FIN 300 Lecture Notes - Lecture 2: Effective Interest Rate, Annual Percentage Rate, Jargon

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12 Oct 2016

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When we look at an interest rate such as 10% per year compounded semi-annually it does not actually mean 10% per year it really means 5% every 6 months. We just like to quote rates on an annual basis so the 5% number just gets multiplied by 2 (i. e. two. Another example would be a credit card company that is charging 24% per year compounded monthly on over due amounts. Again they are not charging 24% per year but 2% every month. It turns out that 24% per year and 2% per month are not the same thing. It is important that we specify the compounding frequency when quoting interest rates they are the units of the interest rate. Almost all interest rates are quoted as rates per year. But it is the compounding frequency that represents the units of the interest rate. If i don"t specify the compounding frequency its like telling you the temperature outside is.

Related Questions

All:

Everyone today has to be concerned about being able to retire comfortably when they keep telling us that Social Security will be bankrupt in 2037, a mere 22 years from now, and that it is an entitlement, not something that we and our employers all paid into since we got our first job.

A retirement planner is attached to this message so you can estimate how much money you will need to save to be able to do the things most retirees want to do when they are no longer working.

Then provide your calculations to the class and make a statement as to what you think and if you can achieve it?

For Week 3, please turn in the answers to the following questions:

1. Define the following terms as they apply to bonds:

a. Face value

b. Maturity date

c. Coupon interest (including coupon interest rate)

d. Current yield

e. Yield to maturity (YTM)

f. Yield to call (YTC)

g. Call premium

2. What are âZero-couponâ bonds?

3. Suppose you see the following bond price quote in the newspaper:

McDonalds 5.7% 2039â¦â¦..122.733

What can you tell about this bond from reading the price quote?

4. (calculating the present value of a bond) If a corporate bond with a face value of $1,000 has 24 years to go until it matures, has a coupon interest rate of 5.7% and a yield to maturity (YTM) of 4.201%, what should be its price in the bond market (ie, PV)?

5. (calculating the current yield of a bond) If a corporate bond with a face value of $1,000 has 24 years to go until it matures, has a coupon interest rate of 5.7% and a market price of $1,223.92, what is its current yield?

6. (calculating the YTM of a bond) If a corporate bond with a face value of $1,000 has 24 years to go until it matures, has a coupon interest rate of 5.7% and a market price of $1,223.92, what is its yield to maturity (YTM)?

7. (calculating the YTC of a bond) Assume a callable corporate bond with a face value of $1,000, a coupon interest rate of 5.7%, a market price of $1,223.92, and a call premium of 6%. Assume also that the bond has 24 years to go until it matures, but it is callable after 14 years. What is the bondâs yield to call (YTC)?

8. (calculating the present value of a bond with semi-annual coupon interest payments) If a corporate bond with a face value of $1,000 has 24 years to go until it matures, has a coupon interest rate of 5.7%, paid semiannually, and has a yield to maturity (YTM) of 4.2%, what should be its price in the bond market (ie, PV)?

9. (calculating the YTM of a bond with semiannual interest payments) If a corporate bond with a face value of $1,000 has 24 years to go until it matures, has a coupon interest rate of 5.7%, paid semiannually, and has a market price of $1,223.92, what is its yield to maturity (YTM)?

10. Define the following terms as they apply to interest rates:

a. The real risk-free rate (r*)

b. The nominal risk-free rate (Rrf)

c. The inflation premium (IP)

d. The default risk premium (DRP)

e. The liquidity premium (LP)

f. The maturity risk premium (MRP)

11. Assume the real risk-free rate is 1%. Assume also that inflation is expected to be 1% in the coming year (year 1), 2% in the next year after that (year 2), and 3% in the year after that (year 3). Assume also that the default risk premium, the liquidity premium, and the maturity risk premium are 0%. Given these conditions, what would be the yield on three-year treasury bonds today?

12. Suppose the First Bank of St Louis was offering the following rates on certificates of deposit (CDs) this week:

Maturity Rate

3 month 1.50%

6 month 1.75%

1 year 2.00%

2 year 2.25%

3 year 2.50%

5 year 2.75%

10 year 3.00%

20 year 3.15%

a. Plot the above data on a yield curve. Label the graph and the axes appropriately.

b. Comment on the implications of this curve to you, as a potential investor in CDs.

