Dr. P.V. Viswanath



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Pace University
Fin 301 Introduction to Financial Management
Summer 2005
Prof. P.V. Viswanath



Final Exam

  • Show all your computations and formulae; even if you use a calculator or a spreadsheet to get the answers, you must show the formula that you are using.  No points will be given if I don't see the formula and how you got your answer.  Make all your assumptions explicit.  If your approach is correct, you will get some credit, even if your arithmetic answer is wrong.  So concentrate on getting your logic right.
  • If you answer a question, I have the discretion to award you some points, even if you are completely wrong.  If you don't attempt the question at all, I can give you no points!  So attempt every question.
  • Any cheating or plagiarism will result in your getting zero credit for the exam.
  • One 8.5 x 11 sheet will be allowed, which may contain formulas only!  No worked out examples, nothing else.  Violation of this rule will be considered cheating.

1. (20 points) Pfizer Inc. has a beta of 0.433 according to Yahoo.

  1. If the return on the 10-yr Treasury bond is 4.075%, and you estimate the market risk premium to be 6% per annum, what is the required rate of return on Pfizer?
  2. According to Yahoo, the dividend paid last year was 72 cents per share. According to Yahoo, once again, the growth rate in earnings for next year is expected to be 8%. If you assume that dividends will increase at that rate for one more year (i.e. for the next two years), and thereafter at the rate of 3% forever, what should Pfizer stock sell at?

2. (20 points) Answer the following questions.

  1. Pfinzer Bros. has issued a bond with a coupon rate of 6% (semi-annual coupons) and a maturity of 10 years. If the yield to maturity of the bond is 8%, what is the price of the bond?
  2. Jastrow Inc. has issued a bond with a coupon rate of 7% (semi-annual coupons). Similar bonds can be obtained on the market with a yield-to-maturity of 8%. Would you buy the bond at par? Explain why or why not?

3. (15 points) You have bought a car for $20,000. Now it's time to pay for it! And you only have $2000 for a downpayment. Fortunately, the car dealer is willing to lend you the rest of the money. If the dealer's opportunity cost is 15% p.a. (i.e. investing $100 today will yield him $115 at the end of the year), how much would you have to pay every quarter, if the dealer requires you to make 20 equal quarterly payments?

4. Read the following article, "Lenders Retool Long-Term Mortgages" from the Wall Street Journal of June 16, 2005 and answer the following questions:

  1. (10 points) Suppose you have borrowed $20,000 using an interest-only mortgage, where you pay only interest for the first 10 years. If the APR on the loan is 12%, and you elect to make monthly payments for the next ten years (after the first 10 years of interest-only payments) to pay off the loan in its entirety, what will be your monthly payments for the first ten years, and then for the second ten years?
  2. (10 points) Towards the end of the article, we read "With a $200,000 mortgage with a 5.75% fixed rate, a borrower with a 40-year mortgage will pay roughly $312,000 in interest over the life of the loan, according to HSH Associates, versus about $220,000 in interest if the same loan has a 30-year term, assuming both loans carry the same interest rate. If the rate on the 40-year mortgage is 6%, the total interest payments jump to about $328,000." What is the problem with computing the total interest payments in this manner?
  3. (10 points) North Fork Bancorp Inc. is traded on the NYSE. It's beta is provided by Yahoo as 0.191. If the standard deviation of returns on the market portfolio is 25%, this means that the non-diversifiable part of the variance of the returns on North Fork would be (0.191)2 x (25)2 or 22.8 percent-squared, whereas the total variance of returns on North Fork is 202 or 400 percent-squared. Your friend claims that the remaining variance (i.e. 400 - 22.8 or 377.2 is irrelevant to most investors, since they would hold diversified portfolios. Is your friend correct, and why?
  4. (Bonus - 10 points) Assuming, once more that the standard deviation of returns on the market portfolio is 25%, and the standard deviation of returns on North Fork is 20%, what would be the R2 of the regression of returns on North Fork Bancorp stock on the market return (keeping in mind that the beta of North Fork stock is 0.191)?

Lenders Retool Long-Term Mortgages
By RUTH SIMON, Staff Reporter of THE WALL STREET JOURNAL, June 16, 2005; Page D1

The mortgage industry is starting to make the move from short to long.

Lenders are rolling out a new crop of 30-year fixed-rate mortgages that let homeowners make low, interest-only payments for as long as 10 or 15 years. It is the latest effort to snare borrowers seeking lower monthly payments. Also getting a new push: mortgages that stretch for as long as 40 years.

The newest crop of products is largely aimed at borrowers who are looking for lower payments but are also concerned about interest-rate risk. In recent months, mortgage experts have been surprised by the continued strong interest in adjustable-rate mortgages at a time when borrowers can still lock in a fixed-rate loan at rates well below 6%. With rising short-term interest rates reducing the relative attractiveness of adjustable loans, lenders are seeing greater interest in loans that protect borrowers from rising interest rates -- and are introducing products for that market.

Last month, Wells Fargo & Co. rolled out a 30-year fixed-rate mortgage that is interest-only for the first 10 or 15 years. The interest rate remains the same throughout the life of the loan, but the monthly payment is recalculated after the interest-only period ends so that the mortgage balance is paid off over the remaining 15 or 20 years. U.S. Bank Home Mortgage, a unit of U.S. Bancorp, plans to introduce a 20-year fixed-rate mortgage with an interest-only feature for the first 10 years. Bank of America Corp., IndyMac Bancorp Inc. and LendingTree.com, a unit of IAC/InterActive Corp., all have fixed-rate interest-only mortgages in the works.

