Dr. P.V. Viswanath

 

pviswanath@pace.edu

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Summer 2005
 
   
 
 
 

Practice Midterm

  • 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.
  • No bonus points -- on question 6 -- will be awarded unless you have attempted all subsections of all the other questions. So you are better off concentrating on the non-bonus part of the exam, first!
  • 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. Bond A pays 8% coupons, makes annual coupon payments and is priced at 98% of par. Can you provide bounds on the yield-to-maturity of the bond? (That is, can you give a maximum or a minimum value for the yield?)
Bond B pays semi-annual coupons and sells for 98% of par as well. If the yield-to-maturity on Bond B is 10.15%, and its maturity is 2 years, what is its coupon rate?

2. You want to buy a pair of speakers that you have had your eye on, for a long time. Unfortunately, you don't have the $400 that they cost. Luckily, through the intercession of a friend of yours, the manager gives you the following alternative ways of paying for the speakers:

  • Pay $200 up front and $20 a month for 14 months.
  • Pay $30 a month for 17 months.

Which alternative would you take, if the APR is 14%?
Bonus question: Suppose you do have the $400, but you still want to consider paying for the speakers at the rate of $30 a month. What is the maximum number of months that you would be willing to make these $30 monthly payments?

3. It is Jan. 1, 1994. Utopia Power Company has just paid last year's dividend, and is expected to maintain its 1994 dividend at the same level as 1993. However, thereafter, it is expected to maintain a constant 5 percent growth rate in its dividends indefinitely. If the company has a dividend yield of 5.5%, what is the required rate of return on the power company's stock?


Midterm

  • 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. (10 points) Allona Corporation has issued consol bonds. The coupon payments on these bonds are $50 per year. If the required rate of return on these bonds is 10%, at what price would they trade?

2. (15 points) Brite-Aid Corporation paid a dividend of $2/share yesterday. They expect to pay dividends of $2/share for the next five years; thereafter, dividends are expected to increase at the rate of 5% per annum. TruLook Company is in the same industry as Brite-Aid, while Shineware company is in a different industry; however, Shineware common stock has similar risk to that of Brite-Aid shares. Investors expect to earn an average return of 12% per annum on TruLook's shares, while they expect to get 15% if they invest in Shineware. At what price should Brite-Aid's shares sell today?

3. You have the following data for the following two companies for 2004 (in millions of dollars):
 
SinoVac
Sifco Industries
Revenue
120
140
Net Income
35
10
Total Assets
1000
500
Total Liabilities (excluding Shareholders Equity)
200
200

  1. (10 points) What can you say about the different marketing strategies that the two firms are using?
  2. (5 points) What is the return on the two firms' equity?
  3. (10 points) You will note from your answer to the previous question that Sifco Industries has a lower return to equity. If you were using the Dupont Model, what might you suggest to Sifco's CEO to improve his return on equity? Are there any risks in going this route?

4. (20 points) Answer any four the following questions briefly:

  1. If a firm has cashflow from operations of $2 per share, how much can it afford to pay out in dividends? Why is your answer not $2? Explain how you would come up with the right answer.
  2. If a firm buys a machine for $200,000, it usually has to pay the seller of the machine right away. Nevertheless, a firm would not subtract the $200,000 from its revenues in the year that it buys (and pays for) the machine. Why not?
  3. What is working capital? Can a firm have negative working capital? Explain.
  4. A firm has a current ratio of 1.2. If it's current liabilities equal $400m., how much is its working capital?
  5. What is Tobin's Q ratio? What does it measure?
  6. Trip Co.'s after-tax income in 2003 was $140. It paid $40 in interest in that year. Assuming that its tax rate is 35%, what is its interest coverage ratio?

5. (15 points) You wish to buy a house, which costs $200,000. You wish to finance the entire amount with a bank. The bank's alternative investment is a project of similar risk where it would get back 15 cents more at the end of the year for every dollar it invested. What is your monthly payment if you wish to pay off the entire loan within a year?

6. (30 points) Cenuco Inc. has issued a 10 year bond with a coupon rate of 10%. The yield-to-maturity on this bond is 12%.

  1. What is the price of the bond today?
  2. What will the bond be worth at the end of 1 year if the yield-to-maturity at that time stays at 12%?
  3. If you sell the bond at that time, what rate of return would you have obtained?

