Name: _____________________________________
GEO 200
ICA 5: Atmosphere, Energy, and Temperature
Atmospheric Composition_________________________________________________
Depending on height above the surface, the atmosphere has a different chemical composition. There are two distinctly different regions within the larger atmosphere that we call the heterosphere and the homosphere. The homosphere is the region that is closest to the surface and because this region experiences turbulence, it is composed of a well-mixed layer of gases that include nitrogen (N2), Oxygen (O2), Argon, (Ar), carbon dioxide (CO2), and trace amounts of various other gases. This region exists from the surface up to approximately 50 mi above the surface. Above this region is the heterosphere, which does not experience turbulence. Thus, the gases within the heterosphere separate by atomic weight. First there is a region of nitrogen (N2) that extends to approximately 150 mi above the surface, then a region of atomic oxygen (O) that extends to approximately 600 mi, then a region of helium (He) that extends to approximately 1500 mi, and finally a region of hydrogen atoms (H) that extends to over 6000 mi.
Use the information in the previous paragraph to complete the following:
7
1. Draw a line on the given atmospheric column that indicates the division between the heterosphere and the homosphere.
2. Shade the homosphere with any color.
3. In the section that represents the heterosphere, draw lines parallel to the surface that indicate the divisions between its sub regions of lighter gases.
4. Label each gas sub region in the Heterosphere with the name of its gas and the appropriate chemical symbol. Shade each of these regions with a different color.
Refer to the thermal structure of the atmosphere depicted above, and compare it with your sketch of the gas regions in the atmosphere to answer the following questions:
1. How much of the Troposphere is contained within the homosphere?
2. Which gases would be found within the Mesosphere?
3. Would the gases in the Stratosphere be well mixed or separated into distinct layers?
4. Would the gases in the Thermosphere be well mixed or separated into distinct layers?
Radiation and the Greenhouse Effect
Energy from the Sun enters Earth’s atmosphere in the form of shortwave radiation (insolation). The average amount of energy received at the top of the atmosphere is known as the solar constant, and is approximately 1373 W/m2 (watts per square meter). Upon entering the atmosphere, approximately 26% of the insolation is either immediately reflected back to space or scattered by particles in the air; an additional 19% of the insolation is absorbed by water molecules in the atmosphere (clouds).
After traveling in the atmosphere, another 4% of the incoming shortwave radiation is reflected by the Earth’s surface. The proportion of solar radiation reflected by a surface is the albedo, which is controlled by surface color and texture. Light-colored, smooth surfaces (high albedo) reflect a larger proportion of insolation, while dark-colored, rough surfaces (low albedo) reflect smaller proportions.
Of the 1373 W/m2 of solar energy that enters the top of the atmosphere, an average of 51% is finally absorbed by the surface of the Earth. It is this energy that is available for heating the ground and air.
While the Earth absorbs shortwave radiation from the Sun, it emits energy in the form of longwave radiation. Clouds, water vapor, and other greenhouse gases in the atmosphere absorb the longwave radiation emitted by the Earth’s surface. The clouds and greenhouse gases then reradiate longwave energy back to the surface, preventing the loss of all longwave radiation to space. This naturally occurring process, the greenhouse effect, serves to keep the Earth’s surface warm and habitable. Global warming is the concern that an increase in greenhouse gases is intensifying the natural greenhouse effect to the detriment of society.
1. Recall that of the 1373 W/m2 solar energy that enters the top of the atmosphere, only 51% reaches Earth’s surface. Express this value in W/m2. What is 51% of 1373 W/m2?
2. If the Earth experienced an increase in average albedo from 4% to 8%...
a. Would this increase or decrease the solar radiation that reaches the surface?
b. Calculate the amount of solar energy that would reach Earth’s surface, expressed in W/m2.
3. List two natural phenomena that might cause the Earth’s albedo to increase (Note: “Global warming” or “the Greenhouse Effect” are NOT correct responses).
