupon of $100. What is the yield to maturity?

N: 16 *I: 14.2596 PV: 736.68 PMT: 100 FV: 1000

Assume that you wish to purchase a 20-year bond that has a maturity value of $1,000 and makes semiannual interest payments of $40. If you require an annual 10 percent rate of return on this investment, what is the maximum price you should be willing to pay for the bond?

N: 20 I: 10% *PV: 829.7287 PMT: 40 x2 =80 FV: 1000

What is the value of a bond with 20 years left to maturity, a coupon payment of $50 every 6 months, and a $1,000 face value if the yield to maturity is 8%?

N: 20 I: 8% *PV: 1,196.3629 PMT: 50 x 2= 100 FV: 1000

Fish & Chips Inc. has two bond issues outstanding, and both sell for $701.22. The first issue has an annual coupon rate of 8 percent and 20 years to maturity. The second has an identical yield to maturity as the first bond, but only 5 years until maturity. Both issues pay interest annually. What is the annual interest payment on the second issue?

N: 20 N: 5 I: 12 I: 12 PV: 701.22 PV: 701.22 *PMT: 8 x 1000= 80 PMT: 37.1155 FV: 1000 FV: 1000

If the YTM on the following bonds are identical except, what is the price of bond B? Bond A Bond B Face value $1,000 $1,000 Semiannual coupon $45 $35 Years to maturity 20 20 Price $1,098.96?

N: 20x 2= 40 N: 40 *I: 4 x 2 =8 I: 8/2=4 PV: 1098.96 Pv: 1098.96 PMT: 45x 2= 90 PMT: 35x 2=70 FV: 1000 FV: 1000

What is the coupon rate for a bond with three years until maturity, a price of $1,053.46, and a required rate of return of 6%?

N: 3 I: 6% PV: 1,053.46 *PMT: 79.999 FV: 1000

What is the yield to maturity of a bond with a coupon rate of 8%, semi-annual payments, current price of $960 and three years until maturity?

N: 3 x 2= 6 *I: 4.7826 PV: 960 PMT: 8% x 1000 =80/2 =40 FV: 1000

J&J Manufacturing just issued a bond with a $1,000 face value and a coupon rate of 7 percent. If the bond has a life of 30 years, pays annual coupons, and the yield to maturity is 9 percent what will the bond sell for?

N: 30 I: 9% PV: 794.5269 PMT: 7% x 1000= 70 FV: 1000

Delta Corporation has a bond issue outstanding with an annual coupon interest rate of 9 percent and 4 years remaining until maturity. The par value of the bond is $1,000.What is the current yield of the Delta Corporation bond is the bond currently sells for $713.75?

N: 4 I: PV: 713.75 PMT: 9% x1000= 90 FV: 1000 *Current yield: 90/ 713.75= 0.1261

What is the current yield of a bond with a 6% coupon, four years until maturity, and a price of $750?

N: 4 I: PV: 750 PMT: 6% x1000 =60 FV: 1000 *Current yield= 60/ 750= 0.0800

Macrohard, Inc. carry a 10% annual coupon, have a $1,000 face value, and mature in 4 years. Yield to maturity is 7%. What is the market value of Microhard's bonds?

N: 4 I: 7% *PV: 1101.6163 PMT: 10 x 1000= 100 FV: 1000

The $1,000 face value EFG bond has a coupon of 10% (paid semi-annually), matures in 4 years, and has current price of $1,140. What is the EFG bond's yield to maturity?

N: 4 x 2= 8 I: 3% (find first) PV: $1,140 PMT: $100/2= $50 FV: $1000 *Yield-to-maturity: 3% x 2= 6%

Cornerstone Industries has a bond outstanding that has a 7% coupon rate and a market price of $887.76. If the bond matures in 5 years, what is the yield to maturity on the bond?

N: 5 *I: 9.9577 PV: 887.76 PMT: 7% x 1000= 70 FV: 1000

The Whitesell athletic Corporation's bonds are currently selling for $900. Each has a face value of $1,000 and a 10% coupon paid semi-annually until maturity 5 years from now. What is the bond's current yield?

N: 5 I: 12.8315 PV: 900 PMT: 10% x 1000= 100 FV: 1000 *Current yield: 100/900= 0.111

The $1,000 face value ABC bond has a coupon rate of 6%, with interest paid semi-annually, and matures in 5 years. If the bond is priced to yield 8%, what is the bond's value today?

N: 5 x 2 = 10 I: 8% /2= 4% *PV: $918.89 PMT: $60/2 = $30 FV: $1000

The NOP bond has an 8% coupon rate (semi-annual interest), a maturity value of $1,000, matures in 5 years, and a current price of $1,200. What is the NOP's yield-to-maturity?

