BUS 173A Exam #2
What are the two formulas for computing YTM?
YTM= CY+CGY YTM=r+IP+DRP+LP+MRP
You plan to make a total of 5 deposits of $100 each, one every 6 months, with the first payment being made today. The bank pays a nominal interest rate of 12% but uses semiannual compounding. You plan to leave the money in the bank for 10 years. How much will be in your account after 10 years?
FV10= 1432.02
You are looking at two savings accounts. One pays 5.25%, with daily compounding. The other pays 5.3% with semiannual compounding. Which account should you use?
You should use account 1 because it has a higher EAR
Net sales last year were $525 million. If sales grow at 7.5% per year, how large (in millions) will they be 8 years later?
$936.33
An 8% semiannual coupon bond matures in 5 years. The bond has a face value of $1,000 and a current yield of 8.21%. What are the bond's price and YTM?
price=coupon/cy= 80/0.0821= 974.42 YTM=4.32*2=8.64%
Christopher receives an ordinary annuity of $1000 paid quarterly for 10 years (interest rate is 8%). What is the present value of the annuity?
$27355.48
How much must Manual have in his investment account on his 65th birthday so that he can withdraw $30,000 on that birthday and on each of the next 19 birthdays (interest rate is 8%)?
$318,108
HOA invests $4500 today and $2000 at the end of next year (year 2). What is the total amount in HOA's account at the end of year 3 if annual interest is 6%?
$7479.57
A bond has a $1,000 par value, 10 years to maturity, and a 7% annual coupon and sells for $985. 1. What is its yield to maturity? 2. Assume that the yield to maturity remains constant for the next 3 years. What will the price be 3 years from today?
1. 7.22 2. 988.46
The yield to maturity is:
1. The rate that equates the price of the bond with the discounted cash flows 2. The expected rate to be earned if the bond is held to maturity 3. The rate that is used to determine the market price of the bond 4. Equal to the current yield for bonds priced at par
Your great aunt Matilda put some money in an account for you on the day you were born. This account pays 8% interest per year. On your 21st birthday the account balance was $5,033.83 1.) What is the amount of money that your great aunt Matilda originally put in the account? 2.) What is the amount of money that would be in the account if you left the money there until your 65th birthday?
1.) PV=1000 2.) FV= 148779.85
What is the price of a 5% annual coupon bond, with a $1,000 face value, which matures in 3 years? Assume a required return of 2.15%.
1081.95
What is the price of a 3 year 5% coupon bond if the required rate of return is 2.15% and the coupons are paid semi-annually? Par value is $1000.
1082.37
A company earned $1.50 per share five years ago. Its earning this year were $3.20. What was the growth rate in earnings per share (EPS) over the 5-year period?
16.36%
Your bank pays 4% interest annually. You have $500 invested in the bank. How long will it take for your funds to double?
17.67
Jessica has just won a lottery jackpot. She will get the money in 26 equal investments of $307,692 each, starting immediately. The Li Li Finance company offers her $200000 cash if she signs the payments over to them. What interest is the Li Li Finance Company earning on this offer?
17.9%
The coupon rate of a floating rate note that makes semi-annual interest payments in June and December is expressed as a six-month Libor plus 150 bps. In December, the six-month Libor is 3.25%. The interest rate that will apply to the payment due in June will be ___________. In June, the six-month Libor decreases to 3.15%. The interest rate that will apply to the payment due in December will decrease to __________.
4.75 (3.25+1.5); 4.65(3.15+1.5)
A perpetuity pays $85 per year and costs $950. What is the rate of return?
8.95%
You are comparing two annuities which offer monthly payments for ten years. Both annuities are identical with the exception of the payment dates. Annuity A pays on the first of each month while annuity B pays on the last day of each month. You know that Annuity ___ has higher present value and Annuity ___ has higher future value.