4. How would an increase in the Earth’s albedo likely affect the climate of the Earth?
5. Describe surface air temperatures on cloudy nights.
6. Describe surface air temperatures on clear nights.
Insolation and Temperature
The atmosphere is primarily transparent to shortwave radiation and reactive to longwave radiation. The Earth’s surface emits longwave radiation that slowly warms the atmosphere above the surface of the Earth, and in turn, the lower atmosphere helps to reheat the Earth’s surface. Thus, the relationship between insolation and air temperature is not direct; there is a lag effect. The warmest time of day occurs at the moment of maximum longwave radiation emitted to the atmosphere from the ground, and not at the moment of maximum insolation.
Image: The typical diurnal cycle of surface temperature and the net energy rate due to incoming solar and outgoing longwave radiation.
Encanto Golf Course is located in central Phoenix, AZ. The table below lists insolation and temperature readings taken at Encanto Golf Course on a summer day.
Table: Insolation and Air Temperature Observations for Encanto Golf Course on June 26, 1990.
|
Hour |
Insolation (W/m2) |
Air Temperature °F |
|
0200 |
0 |
80 |
|
0400 |
0 |
81 |
|
0600 |
11 |
79 |
|
0800 |
256 |
87 |
|
1000 |
767 |
105 |
|
1200 |
961 |
110 |
|
1400 |
967 |
114 |
|
1600 |
742 |
116 |
|
1800 |
367 |
115 |
|
2000 |
19 |
110 |
|
2200 |
0 |
104 |
|
2400 |
0 |
94 |
Answer the following questions using the table.
7. Why is the insolation zero during some hours?
8. List the time of the maximum air temperature. List the time of the maximum solar radiation.
9. List the time of the minimum air temperature. List the time range of the minimum solar radiation.
10. Notice there is a “lag” or delay between the receipt of maximum solar radiation and the maximum temperature; there is also a lag or delay between the minimum solar radiation and the minimum temperature. Why is there a delay? Explain.
Elevation and Temperature
Within the troposphere, temperatures decrease with increasing altitude above the Earth’s surface: the normal lapse rate of temperature change with altitude is 6.4 C°/1000 m, or 3.5 F°/1000 ft. Worldwide, mountainous areas experience lower temperatures than do regions near sea level, even at similar latitudes. The consequences are that average air temperatures at higher elevations are lower, nighttime cooling increases, and the temperature range between day and night and between areas of sunlight and shadow also increases. Temperatures may decrease noticeably in the shadows and shortly after sunset. Surfaces both gain heat rapidly and lose heat rapidly due to the thinner atmosphere.
Temperature data are presented in Table 8.1 for La Paz and Concepción. Both stations are approximately the same distance south of the equator but differ in elevation. La Paz is at 4103 m (13,461 ft), whereas Concepción is at 490 m (1,608 ft) above sea level. The hot, humid climate of Concepción at its much lower elevation stands in contrast to the cool, dry climate of highland La Paz.
People living around high-elevation La Paz actually grow wheat, barley, and potatoes – crops characteristically grown in the cooler midlatitudes at lower elevations. These crops do well despite the fact that La Paz is 4,103 m above sea level. The combination of elevation (moderating temperatures) and equatorial location (producing higher Sun altitude and consistent daylength) guarantee La Paz these temperature conditions, averaging about 9 C° (48 F°) for every month. Such moderate temperature and moisture conditions lead to the formation of more fertile soils than those found in the warmer, wetter climate of Concepción.
11. Since we want to compare temperatures at different elevations; why does it matter that we select two locations at a similar latitude?
12. Using the temperature graphs provided, plot the data from Table 8.1 for these two cities. Use a smooth curved line graph to portray the temperature data.