Forty-year mortgages -- which keep monthly payments down but cost more over the long term -- also are attracting more notice in the wake of Fannie Mae's recent decision to expand its purchases of these loans. First offered in the 1980s, 40-year loans account for less than 1% of mortgage originations, according to the Mortgage Bankers Association. More banks may be willing to offer them now that they know they can be sold to Fannie Mae, which has been purchasing 40-year mortgages since September 2003 under a pilot program with 22 credit unions. Fannie will purchase both fixed- and adjustable-rate 40-year mortgages.

Next month, IndyMac Bancorp will reintroduce its 40-year mortgage, which was mothballed last year because of a lack of interest. Fannie Mae's move "helps by bringing attention to the product and credibility to it," says IndyMac Executive Vice President Frank Sillman. "It also brings a host of investors that will purchase 40-year loans." Washtenaw Mortgage Co. in Ann Arbor, Mich., a unit of Washtenaw Group, began offering these loans in May. Old National Bancorp. in Evansville, Ind., says it will add them this summer.

Some lenders have been offering more and more interest-only mortgages in recent years to eager borrowers, though the vast majority of them have been adjustable-rate loans with interest-only features. These include both short-term adjustables, with rates that can adjust as often as once a month, and so-called hybrid ARMs that can carry a fixed rate for as long as 10 years, after which the rate can adjust annually.

ARMs and interest-only mortgages have been especially attractive to borrowers looking to keep their monthly payments down in the face of skyrocketing home prices. These loans accounted for nearly two-thirds of mortgage originations in the second half of last year, according to the Mortgage Bankers Association. Among the increasingly popular choices: so-called option ARMs, which are short-term ARMs that carry introductory rates of as low as 1% and give borrowers multiple payment options. Because these loans allow borrowers to afford more house with a lower payment, some observers worry that they have helped fuel a heated housing market.

The growing popularity of interest-only and adjustable-rate mortgages has also raised fears that borrowers and lenders are taking on additional risks that could create problems down the road. "The apparent froth in housing markets may have spilled over into mortgage markets," Federal Reserve Chairman Alan Greenspan told Congress last week. He called the "dramatic increase in the prevalence of interest-only loans, as well as the introduction of other relatively exotic forms of adjustable-rate mortgages ... developments of particular concern."

Lenders that now offer fixed-rate loans with interest-only features say they have seen a spurt of interest in these products in recent weeks as the yield curve has flattened, making ARMs relatively less attractive. At Greenpoint Mortgage, a unit of North Fork Bancorporation Inc., interest-only loans now account for about 30% of fixed-rate mortgages, up from 15% earlier this year. Countrywide Financial Corp. says activity in fixed-rate interest-only mortgages has been "brisk" recently.

Because they allow borrowers to lower their monthly payments, the newer breed of mortgages is aimed at homeowners concerned about affordability and those who want to free up cash for other purposes. Unlike ARMs, which allow borrowers to get a lower rate in exchange for accepting the risk of future rate increases, fixed-rate interest-only mortgages carry the same interest rate over the life of the loan.

But like other interest-only loans, they tend to be more costly than standard mortgages. At Countrywide, the interest rate on an interest-only loan is typically one-eighth of a percentage point higher than the rate on a comparable loan without the interest-only feature. Wells Fargo says its borrowers typically pay about one-quarter point more in upfront costs -- or $500 on a $200,000 mortgage.

Borrowers can face payment shock when the interest-only period ends. A borrower with a $200,000, 5.50% 30-year mortgage that's interest-only for the first 15 years would see the monthly payment increase to $1,634 from $917 when the loan recasts so that the mortgage can be paid off in the remaining years, according to HSH Associates in Pompton Plains, N.J.

Some lenders and borrowers are looking to 40-year mortgages as an alternative to interest-only mortgages. The 40-year loans are likely to appeal to borrowers "in the middle of the country, who tend to be more conservative," says James Cotton, vice president for single-family marketing at Freddie Mac, which is looking at buying 40-year mortgages.

Forty-year mortgages can be costly over the long haul. Rates on these loans tend to be about 0.25 to 0.375 percentage point higher than the rate on a comparable 30-year mortgage. Borrowers also pay more interest over time because the loan is stretched over an additional 10 years. With a $200,000 mortgage with a 5.75% fixed rate, a borrower with a 40-year mortgage will pay roughly $312,000 in interest over the life of the loan, according to HSH Associates, versus about $220,000 in interest if the same loan has a 30-year term, assuming both loans carry the same interest rate. If the rate on the 40-year mortgage is 6%, the total interest payments jump to about $328,000.

Some lenders are tweaking the formula. Hingham Institution for Savings in Hingham, Mass., last year introduced a 20-20 mortgage, a 40-year loan with a single rate adjustment after the first 20 years. Because it is essentially two 20-year loans, the rate on the mortgage is one-quarter to one-eighth of a point below the rate on a standard 30-year loan. "It's been our most popular product," says Hingham vice president Michael Sinclair.

5. (20 points) You have constructed the following probability distribution of returns on Countrywide Financial Corp's stock over the next year:

  1. What is the expected return on Countrywide's stock over the next year?
  2. What is the standard deviation of returns on Countrywide's stock over the next year?