End of assignment questions

(see answers to numerical problems on the next page)

Answers to numerical problems:

Question 4: $1,223.92

Question 5: 4.66%

Question 6: 4.2%

Question 7: 3.92%

Question 8: $1,225.44

Question 9: 4.21%

Question 11: 3.0%

The payment made each period on an amortized loan is constant, and it consists of some interest and some principal. The closer we are to the end of the loan's life, the smaller the percentage of the payment that will be a repayment of principal.

a. True
b. False

2. The market value of any real or financial asset, including stocks, bonds, or art work purchased in hope of selling it at a profit, may be estimated by determining future cash flows and then discounting them back to the present.

a. True
b. False

3. A bond has a $1,000 par value, makes annual interest payments of $100, has 5 years to maturity, cannot be called, and is not expected to default. The bond should sell at a premium if interest rates are below 10% and at a discount if interest rates are greater than 10%.

a. True
b. False

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

a. Market interest rates decline sharply.

b. Market interest rates rise sharply.

c. Inflation increases significantly.

d. The company's financial situation deteriorates significantly.

e. The company's bonds are downgraded.

5. A 15-year bond has an annual coupon rate of 8%. The coupon rate will remain fixed until the bond matures. The bond has a yield to maturity of 6%. Which of the following statements is CORRECT?

a. If market interest rates remain unchanged, the bond's price one year from now will be lower than it is today.

b. The bond is currently selling at a price below its par value.

c. If market interest rates decline, the price of the bond will also decline.

d. If market interest rates remain unchanged, the bond's price one year from now will be higher than it is today.

e. The bond should currently be selling at its par value.

6. Which of the following statements is CORRECT?

a. The expected return on a corporate bond will generally exceed the bond's yield to maturity.

b. If a bond's coupon rate exceeds its yield to maturity, then its expected return to investors exceeds the yield to maturity.

c. All else equal, senior debt generally has a lower yield to maturity than subordinated debt.

d. Under our bankruptcy laws, any firm that is in financial distress will be forced to declare bankruptcy and then be liquidated.

e. An indenture is a bond that is less risky than a mortgage bond.

7. Your investment account pays 6.8%, compounded annually. If you invest $5,000 today, how many years will it take for your investment to grow to $9,140.20?

Select the correct answer.

a. 10.47

b. 11.77

c. 9.17

d. 13.07

e. 7.87

8. 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?

a. $16,918

b. $19,584

c. $16,112

d. $17,763

e. $18,652

9. Suppose you earned a $135,000 bonus this year and invested it at 8.25% per year. How much could you withdraw at the end of each of the next 20 years?

Select the correct answer.

a. $14,006.84

b. $13,994.04

c. $13,997.24

d. $14,000.44

e. $14,003.64

10.Your older brother turned 35 today, and he is planning to save $30,000 per year for retirement, with the first deposit to be made one year from today. He will invest in a mutual fund that's expected to provide a return of 7.5% per year. He plans to retire 30 years from today, when he turns 65, and he expects to live for 25 years after retirement, to age 90. Under these assumptions, how much can he spend each year after he retires? His first withdrawal will be made at theend of his first retirement year.

Select the correct answer.

a. $119,069

b. $119,090

c. $119,076

d. $119,097

e. $119,083

11. Rogoff Co.'s 15-year bonds have an annual coupon rate of 9.5%. Each bond has face value of $1,000 and makes semiannual interest payments. If you require an 11% nominal yield to maturity on this investment, what is the maximum price you should be willing to pay for the bond?

Select the correct answer.

$888.91

$882.64

$886.82

$891.00

$884.73

12. Haswell Enterprises' bonds have a 10-year maturity, a 6.25% semiannual coupon, and a par value of $1,000 . The going interest rate (r_d) is 9.75%, based on semiannual compounding. What is the bond's price?

Select the correct answer.