13. Calculate the average annual temperature for each city (to calculate: (maximum + minimum)/2).
14. Calculate the annual temperature range for each city (maximum – minimum).
15. Why are the temperatures at La Paz more moderate in every month and so consistent overall as compared to Concepción?
16. The annual march of the seasons and the passage of the subsolar point between the Tropics of Cancer and Capricorn affect these stations. Can you detect from your temperature graphs these seasonal effects? Explain.
Marine vs. Continental Effects
The irregular arrangement of landmasses and water bodies on Earth contributes to the overall pattern of temperature. The physical nature of the substances themselves—rock and soil versus water—is the reason for these land-water heating differences. More moderate temperature patterns are associated with water bodies compared to more extreme temperatures inland.
These contrasts in temperatures are the result of the land-water temperature controls: evaporation, transmissibility, specific heat, movement, ocean currents, and sea-surface temperatures. The term marine, or maritime, is used to describe locations that exhibit the moderating influence of the ocean, usually along coastlines or on islands. Continentality refers to the condition of areas that are less affected by the sea and therefore have a greater range between maximum and minimum temperatures diurnally (daily) and yearly.
The Canadian cities of Vancouver, British Columbia, and Winnipeg, Manitoba, exemplify these marine and continental conditions. Both cities are at approximately 49°N latitude. Respectively, they are at sea level and 248 m (814 ft) elevation. However, Vancouver has a more moderate pattern of average maximum and minimum temperatures than Winnipeg. Vancouver’s annual range of 11.1 C° (20.0 F°) is far below the 38.8 C° (70.0 F°) temperature range in Winnipeg. In fact, Winnipeg’s continental temperature pattern is more extreme in every aspect than that of maritime Vancouver.
17. Using the data given in Table 8.2, plot the temperatures for these two cities and portray with a smooth curved line graph on the temperature graph in Figure 8.3. Calculate the average annual temperature and temperature range for each city.
0
1000
2000
3000
4000
5000
6000
Height Above Surface (Miles)
Case 48: Sun Microsystems
Done by: Nour Abdulaziz
Maryam Barifah
Shrouq Al-Jaadi
Balqees Mekhalfi
Yara El-Feki
Introduction
•In 2009, Oracle was planning to acquire Sun Microsystems.
•This acquisition would allow Oracle;
•to further diversify their brand, customers and acquire various new platforms that would be added to their portfolio such as MySQL, Solaris and Java.
•Oracle originally placed an offer of $9.50 per share price which is considerably higher than Sun Microsystem’s price that is $6.69.
•This will cut the production costs and make the company more efficient throughout all the value chain.
•Oracle aimed to capitalize on Sun Microsystem’s decline by getting particular assets or the whole company at the deflated price.
Is Sun Microsystems a good strategic fit for Oracle? Should Oracle acquire Sun Microsystems?
- as it will allow them to achieve their vision of becoming the Apple of the software industry.
- it will allow the company to deliver high-quality customer products by combining both hardware and software components, hence reducing the consumer setup process.
Continue
It will provide Oracle with the needed expansion.
-This acquisition fits Oracle’s overall strategy which is to improve through acquiring and effectively integrating other companies
Worth of Sun Microsystems and Valuation Approaches
To know how much Sun Microsystems worth, we must find the Stand Alone Value of the company.
The Stand Alone value represents the present value of Sun Microsystem individually before factoring the synergy that would be created when Oracle acquires Sun.
Another method is the value of Sun Microsystem with synergies, which after being acquired by Oracle, must be found. This is done to see whether or not the acquisition was a proper strategic decision or not
Another method of valuing the Sun Microsystem is through the comparative company analysis (CCA). That is done through the thorough assessment of rival and peer businesses of similar size and industry.
Finally, the acquisition price, which is the price that is paid to the target when it is first acquired, is also used as a separate method of valuation. The value of the acquisition price ranges between the values of the stand-alone and the synergies.