Solutions to Midterm

  1. The price of the consol bonds would be 50/0.1 or $500
  2. The present value of the cashflows for the next 5 years can be treated as an annuity and would equal =$6.70.  The value of the subsequent dividends, as of time 5 would be 2(1.05)/(0.15-0.05) = $21.  The present value of those $21 are 21/(1.15)5 = $10.44.  Hence the price of the stock would be 10.44 + 6.70 or $17.14.
  3. The financial ratios of the two companies are as follows:

 

SinoVac

Sifco Industries

Net Margin = Net Income/Revenue

35/120 = 29.17%

10/140 = 7.14%

Asset Turnover Ratio = Sales/Total Assets

120/1000 = 0.12

140/500 = 0.28

Equity Multiplier = Total Assets/Total Equity

1000/(1000-200) = 1.25

500/(500-200) = 1.67

Return on Equity = Net Income/Total Equity

35/(1000-200) = 4.375%

10/(500-200) = 3.33%

a.       SinoVac is working with a high margin, low volume approach, whereas Sifco has a lower margin, but higher volume approach, as can be seen from the components of the firmís ROE numbers.

b.      The return on equity of the two firms are 4.375% and 3.33%.

c.       Sifco could improve performance by increasing leverage; however, this would increase its risk, as well.

  1. a. A firm has to keep back the funds it would need for profitable expansion, viz. increase in working capital, as well as increase in capital expenditures.  Else, it would decrease its market value.

    b. It would not expense the entire $200,000 in that year because of the accounting principle of revenue matching.  Outlays that would contribute to the generation of future cashflows would be kept as an asset.  Only outlays that could be matched with current revenues are considered current expenses, even if they were actually incurred previously, and even if they have not yet been paid for.

    c. Working Capital is the extent of self-financing of the firmís short-term operations.  A negative working capital means that current assets are lower than current liabilities, or that the firmís suppliers are partially financing the firmís short-term operations.

    d. Since the current ratio equals current assets/current liabilities, a current ratio of 1.2 implies that current assets equal $500m.  Hence, its working capital is $500m. - $400m. or $100m.

    e. Tobinís Q ratio is computed as the market value of the firmís assets divided by the replacement cost of the firmís assets.  It measures the extent of the firmís growth opportunities and its real options Ė the extent to which the firm has been able to add value over and above the simple worth of its assets.

    f. The firmís interest coverage ratio is (NI + Taxes + Interest)/(Interest).  Since NI is $140, and the firmís tax rate is 35%, the firmís taxable income is 140/(1-.35) = $215.38.  Hence the interest coverage ratio = (215.38 + 40)/40 = 6.384.
  2. The EAR is 15%; hence the effective monthly rate is (1.15)(1/12) -1 = 1.17%.  Solving the following equation: for C, we get C = 17,962.87.
  3. a. Assuming annual coupons, the price of the bond is worth  = $887. 
    b. At the end of a year, it should be worth 887(1.12) or $993.44, since 12% is still the expected return.
    c. Obviously, the return at the end of the year would be 12%.

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 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:

Return
Probability
5%
0.2
20%
0.7
40%
0.1
  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?

Solution to Final

1.a. The expected return on the stock is 4.075 + 0.433(6) = 6.673%
b. The dividend next year is (0.72)(1.08) and the dividend the year after that is (0.72)(1.08)2.  The sum of the present values of these dividends equals $0.729 + $0.738 = $1.467.  The price of the stock at the end of the second year will be (0.72)(1.08)2(1.03)/(.06673-0.03) = $23.55, or in present value terms, $20.692.  Adding this to 1.467, we get $22.16

 2 a. The price of the bond is PV(annuity of $30 per period for 20 periods; periodic rate of 4%) + 1000/(1.04)20 = $864.10
b. The bond should be selling at a discount, since the YTM > the coupon rate; hence you should not buy it at par.

 3. The EAR is 15%; hence the quarterly rate is (1.15)0.25 Ė 1 or 3.5558%.  We can use this and the annuity formula, to compute the periodic payment to be $1272.90

 4. a. Since you are paying interest only for the first ten years, you will pay, each month, 20000(1.01) or $200.  At the end of the period, you will still owe the entire principal of $20,000.  Hence your monthly payments will simply be the monthly payments on a 10 year loan of $20,000 at an APR of 12%, i.e. $286.94.
b. The problem is that interest paid in different months are simply being added Ė this ignores the time value of money.
c. Your friend is correct, since the diversifiable uncertainty will disappear in a diversified portfolio; it will not add to the total variance of a diversified portfolio.
d. The R2 is equal to 22.8/400 = 0.057

 5. The expected returns equal 5(0.2) + 20(.7) + 40(0.1) = 19%; the variance of returns, as shown below works out to 81 percent-squared; hence the standard deviation of returns is 9.165%

Prob

Return

sq dev

0.2

5

196

0.7

20

1

0.1

40

441

 

19.0

84.0