$782.32

$787.80

$779.58

$785.06

$790.54

tanrhinoceros524

Assume that you are nearing graduation and that you have appliedfor a job with a local bank. As part of the bankâs evaluationprocess, you have been asked to take an examination that coversseveral financial analysis techniques. The first section of thetest addresses time value of money analysis. See how you would doby answering the following questions:

a. Drawcash flow time lines for (1) a $100 lump-sum cash flow at the endof Year 2, (2) an ordinary annuity of $100 per year for threeyears, (3) an uneven cash flow stream of $50, $100, $75, and $50 atthe end of Years 0 through 3.

b. (1)What is the future value of an initial $100 after three years if itis invested in an account paying 10%annual interest?

(2) What is the present value of $100 to bereceived in three years if the appropriate interest rate is10%?

c. Wesometimes need to find how long it will take a sum of money (oranything else) to grow to some specified amount. For example, if acompanyâs sales are growing at a rate of 20%per year, approximatelyhow long will it take sales to triple?

d. Whatis the difference between an ordinary annuity and an annuity due?What type of annuity is shown in the following cash flow time line?How would you change it to the other type of annuity?

0 1 2 3

100 100 100

e. (1)What is the future value of a 3-year ordinary annuity of $100 ifthe appropriate interest rate is 10%?

(2) What is the present value of the annuity?

(3) What would the future and present values be ifthe annuity were an annuity due?

f. What is the present value of the following uneven cash flow stream?The appropriate interest rate is 10%, compounded annually.

0 1 2 3 4

100 300 300 150

g. Whatannual interest rate will cause $100 to grow to $125.97 in 3years?

h. (1)Will the future value be larger or smaller if we compound aninitial amount more often than annuallyâfor example, every 6months, or semiannuallyâholding the stated interest rateconstant? Why?

(2) Define the stated, or quoted, or simple, rate,(r_SIMPLE), annual percentage rate (APR), the periodicrate (r_PER), and the effective annual rate(r_EAR).

(3) What is the effective annual rate for a simplerate of 10%, compounded semiannually? Compounded quarterly?Compounded daily?

(4) What is the future value of $100 after threeyears under 10%semiannual compounding? Quarterly compounding?

i. Will the effective annual rate ever be equal to the simple (quoted)rate? Explain.

j. (1) What is the value at the end of Year 3 of thefollowing cash flow stream if the quoted interest rate is 10%,compounded semiannually?

0 1 2 3

100 100 100

(2) What is the PV of the same stream?

(3) Is the stream an annuity?

(4) An important rule is that you should nevershow a simple rate on a time line or use it in calculations unlesswhat condition holds? (Hint: Think of annual compounding,when r_SIMPLE = r_EAR = r_PER.) Whatwould be wrong with your answer to parts (1) and (2) if you usedthe simple rate 10%rather than the periodic rater_SIMPLE/2 = 10%/2 = 5%?

k. (1)Construct an amortization schedule for a $1,000 loan that has a10%annual interest rate that is repaid in three equalinstallments.

(2) What is the annual interest expense for theborrower, and the annual interest income for the lender, duringYear 2?

l. Suppose on January 1 you deposit $100 in an account that pays asimple, or quoted, interest rate of 11.33463%, with interest added(compounded) daily. How much will you have in your account onOctober 1, or after 9 months?

m. Now suppose youleave your money in the bank for 21 months. Thus, on January 1 youdeposit $100 in an account that pays a 11.33463%compounded daily.How much will be in your account on October 1 of the followingyear?

n. Suppose someone offered to sell you a note that calls for a $1,000payment 15 months from today. The person offers to sell the notefor $850. You have $850 in a bank time deposit (savings instrument)that pays a 6.76649%simple rate with daily compounding, which is a7%effective annual interest rate; and you plan to leave this moneyin the bank unless you buy the note. The note is not riskyâthat is,you are sure it will be paid on schedule. Should you buy the note?Check the decision in three ways: (1) by comparing your futurevalue if you buy the note versus leaving your money in the bank,(2) by comparing the PV of the note with your current bankinvestment, and (3) by comparing the r_EAR on the notewith that of the bank investment.

o. Suppose the note discussed in part n, above, costs $850, but callsfor five quarterly payments of $190 each, with the first paymentdue in 3 months rather than $1,000 at the end of 15 months. Wouldit be a good investment?

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FIN 300 Lecture Notes - Lecture 2: Effective Interest Rate, Annual Percentage Rate, Jargon

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