USING THE DCF
To be able to find the values of both, the Stand Alone and the synergies, we have decided the best way to do so is by calculating the discounted cash flow (DCF) by using the multiples and the perpetuity growth methods and finding the average of both.
| DCF Using Multiples Method | DCF Using Perpetuity Growth Method |
| It does not consider long-term growth rate or the economics of business. | This method seems inaccurate as the company assumes a certain growth rate will remains the same 2014 onwards (forever) which is unrealistic. |
| It is considered a challenging method to use as it is very difficult to identify truly comparable companies. |
USING THE WACC
The weighted average cost of capital (WACC) is the average of the cost of individual sources of capital. The capital is comprised of equity that has been invested, or simply debt that lenders decided to invest in; with each source of equity being proportionally weighted.
WACC can be defined as the minimum rate of return. Companies must generate returns greater than their WACC to be above the break-even point. In case a company goes below, they would enter a deficit.
The formula: WACC = Wd x Rd x (1-T) + We x Re
Wd= weight of debt (Debt/(Debt + Market Capitalization))
Rd= cost of debt
We= weight of equity (1-Wd or 1-%Debt)
Re= cost of equity (Using CAPM) = Rf + Beta x (Rm).
T= tax rate = 35%
Providing us with a WACC of 12.05%.
Comparable Companies Analysis (CCA)
The analysis will be based on the following companies. Apple, Dell, Hewlett-Packard (HP), Intel and International Business Machines (IBM).
In Exhibit 9 the levered beta of comparable companies are given, reflecting an industry’s median 1.12 and a levered beta of Sun Microsystems of 1.73
Calculated the debt to equity (D/E) ratio to get the unlevered beta, using a tax rate of 35% as assumed in question 2, showcasing an industry median of 9.35% and an industry’s unlevered beta of 1.58, while Sun Microsystems’ (D/E) ratio is 25.44% and its unlevered beta is 2.13
Calculated the cost of equity using capital market structure[1] using the risk free rate of 2.82% and market premium of 6%
The WACC was calculated to conclude an industry’s median of 9.50% against Sun Microsystem’s that is of 12.05%
This indicates that investing in the company is much riskier compared to its rivals in the same industry.
Multiples of the Comparable Companies
| EBIT Multiple | EBITDA Multiple | Sales Multiple | |
| Sun Microsystems | -1.41 | -13.51 | 1.72 |
| Median | 9.40 | 6.28 | 1.39 |
Incorporated the averages of these multiples to calculate the firm’s implied enterprise value.
Used the average of the EBIT, EBITDA, and Sales for the comparable companies analysis (for the years 2007 and 2008).
We reached an average share price of $13.06
Economic fundamentals reflected in the multiples
We used the 10 years U.S. treasury bills yield as risk-free rate used as growth rate.
When calculating the average share price, our implied enterprise value was calculated based on the average of the multiples.
There could be a miscalculation of the actual worth of the firm because some of the companies are much more financially stable in comparison to Sun Microsystems such as Apple and Dell.
Stand-Alone Sensitivity Analysis:
Synergy Value Sensitivity Analysis
Summary of Results
What price should be offered by Oracle?
| Sun Microsystems Implied Offer Price | Perpetuity Growth Method | Exit Multiple Method | Sun Microsystems Share Price |
| DCF using the Standalone Value | $7.40 | $9.44 | $8.42 |
| DCF using the Synergy Value | $12.79 | $16.32 | $14.55 |
| Average CCA | $13.06 | ||
| Current Offer Price by Oracle | $9.50 |
Oracle could offer Sun Microsystems a price within the range of $8.42 to $14.55
The price per share using the comparable company analysis ($13.06) method and the current offer price by Oracle ($9.50) are both included within this range
We believe that the optimal price that should be offered by Oracle should be $11.38 per share.
Conclusion
The acquisition of Sun Microsystems by Oracle,
Would add additional platforms to their portfolios such as MySQL, Solaris, and Java.
The combination of the two companies would allow Oracle to expand its market share by dealing with lower-end consumers.
