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FHCE 2100 Lecture Notes - Lecture 30: Interest Rate, Negative Amortization, United States Treasury Security

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School
University of Georgia
Department
Financial Planning, Housing and Consumer Economics
Course
FHCE 2100
Professor
Dr.Kabaci

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Document Summary

Mortgage with an interest rate that will change or adjust from time to time. Typically, the rate on an arm will change every year after an initial period of remaining fixed interest rate. A hybrid arm loan is one that starts off with a fixed or unchanging interest rate, before switching over to an adjustable rate. Every twelve months, the interest rate is recalculated. The interest rate with this type of loan is tied to a financial index that can move up and down. This type of mortgage is preferred by those that need to get the lowest rate possible to be able to afford their mortgage payments. A very risky loan because your payment could potentially go up every year. The lender recalculates the interest rate every three years. This means that you will have the same interest rate and monthly payment for three years at a time before it changes.

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Related Questions

Alan recently joined Friendly Investment and Financing Options(FIFO) as a loan officer. FIFO is a national company thatspecializes in mortgage lending. One of Alan’s responsibilities isto increase the amount of mortgages FIFO initiates. In a meeting hehad with the CEO yesterday, Alan was told about a new mortgage thatFIFO intends to market. The new mortgage is called an optionadjustable rate mortgage, or an option ARM for short, and its mostattractive feature is that homeowners can choose to make relativelylow monthly payments at the beginning of the mortgage period.However, the payments increase significantly later in the life ofthe mortgage. In fact, depending on the amount the borrower choosesto pay early (hence, the term “option”), the amounts that must bepaid later could be substantial—as much as four to five times theinitial payments. In many cases, when a homeowner chooses to paythe minimum amount or an amount that he or she can afford, themortgage turns “upside down,” which means that the amount due onthe mortgage grows to an amount that is greater than the value ofthe house. The primary benefit of option ARMs to borrowers is thatsuch loans allow those who cannot afford the monthly paymentsassociated with conventional mortgages the opportunity to purchasehouses. A borrower with income that is lower than is needed toqualify for a conventional mortgage can borrow using option ARMs,choose an affordable (lower than conventional) payment in the earlyyears of the mrotgage, and then make the higher payments in lateryears, when their incomes presumably will be higher. Thus, optionARMs permit those who can’t afford conventional mortgages to buyhouses today that they otherwise couldn’t afford until years intothe future. Lenders such as FIFO like selling option ARMs becausethey can recognize as current revenues the monthly payments thatwould be required if the loans were conventional mortgages,regardless of the amounts that the borrowers opt to pay. In otherwords, companies can “book” revenues that will not be collected fora few years. Unlike most people, including many professionals, Alanunderstands the complexities of option ARMs. He knows that manyborrowers who choose such mortgages will lose their houses three tofive years after buying them because the payments increase sosignificantly after the low-payment option period expires thatthese borrowers cannot afford the new monthly payments. And,although they would like to refinance with conventional mortgages,often these homeowners do not have good enough credit. Thisscenario is quite disturbing to Alan. He would like to explain tohis customers in clear terms the possible pitfalls of option ARMs,but the CEO of FIFO has instructed Alan that he should provide onlythe information that is required by law and to follow companypolicy, which states that lending officers should provide basicprinted material, give simple advice, and answer questions thatmight provide negative information only when asked. Alan has a badfeeling about option ARMs. He knows that they are greatlending/borrowing tools when used as intended. He is afraid,however, that FIFO is more concerned about booking revenues thanabout the financial wellbeing of its customers (borrowers). Whatshould Alan do? How would you handle this situation if you wereAlan?

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 25th payment.

Calculate the amount of interest and, separately, principal paid in the 225th 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?

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,(rSIMPLE), annual percentage rate (APR), the periodicrate (rPER), and the effective annual rate(rEAR).

(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 rSIMPLE = rEAR = rPER.) Whatwould be wrong with your answer to parts (1) and (2) if you usedthe simple rate 10%rather than the periodic raterSIMPLE/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 rEAR 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?