N: 5 x 2= 10 I: 1.797% (find first) PV: $1,200 PMT: 8/2= 4x 10= $40 FV: $1000 *Yield-to-maturity: 1.797% x 2= 3.594%

The HIJ bond has a current price of $800, a maturity value of $1,000, and matures in 5 years. If interest is paid semi-annually and the bond is priced to yield 8%, what is the bond's annual coupon rate?

N: 5 x 2= 10 I: 8%/2 = 4% PV: $800 PMT: $15.34 (find first) FV: $1000 *Coupon rate= $15.34 x 2 = $30.68

Cold Boxes Ltd. has $1,000 par value bonds outstanding. The yield to maturity on these bonds is currently 10 percent. The bonds mature in 5 years, pay interest semi-annually, and have a current market value of $768.35 per bond. What is the annual coupon interest rate?

N: 5x 2=10 I: 10%/2 =5 PV: 768.35 *PMT: 20.0003 FV: 1000

The Whitesell Athletic Corporation's bonds have a face value of $1,000 and a 10% annual coupon, paid semiannually until maturity 5 years from now. What is the current yield that would be reported in the Wall Street Journal if the yield to maturity is 8%? Hint, current yield is stated on an annual basis.

N: 5x2= 10 I: 8%/2= 4 PV: 1081.1090 PMT: 10 x 1000= 100/2 =50 FV: 1000 *Current yield: 50/ 1081.1090

You are evaluating a 9% coupon corporate bond with a face value of $1000. The bond matures in six years. The yield to maturity is 6.8% and the coupon is paid annually. a. What should be the current price of the bond?

N: 6 I: 6.8% *PV: 1,105.5145 PMT: 9% x 1000= 90 FV: $1000

Neverwho Co. has 7 percent coupon bonds on the market with eight years left to maturity. The bonds make annual payments. If the bonds currently sell for $902.25, what is YTM?

N: 8 *I: 8.7497 PV: 902.25 PMT: 7 x 1000= 70 FV: 1000

Whitesell Athletic Corporation's bonds have a face value of $1,000 and a 9% coupon; the bonds mature in 8 years. What is the current yield on the bonds assuming that the required rate of return is 7%?

N: 8 I: 7% PV: 1119.4260 PMT: 9% x 1000= 90 FV: 1000 *Current yield: 90/1119.4260= 0.0804

The required rate of return on a bond issued by Who LTD is 11 percent. "Who" has a bond issue outstanding that pays interest semiannually, is selling for $845 and matures in 8 years. What is the annual coupon rate on the outstanding bond?

N: 8 x 2= 16 I: 11%/2= 5.5 PV: 845 *PMT: 40.1847 FV: 1000

Consider a $1,000 par value bond with a 7 percent annual coupon. The bond pays interest annually. There are 9 years remaining until maturity. What is the current yield on the bond assuming that the required return on the bond is 10 percent?

N: 9 I: 10 PV: 827.2293 PMT: 7x 1000= 70 FV: 1000 *Current yield: 70/827.2293= 0.0846

What is the yield to maturity of a zero-coupon bond selling for $493.63, with nine years to maturity? Assume semiannual compounding.

N: 9 x 2 = 18 *I: 4 (3.999) x2 = 8% PV: -493.63 PMT: 0 FV: 1000

A bond with a fixed coupon rate has the following relationship between its market price and the market required return other things being equal

Negative

The Dallas Development Corporation is considering the purchase of an apartment project for $100,000. They estimate that they will receive $15,000 at the end of each year for the next 10 years. At the end of the 10th year, the apartment project will be worth nothing. If the company insists on a 9 percent return compounded annually on its investment, is this a good investment?

No you pay more than its worth

The E. Harris Company issued bonds in September of 2003. When issued, the bonds had 20 years to maturity, a coupon rate of 7.5% and sold for their face value of $1,000. Now, in September of 2013, the bond price has risen to $1,110.40. What is the current yield to maturity (assume that the bonds make annual coupon payments)?

Original N: 20 I: PV: -1,110.40 PMT: 7.5 x10= 75 FV: 1000 Current yield N: 10 *I: 6 PV: -1,110.40 PMT: 75 FV: 1000

*Here are the expected returns from two stocks: Probabilities A B .5 20% -11% .1 10% 5% -4% 18%

Probability: .4 1. If you form a portfolio with 40% of A and 60% of B, what is the expected return for this portfolio? .4(.20)+.6(-.11)= 1.4 .4(.10)+.6(.5)= 7.0 .4(-.04)+.6(.18)= 9.2 .5 x 1.4 = .7 .1 x 7.0 = .7 .4 x 9.2 = 3.68 Expected return = 5.08% (1.4-5.08)2 x .5= (0.7-5.08)2 x .1= (9.2-5.08)2 x .4= var= 13.92 2. What is the standard deviation of this portfolio? = 3.72%

If you knew the required rate for BBI was 17%, and with the same Beta (2.3) and risk for being in stocks of 7%, what would be the risk free rate in this scenario?