Sun Microsystems calculated WACC is equal to 12.05% which means that investing in Sun would provide an appealing however with a high risk.
Discounted cash flow method and the multiples valuation method was used to know which price should Oracle give to Sun Microsystem’s shares.
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[Type text] [Type text] [Type text]
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Student Name and ID # |
Tuleen Basrawi 1310186 Lara Hamza 1310042 Heba Bannoub 1320048
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Course |
Financial Policy BNFN 4304 |
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Section |
1 |
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Assignment # |
Case 48: Sun Microsystems
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Due Date |
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Instructor |
Masood Aijazi |
Executive Summary
Oracle is among the leading, legitimate database management system vendors including other related programming services. Oracle wants to acquire Sun Microsystems. Sun Microsystems deals with storage, hardware equipment, and offers various services at the enterprise level. If the acquisition succeeds then, the combination will be similar to Walmart but operating in the programming industry. The ultimate purpose of this report is to evaluate whether Sun Microsystems is a perfect match for Oracle and the best price to settle at. With regards to Sun Microsystems, Base-Case or Stand Alone and the expected synergies after acquisition were used to make valuations. Ways were devised to better value Sun Microsystem. First, debt and market capitalization were included to arrive at $6.20 billion enterprise value. In the second case, a multiple analysis focused on comparable companies was utilized. The objective was to establish the enterprise value estimated at $3.87 billion. Third, discounted cash flow method was used. The enterprise value was estimated at $4.53 billion as stand-alone which is around $8.95 billion. It is notable that the values from the various ways are different and is due to the assumptions.
Table of Contents Executive Summary 3 Introduction 5 1. Is Sun Microsystems a good strategic fit for Oracle? Should Oracle acquire Sun Microsystems? 5 2. How much is Sun worth? What approaches would you use to place a value on Sun Microsystems? (Hint: Stand-Alone Value, Acquisition Price and Value with Synergies) 7 The Stand Alone and Value with Synergies methods for valuation using the WACC was calculated as follows: 8 Steps for WACC calculation are seen in the excel sheet: 9 3. Assuming a discounted cash flow valuation: 9 a. What rate of return should Oracle require on the acquisition? 10 b. What base-case cash flows do you forecast? 10 c. What is your estimate of terminal value? 11 d. What is the enterprise value of Sun Microsystems? What is the equity value? 12 4.Conduct a compare companies or multiples analysis to value Sun. What economic fundamentals are reflected in the multiples? 12 Multiples of Comparable Companies 13 Multiples Analysis 15 Economic Fundamentals 16 5. Identify the synergies and conduct a sensitivity analysis to estimate the effect of synergies on enterprise value. 16 The below table shows the sensitivity analysis for the two approaches: 20 Stand-Alone Sensitivity Analysis: 20 Synergy Value Sensitivity Analysis: 21 Summary of Results: 21 6. If a competing bidder appears, how high a price should Oracle be willing to offer? 22 Conclusion 23
Introduction
The computer industry is extremely competitive and the organizations are always searching for new way to evolve to be a step ahead of the competition at all times. In 2009, Oracle was planning to acquire Sun Microsystems. This acquisition would allow Oracle to further diversify their brand, customers and acquire various new platforms that would be added to their portfolio such as MySQL, Solaris and Java. Oracle originally placed an offer of $9.50 per share price which is considerably higher than Sun Microsystem’s price that is $6.69. In addition to this, Oracle levered the company’s value with the acquisition of Sun Microsystems through complementing their system with hardware manufacturing. This will cut the production costs and make the company more efficient throughout all the value chain. The acquisition will pool Oracle’s leading position in the software area with Sun Microsystem’s proficiency in hardware and networking. Moreover, Oracle aimed to capitalize on Sun Microsystem’s decline by getting particular assets or the whole company at the deflated price. The main issue that Oracle needed to confront was to make an accurate valuation model to think of a reasonable price for Sun Microsystems share price. Additionally, Oracle had to ensure that acquiring Sun Microsystem would convey benefits and productivity to its operation.
