Questions
1. You observe the yields-to-maturity for two treasury securities:
Bond X is a 2% coupon bond maturing in 5 years; its yield-to-maturity is 2.100%.
Bond Y is a 5% coupon bond maturing in 5 years; its yield-to-maturity is 2.200%.
Both bonds have face value of $100, and pay coupons semi-annually. (Hint: this means the compounding period is 6 months.) The next coupon payments are exactly 6 months from now.
a) What are the prices of the two bonds, per $100 of face value (please provide the answer to 3 decimal places)? Remember to provide justification.
b) Bond A is an annuitythat pays $10 every 6 months for the next 5 years. The next payment is exactly 6 months from now. Assuming no default, what is the price of Bond A so that there is no arbitrage profit between Bonds A, X and Y? What is the yield-to-maturity of Bond A? Remember to provide justification.
c) Which one of the following 3 statements is most likely to be true:
i. The zero-coupon (or “spot rate”) yield curve is upward sloping.
ii. The zero-coupon (or “spot rate”) yield curve is flat.
iii. The zero-coupon (or “spot rate”) yield curve is downward sloping.
Please provide the reason for your selection.
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2. You want to take out a 15 year fixed rate mortgage of $200,000. Current mortgage rates are 5.50% (APR or stated rate, compounded monthly).
a) Calculate your monthly payment on this mortgage. Remember to provide justification.
b) Prepare an amortization schedule for this mortgage showing principal outstanding and the portion of each month's payment towards interest and principal. The current date is the end of Month 0.The first monthly payment is made at the end of Month 1. In your answer, please provide the schedule for months 0-12 and the last 12 payments of this amortization schedule. Remember to provide justification.
c) At the end of Month 13, you use your $50,000 annual bonus to reduce the principal outstanding on your mortgage. You continue making the same monthly payment that was calculated in part (a). When will the loan be fully paid off? In your answer, please provide the schedule for months 13 through 24, and the last 12 payments of the new amortization schedule. Remember to provide justification.
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3. Consider a firm whose earnings per share was $3.00 during the current year (period 0). In other words, E0 is $3.00. The firm reinvests 50% of earnings as capital investments, to maintain annual earnings growth of 5%. The required return (or discount rate) is 12% per year.
a) What is the stock price, i.e., P0? Remember to provide justification.
b) What is the expected stock price one year from now, i.e., P1? Remember to provide justification.
c) What is the historical P/E ratio? What is the forward P/E ratio? Remember to provide justification.
d) What is the historical dividend yield? What is the forward dividend yield? Remember to provide justification.
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4. An oil company’s resources are being depleted and known reserves are becoming scarcer. As a result, the company’s earnings and dividends are declining at a rate of 2% each year. The dividend was $5.6 per share during the current year (period 0). In other words, D0 is $5.60. The required rate of return (or discount rate) is 11% per year. What is the price per share of the company’s common stock, i.e., P0? Remember to provide justification.
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5. This problem deals with Unit 3 (Equity Valuation). First, read the following Reuters Story about the Red Hat IPO.
Red Hat shares soar into "nosebleed territory"
Reuters Story - August 12, 1999 20:12
By Therese Poletti
SAN FRANCISCO, Aug 12 (Reuters) - Shares of Red Hat Inc., surged 40 percent to levels analysts called "nosebleed territory" Thursday, giving the distributor of the Linux operating system a market capitalization of nearly $5 billion a day after its debut.
Red Hat had already seen the price of its freshly issued shares more than triple Wednesday to close at $52.0625, after raising its IPO target price range and selling six million shares at $14 a share.
On Thursday, shares of the Durham, N.C.-based firm rose to $72.625, giving the fast growing but money losing company a market capitalization of about $4.8 billion based on 66.6 million common shares outstanding. That total does not include shares reserved for employee stock options.
"These levels are nosebleed territory and the stock does not belong at these levels," said David Menlow of the IPO Financial Network in Millburn, N.J. "It's totally unsustainable."
Analysts said Red Hat's IPO was so well received -- especially during a major downturn in the Internet IPO market -- because it is the leader in the emerging market of Linux software. Linux is a version of the UNIX operating system created by Finnish programmer LinusTorvalds. It now competes with Microsoft Corp.'s Windows NT in some areas such as running Web servers and e-mail servers.
Red Hat received a tremendous amount of publicity as the first company in the quirky Linux community to go public. Its IPO was held during a major trade show for Linux in Silicon Valley this week.