A,A
Andy deposited $3,000 this morning into an account that pays 5 percent interest, compounded annually. Barb also deposited $3,000 this morning at 5 percent interest, compounded annually. Andy will withdraw his interest earnings and spend it as soon as possible. Barb will reinvest her interest earnings into her account. Given this, which one of the following statements is true?
Barb will earn more interest in Year 2 than Andy
A ______________ is a debt security that allows bond issuers to borrow money from investors. It is a contract that legally obligates the issuer to make specified payments to the bondholder at specified future dates. It is known as the fixed-income security.
Bond
A company has bonds on the market with 11.5 years to maturity, a YTM of 7.6%, and a current price of $1,060. The bonds make semiannual payments. What must the coupon rate be on these bonds? Par value is $1000.
COUPON RATE= coupon/par=41.96*2/1000=8.39%
How is the value of a callable bond determined?
Call price
duration
Callable bonds gives the issuer the right to redeem all or part of the bond before the maturity date. The protect the issuer against a decline in interest rates. This decline can come either from market interest rates falling or from the issuer's credit quality improving. If market interest rates fall or credit quality improves, the issuer of a callable bond has the right to replace an old, expensive bond issue with a new, cheaper bond issue. Callable bonds present invest with a higher level of investment risk than non-callable bonds. Therefore, callable bonds have to offer a higher yield and sell at a lower price than otherwise similar non-callable bonds. Convertible bonds give their owners the right to exchange the bonds for a pre-specified number of shares of stock anytime up and including the maturity date of bond.
The interest earned on both the initial principal and the interest reinvested from prior periods is called:
Compound interest
___________________ is the percentage of par value that is paid out as interest. Can be fixed or floating.
Coupon rate
Suppose a five-year, $1000 bond with annual coupons has a price of $900 and a yield to maturity of 6%. What is the bond's coupon rate?
Coupon rate=coupon/par=36.26/1000=3.63
A credit card company quotes you an APR of 18.9 percent. What is the actual rate of interest you are paying if interest is computed monthly?
EAR=20.63%
You want to purchase a motorcycle 4 years from now, and you plan to save $3,500 per year, beginning immediately. You will make 4 deposits in an account that pays 5.7% interest. Under these assumptions, how much will you have 4 years from today
FV= 16,111.99
Ana has $200 to invest. If she invests the money at 8% compounded semiannually for 3 years, what is the future value?
FV= 253.06
At a rate of 6.5%, what is the future value of the following cash flow stream? Years 0 1 2 3 4 CF's 0 75 225 0 300
FV= 645.79
Your Aunt Ruth has $500,000 invested at 6.5%, and she plans to retire. She wants to withdraw $40,000 at the beginning of each year, starting immediately. How many years will it take to exhaust her funds, i.e., run the account down to zero?
N= 22.86
If a bank compounds savings accounts quarterly, the annual percentage rate will exceed effective annual rate.
False
You are determined to purchase a $250,000 home without incurring any debt. You plan to save $2,500 a quarter for this purpose and expects to earn 6.65 percent, compounded quarterly. How long will it be until you can purchase a home?
N=59.39 quarters = 14.85 years
If market interest rates rise, the value of bonds________.
Goes down
A bond will sell at a discount when the yield to maturity is _________ than the coupon rate.
Higher
Sixty years ago, your mother invested $4,500. Today, that investment is worth $430,065.11. What is the average annual rate of return she earned on this investment?
I=7.90
You just paid $480,000 for an annuity that will pay you and your heirs $15,000 a year forever. What rate of return are you earning on this policy?
I=PMT/PV=15000/480000=3.125%
You buy a zero coupon bond at the beginning of the year that has a face value of $1,000, a YTM of 7%, and 25 years to maturity. If you hold the bond for the entire year, how much in interest income will you have to declare on your tax return? Assume semiannual compounding
Implicit interest= 191.81-179.05= 12.76
Bond ________________ is the legal agreement between the issuer of a bond and its bondholders that sets forth the obligations of the borrower and the rights of the bondholders.
Indenture
Explain interest rate risk? Define inverse effect, maturity effect, coupon effect, and convexity effect?