1. Is Sun Microsystems a good strategic fit for Oracle? Should Oracle acquire Sun Microsystems?
Oracle’s finance position was better in 2009 unlike Sun Microsystems. Sun Microsystems poor finance position was attributed to steady market share loss in the hardware segment. To improve the revenues, Sun tried to leverage software systems by making the Java Solaris, and acquiring MySQL. However, the improved performance as a result of the leveraging was not long-term. The onset of the recent global finance crisis adversely affected their financial performance. The only option for the company was accepting an acquisition (Nicalao, 2012). Oracle would greatly benefit from the acquisition.
Even though Oracle and Sun are classified in the same industry, they deal with different products. Oracle manufactures software while Sun specializes in networking and hardware. The acquisition is therefore, vertical integration. As a result, Oracle will benefit from products diversification (Kumar, 2012). In 1997, Oracle used Solaris and Java language, Sun’s products. The competition between MySQL and Oracle database systems was indirect as they targeted different customers. Adding MySQL will thus, contribute to the portfolio of Oracle. The company will be able to attract the high-end clients and sell the software to them. Oracle could further add Sun’s strong position in the software industry in relation to Solaris systems, Java, and MySQL to its portfolio.
The technology industry began with hardware, software, peripherals and storage. Uncertain segments however, groped up following industrial development in the new millennium. The other businesses in the technology sector have been influenced by Apple’s store which enables the customers to purchase the needed software, hardware and peripherals from one store to reconsider their strategies in business development.
Sun is perfect match for Oracle. The acquisition will enable Oracle to achieve the vision of becoming a market leader in the technological sector by offering hardware and software components. The acquisition will also help to distribute high-quality products, reducing the customer set-up procedure.
Acquiring Sun Microsystem will also create room for expansion. In fact, the acquisition justifies Oracle's strategy of improving via acquisition and integrating with other companies. Oracle is not new to acquisition strategy. The company has spent at least $30 billion acquiring companies since 2005 hence, familiar with acquisition concept. The company has the ability to study the intended company and perceive possible synergies. Basing on the benefits of the acquisition, Sun Microsystem is therefore considered the best proposal for Oracle.
2. How much is Sun worth? What approaches would you use to place a value on Sun Microsystems? (Hint: Stand-Alone Value, Acquisition Price and Value with Synergies)
It is prudent to choose the best approach for valuing Sun Microsystem before ascertaining its worth. The recommended approaches are stand-alone value, acquisition price, and value with synergies. Stand-alone is Sun’s present value without considering the synergy as a result of the acquisition. It is the excess money received by Sun’s shareholders. It is a way of valuing a firm before any merging or acquisition takes place (Brigham & Ehrhardt, 2013). The value is important to confirm where the target company is overvalued or undervalued by comparing it against the current share prices.
Second, Sun’s value after the acquisition must be calculated. The value helps to verify whether the acquisition was appropriate or not. The company’s value included in the deal will grow if the acquisition is established to be a perfect strategic decision. This is referred to as the synergy effect. The cost saving as well as the gain in revenue and efficiency that is attained when merging occurs is indicated via synergies (see Q.3.2, Q.3.3, Q.5.2, and Q.5.3 in spread sheet and question 5).
Comparative analysis or trading comps is another method of valuing Sun Microsystem. In comparative analysis, the competitors and peer businesses of same size and in same industry is assessed (Brigham & Ehrhardt, 2013). Acquisition price can also be used for valuation. The acquisition price value ranges between the values of stand-alone and synergies. The best way to figure out stand-alone and synergies values are by calculating the discounted cash flow (DCF) by employing multiples and perpetuity growth methods and finding the average of both. These methods however, have challenges. First, the DCF using the multiples method does not consider long-term growth or the econometrics of business. It is also difficult to identify comparable companies (Brigham & Ehrhardt, 2013). Second, the DCF using the perpetuity growth method appears inaccurate as the company assumes a certain growth rate will remain the same which is impossible.
