FNCE10001 Chapter Notes - Chapter 5: Annual Percentage Rate, Effective Interest Rate, Interest Rate

I. Fill in the blank using a number of terms listed below (@1 point). Annuity due, Asset Mgmt ratio, Call, Comparisons, Comparative ratio analysis, Corporation, Covered, Current Ratio, DSO, Du Pont Equation , Equal, Future performance, Greater, Higher, In-the-money, Less, Liquidity, Lower, Option, Ordinary Annuity, Out-of-the-money, Percentage, Perpetuity, Put, PV, Quick, Reduced, TIE, TATO, Trend Analysis, Writer 11. The payment or receipt of equal amounts, at the end of a series of equal periods, for a specified amount of time is called a(n) _______________. 12. When a loan is amortized over a five year term, the amount of interest paid is ________________ each year. 13. You have just won a $5 million lottery to be received in twenty annual equal payments of $250,000. What will happen to the present value of your winnings if the interest rate increases? It will be worth _________________. 14. The more frequent the compounding the _________________ the effective interest rate. 15. More frequent compounding results in _______________ future values and _______________ present values than less frequent compounding at the same nominal interest rate. 16. A(n) _______________ is a financial instrument that agrees to pay an equal amount of money per period into the indefinite future (i.e. forever). 17. A(n) _________________ is a contract which gives its holder the right to buy(or sell) an asset at some predetermined price within a specified period of time. 18. The seller of an option is called the option __________________. 19. An investor who writes call options against stock held in his or her portfolio is said to be selling _______________ options. 20. When the exercise price exceeds the current stock price, a call option is said to be _____________________; however, when the exercise price is less than the current price of the underlying stock, a call option is _________________. 21. An option which gives you the right to sell a stock at a specified price within some future period is called a(n) ______________ option.

Assume that you are nearing graduation and that you have appliedfor a job with a local bank. As part of the bank’s 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 acompany’s 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 annually—for example, every 6months, or semiannually—holding 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 risky—that 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?

It's due tommorow and need help with these following problems.

Please solve the following problems. Show all relevant time lines and calculations and make sure to highlight the final answer to the question. Where MS Excel is required, please either cut and paste the spreadsheet where it belongs or staple the printout directly from MS Excel. For spreadsheets that are too long to print, just include a sample printout of the first and last pages. Note that some questions require a written answer, not just a number.

Vanilla Ice Co. bonds pay an annual coupon rate of 10% and have 5 years to maturity. If investors' required rate of return is now 8% on these bonds…

Will the bonds be selling at a premium or a discount with respect to their $1000 face value? Why?

b. What is the price of the bonds?

Austin Power Co. bonds have a 14% annual coupon rate. Interest is paid semi-annually. The bonds have a par value of $1,000 and will mature 10 years from now. If the (annual) required rate of return is 12%, what is the price of the Austin Power bonds? [Hint: you need to convert your coupon rate, your number of periods, n, and your req. rate of ret. to a semi-annual basis.]

Consider a $1,000 par value bond with a 9 percent annual coupon that is currently selling for $943. The bond pays interest annually. There are 15 years remaining until maturity.

What is the size of the annual coupon payments?

What is the current yield on the bond?

A preferred share of Phillips, Co. is currently selling for $65.00 on the New York Stock Exchange. If this instrument pays a dividend of $5 a year, what is its yield?

Assume that you plan to buy a share of IBM stock today and to hold it for 2 years. Your expectations are that you’ll receive a dividend of 19.00 at the end of Year 1 and a dividend of $19.25 at the end of Year 2. In addition, you expect to sell the stock for $150 at the end of Year 2. If your expected rate of return is 11 percent, how much should you be willing to pay for this stock today?

A share of common stock has just paid a dividend of $2.00. If the expected long-run growth rate for this stock is 15 percent, and if investors require a 19 percent rate of return, what is the price of the stock?

What would be the interest earned on a $6,000 deposit during the second year of its life if no money is withdrawn from the bank during that time, and the deposit pays an annual interest rate of 2.5 percent, with annual compounding?

Using excel, build a monthly amortization table for a 30-year mortgage on a $350,000 home, no money down. Use 7% as the yearly interest on the loan.

Using the amortization table you built for Question 8, answer the following questions.

How much money will you still owe on the loan after making one full year of payments?

How much money will you still owe on the loan after making 10 full years of payments?

If you want to refinance after 15 years of making payments, how much financing would you need to secure from your bank to do so?

How much money can you expect to pay in interests alone during the 30 year life of the mortgage?

You plan to purchase a $100,000 house using a 30-year mortgage obtained from local credit union. The mortgage rate offered to you is 8.25%. You will make a down payment of 20% of the purchase price.

Calculate your monthly payments on this mortgage.

Calculate the amount of interest and, separately, principal paid in the 25^th payment.

Calculate the amount of interest and, separately, principal paid in the 225^th payment.

Calculate the amount of interest paid over the life of this mortgage.

You plan to purchase a house for $115,000 using a 30-year mortgage from your local bank. You will make a down payment of 20% of the purchase price.

Your bank offers you the following two options for payment:

Option 1: Mortgage rate of 9% and zero discount points.

Option 2: Mortgage rate of 8.85% and two discount points.

Which option would you choose?

Your bank offers you the following two options for payment:

Option 1: Mortgage rate of 10.25% and 1 discount point.

Option 2: Mortgage rate of 10% and 2.5 discount points.

Which option would you choose? [Hint: consider only the incremental costs and benefits of Option 2 with respect to Option 1]

You just got a promotion and you are now taking home $75,000 a year before taxes. You are thinking about upgrading your home and moving to a nicer neighborhood. You’ve been living for the past six years in a 1,300 square foot, 3 bed/2 bath home, currently valued at $137,000. Thanks to the strong capital appreciation of the past few years, you estimate that after liquidating the mortgage and covering realtor fees, you’ll be able to walk away with $40,000, which you intend to use as down payment on your new home. Your debt payments ratio is only 7% and your credit rating is 700, so qualifying for a loan won’t be a problem. The best bank rate you’ve found is 5.9% fixed for a 30 year mortgage.

Ignoring mortgage insurance premiums, homeowner’s insurance premiums, and property tax obligations, how much of a home could you afford?

Would your mortgage be considered conforming or non-conforming?

Do you think you’ll be required to obtain private mortgage insurance? Why?