"It is an early mover in what is obviously a hot area," said Paul Bard, an analyst with Renassiance Capital Corp. in Greenwich, Conn. "I think what investors are betting on is the growth of the market for the Linux operating system. Lots of people think this could be really big."
Indeed, Linux was the fastest growing operating system in the network server market, according to International Data Corp., which said that Linux grew faster than Windows NT.
But Linux is still mostly used by hobbyists on the desktop and most analysts do not expect to see Linux overtaking Microsoft's dominant Windows among average PC users. Still, are a growing number of software products, such as KDE from MandrakeSoft, give Linux an easier-to-use interface.
"The risk factors in the prospectus accurately outline the concerns we have for the company," Menlow said.
One of the risk factors in the company's prospectus is that Red Hat is the largest distributor of software that is already given away over the Internet. Red Hat also gives away Linux at its Web site. It sells the shrink-wrapped versions of Red Hat Linux in computer stores for about $50 and plans to make most of its money by software and services for Linux.
Its revenues soared 109 percent in the fiscal year ended February 1999 to $10.8 million, and the company showed a loss of $130,000. Red Hat expects to incur substantial losses in the future, as it increases sales, marketing and research.
Competition is another risk. Because Linux is not owned by any one company, many new companies provide services and support for the software. Torvalds, who wrote the Linux kernel, the core of the operating system, still manages its upgrades and development by a group of far-flung programmers.
Another potential risk factor for all companies developing around Linux is the software's reliance upon Torvalds and a small group of engineers for major upgrades.
"Our reliance on the support of LinusTorvalds and other prominent Linux developers could impair our ability to release major product upgrades and maintain market share," the company said in its prospectus.
Analysts said many investors may be bidding up the stock based on Linux's potential to compete with Microsoft, and therefore they are hoping for the same profit potential.
"It's a completely different business model (from other software companies)," said Bard at Renaissance Capital. "You really can't compare it on a valuation basis. This is open source code. They don't own the code."
Copyright 1999 Reuters Limited. All rights reserved. Republication or redistribution of Reuters content is expressly prohibited without the prior written consent of Reuters. Reuters shall not be liable for any errors or delays in the content, or for any actions taken in reliance thereon.
To make sense of the $5 billion market value of Red Hat, consider the following simplified cash flow statement (based roughly on Red Hat's S-1 registration statement with the SEC, which you do not need to read for the purpose of this assignment):
Fiscal Year (Actual) / Projected1995 / 1996 / 1997 / 1998 / 1999 / 2000
STATEMENT OF OPERATIONS DATA: / (in thousands)
Total revenue...... / 482 / 930 / 2,603 / 5,156 / 10,790 / 22,659
Total cost of revenue...... / 352 / 432 / 1,205 / 2,211 / 4,041 / 8,082
Gross profit...... / 130 / 498 / 1,398 / 2,945 / 6,749 / 14,577
Total operating expenses...... / 257 / 631 / 1,342 / 2,954 / 6,787 / 13,574
Income (loss) from operations...... / -127 / -133 / 56 / -9 / -38 / 1,003
Income (loss) before income taxes...... / -127 / -133 / 56 / -9 / -38 / 1,003
Income taxes...... / 0 / 0 / 19 / 0 / 0 / 341
Net income (loss)...... / -127 / -133 / 37 / -9 / -38 / 662
Please construct a 2-stage valuation model for Red Hat using the following assumptions:
- Assume "today" is Dec 31, 1999. The market value of Red Hat is $5 billion.
- All cash flows occur at the end of each calendar year.
- Red Hat's net income is equal to the free cash flow (FCF) to all security holders, hence the FCF for 2000 is $662,000.
- Red Hat's net income and cash flows are expected to grow at a fast rate from 2000 until 2010.
- After 2010, Red Hat's growth of cash flows will settle down for a constant rate of 6.8% forever.
- Red Hat's discount rate is 12% for all periods.
a) What growth rate (from 2000 until 2010) would be consistent with a market value of $5 billion on Dec 31, 1999, given the above assumptions? Remember to explain your logic.
b) At this growth rate, what should Red Hat's net income (free cash flow) be for 2010? Remember to explain your logic.
c) Is the growth you projected in a) realistic? Remember to explain your logic.
d) How would your answers to a) and b) change if the market value were only $1 billion rather than $5 billion? Remember to explain your logic.
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