RF + 2.3 (7%)= 17% RF= .9

Which of the following statements is most incorrect?

Sinking fund provisions do not require companies to retire their debt; they only establish "targets" for the company to reduce its debt over time.

As a gift from your parents, you just received $50,000 for your education for the next four years. You can earn an annual rate of 8% on your investments. How much can you withdraw each year (end of year) just using up the $50,000?

$15,096

A gallon of milk cost $3.59 today. How much will it cost you to buy a gallon of milk for your grandchildren in 35 years if inflation averages 5% per year?

$19.80

Your grandmother is offered a series of $6,000 starting one year from today. The payments will be made at the end of each of the next 10 years. Similar risk investments are yielding 7%. What should she pay for the investment?

$42,141

You get a twenty-year amortized loan of $100,000 with a 5% annual interest rate. What are the annual payments?

$8,024

Calculate the price of a seven-year $1000 bond with a 5% coupon rate and a yield-to-maturity of 7% with annual coupon payments.

$892.21

Which of the following statements is most correct?

-Sinking fund provisions sometimes work to the detriment of bondholders--particularly if interest rates have declined over time. -If interest rates have increased since the time a company issues bonds with a sinking fund provision, the company is more likely to retire the bonds by buying them back in the open market, as opposed to calling them in at the sinking fund call price.

You just purchased a 15-year bond with an 11 percent annual coupon. The bond has a face value of $1,000 and a current yield of 10 percent. Assuming that the yield to maturity of 9.7072 percent remains constant, what will be the price of the bond one year from now?

1. Bond Today N: 15 I: 9.7072 (yield-to-maturity) PV: $1,099.99 PMT: 1000 x 11%= 110 FV: $1000 2. Because it's in one year. You have to decrease n, the year by 1 N: 14 I: 9.7072 *PV: $1,097 (1096.7758) PMT: 110 FV: $1000

There is a 50% probability that the Plum company sales will be $12 million next year, a 20% chance they will be $7 million and a 30% chance they will be $3 million.

1. How much should Plum expect to sell? .5 x 12M =6M .2 x 7M =1.4M .3 x 3M =900,000 1.0 8.3M .5(12M-8.3M)2 .2(7M-8.3M)2 .3(3M-8.3M)2 var=15.61M 2. What is the standard deviation of their sales? Square root of 15.61= 3.95

You want to know how much your lottery ticket is worth. If it costs $1 and your probability of winning the $30 million dollar prize is 1 in 62,000,000, what is it worth?

1/62M x 30M = 30M/62M = 0.4838

Which of the following is NOT a determinant of interest rates:

All of the above are determinants (inflation, a liquidity premium, a default premium, a maturity risk premium)

Which of the following events would make it more likely that a company would choose to call its outstanding callable bonds?

A reduction in market interest rate

Which of the following statements is most correct?

All else equal, if a bond's yield to maturity increases, its price will fall.

Consider an investment that will pay $680 per month for the next 15 years and will be worth $28,000 at the end of that time. How much is this investment worth to you today at a 5.25 percent discount rate?

Between $10,001 and $25,000

You just purchased a 15-year bond with an 10 percent annual coupon. The bond has a face value of $1000 and a current yield of 10.75 percent. Assuming that the yield to maturity of 9.60 percent remains constant, what will be the price of the bond ten years from now?

Between $996.01 and $1080

Other types (features) of bonds

Convertible bond: may be exchanged for common stock of the firm, at the holder's option Warrant: long-term option to buy a stated number of shares of common stock at a specified price Putable bond: allows holder to sell the bond back to the company prior to maturity Income bond: pays interest only when interest is earned by the firm Indexed bond: interest rate paid is based upon the rate of inflation

The KLM bond has a 8% coupon rate (with interest paid semi-annually), a maturity value of $1,000, and matures in 5 years. If the bond is priced to yield 6%, what is the bond's current price?

N: 10 I: 6%/2= 3% *PV: $1,085 PMT: $40 FV: $1000

You intend to purchase a 10-year, $1,000 face value bond that pays interest of $60 every 6 months. If your nominal annual required rate of return is 10 percent with semiannual compounding, how much should you be willing to pay for this bond?

N: 10 x 2= 20 I: 10%/2= 5% *PV: $1,124.62 PMT: $60 FV: $1000

A corporate bond with a $1,000 face value pays a $50 coupon every six months. The bond will mature in 10 years, and has a nominal yield to maturity of 9 percent. What is the price of the bond?

N: 10 x 2= 20 I: 9%/2= 4% *PV: $1,065.04 PMT: 50 FV: $1000

A corporate bond with a $1,000 face value pays a $50 coupon every six months. The bond will mature in ten years, and has a yield to maturity of 9 percent. What is the price of the bond?

N: 10 x 2= 20 I: 9%/2= 4.5 *PV: 739.8413 PMT: 50/2 =25 FV: 1000