Interest rate risk is the risk that the price of a debt security will fall as a result of increases in interest rates. Interest effect is when the bond price is inversely related to market interest rate (YTM). When YTM increases, bond prices decreases. Maturity effect is when all other things equal, the longer the time to maturity, the greater the interest rate risk. Coupon effect is when all other things being equal, the lower the coupon rate, the greater the interest rate risk. Convexity effect is when all other things being equal, the percentage price change is greater (in absolute value) when the market discount rate goes down than when it goes up.
current yield
It's equal to the bond's annual coupon divided by the bond's price expressed as a percentage. It's the yield from interest payments. Bond's annual return from its interest payment
Your aunt has $500,000 invested at 5.5%, and she now wants to retire. She wants to withdraw $45,000 at the beginning of each year, beginning immediately. She also wants to have $50,000 left to give you when she ceases to withdraw funds from the account. For how many years can she make the $45,000 withdrawals and still have $50,000 left in the end?Begin (annuity due)
N= 17.22
Suppose you inherited $275,000 and invested it at 8.25% per year. What is the maximum amount you could withdraw at the end of each of the next 20 years?
PMT= 28,532.45
You must make a payment of $1,432.02 in 10 years. To get the money for this payment, you will make five equal deposits, beginning today and for the following 4 quarters, in a bank that pays a nominal interest rate of 12% with quarterly compounding. How large must each of the five payments be?
PMT=93.07
What's the present value of $1,525 discounted back 5 years if the appropriate interest rate is 6%, compounded monthly?
PV= 1130.59
You just won the lottery! As your prize you will receive $1,200 at the end of each month for 100 months. If you can earn 18% per year on your money, what is this prize worth to you today?
PV= 61,949.64
You buy an annuity which will pay you $12,000 a year for ten years. The payments are paid on the first day of each year. What is the value of this annuity today at a 7% discount rate?
PV= 90,182.79
You would like to establish a trust fund that will provide $50,000 a year forever for your heirs. The trust fund is going to be invested very conservatively so the expected rate of return is only 2.75%. How much money must you deposit today to fund this gift for your heirs?
PV= PMT/I = 50000/0.0275 = 1,818,181.82
Your father invested a lump sum 28 years ago at 4.05 percent annual interest. Today, he gave you the proceeds of that investment, totaling $48,613.24. How much did your father originally invest?
PV=15994.7
You have a sub-contracting job with a local manufacturing firm. Your agreement calls for annual payments of $50,000 for the next five years. At a discount rate of 12%, what is this job worth to you today?
PV=180,238.81
Your great aunt left you an inheritance in the form of a trust. The trust agreement states that you are to receive $2,500 on the first day of each year, starting immediately and continuing for 20 years. What is the value of this inheritance today if the applicable discount rate is 4.75 percent?
PV=33338.44
Your car dealer is willing to lease you a new car for $190 a month for 36 months. Payments are due on the first day of each month starting with the day you sign the lease contract. If your cost of money is 6.5 percent, what is the current value of the lease?
PV=6232.80
Bond prices are quoted as a percentage of _______.
Par value
_________________ is the amount of principal the issuer must pay back to the bondholder on the maturity date. In general, corporate bonds are issued in denominations of $1,000. This amount can be much greater for government bonds.
Par value
A bond quote above 100 means that the bond is trading above par and is a ______________ bond, while a bond quote below 100 means that the bond is trading below par and is ________________ bond.
Premium; discount
The time value of money concept can be defined as:
The relationship between a dollar to be received in the future and a dollar today
Date 5 on the timeline is the end of the fifth year and the beginning of the sixth year
True
Starting to invest for retirement increases the benefits of compound interest
True
The greater the number of compounding periods within a year, then: 1.) the greater the future value of lump sum investment at time 0, and 2.) the smaller the present value of a given lump sum to be received at some future date
True
The present value of a future sum decreases as either the discount rate or the number of periods per year increases, other things held constant
True