The Stand Alone and Value with Synergies methods for valuation using the WACC was calculated as follows:
Weighted Average Cost of Capital (WACC) refers to cost of individual sources of capital when averaged. It is the minimum return rate from the invested capital (Brigham & Ehrhardt, 2013). The capital considered when calculating WACC is debt and equity. Returns greater than WACC must be generated to stay above the break-even point. Going below it, would create a deficit. WACC must be calculated for the landers and shareholders to able to approximate the returns that their investments might yield. The spreadsheet shows the steps for calculating WACC.
Steps for WACC calculation are seen in the excel sheet:
The formula: WACC = Wd x Rd x (1-T) + We x Re
Wd= weight of debt
Rd= cost of debt
We= weight of equity
Re= cost of equity
T= tax rate
To calculate WACC, the weight of debt in the capital structure must be calculated using: Debt/ (Debt + Market Capitalization)
(The numbers can be found in exhibit 9.
Then, a calculation of the weight of equity must be done by: 1-Wd or 1-%Debt
Furthermore, the corporate bond yield from Exhibit 10 is used for the BB+ ratings since in Exhibit 9 it was shown that the bond rating for Sun Microsystem is Ba1 (Moody’s), which is equivalent to BB+ (S&P).
Moreover, the cost of equity is calculated by using the Capital Asset Pricing Model: Rf + Beta x (Rm).
All using the following data: a market risk premium (MRP) of 6% (assumed) and the 10-year Treasury Yield as the risk-free rate (from Exhibit 10) of 2.82% and a Beta of 1.73 (the levered beta for Sun Microsystem found in Exhibit 9).
Finally, determining the WACC using the assumed tax rate of 35%, providing us with a WACC of 12.05%.
3. Assuming a discounted cash flow valuation:
The Discounted Cash Flow (DCF) Method is considered to the be the superior valuation techniques to use in case of mergers and acquisitions compared to the comparable company’s analysis (CCA) since it is considered to be forward looking and will consider time value of money. DCF in addition focuses on cash flows instead of profits, and reflects on other non-cash charges such as depreciation and amortization and also investment inflows and outflows.
a. What rate of return should Oracle require on the acquisition?
When there is a possibility of acquisition, the acquirer may plan to increase the level of debt or decrease it after the merger because at that moment of time the objectives of the target’s finances is not ideal. The WACC reflects the company’s business risk of the target. An intermediary for this can be acquired from the unlevered beta of the target association’s value or a normal unlevered beat for firm with comparable business risk. The targets premerger unlevered beat should then be re-levered to reflect what the acquirer expected to have as a post-merger capital structure. To un-lever a company’s expected beat, one should use the predominant tax rate and the debt to equity ratio (D/E) of the company which relates to the beta estimate. The equation is below; ßu =ßL/[1+(1– T)D/E
Then, using the unlevered beta to estimate or normalize the unlevered beta estimate if its utilizes numerous companies to appraise the unlevered beta and the to re-lever the beta to the new proposed debt to equity ratio. Using the below formula: ß'L =ßu[1+(1– T)D/E
The rate of return that Oracle should require on the acquisition is equal to the Sun Microsystem’s WACC which is equal to 12.05%.
b. What base-case cash flows do you forecast?
The cash flow projections for the target company could plausibly incorporate co-operative synergies or any cost savings picked from the consolidation of the operations of the target company into those of the acquirer. If the basis of the cash flows does exclude any economic advantages an acquirer may convey to a target, they are then introduced as a stand-alone cash flows.
We then forecasted Sun Microsystem’s free cash flows for 5 years from year 2010 till year 2014. As what is shown in the excel sheet Q3.1, the free cash flows are estimated which is then increased from year 2010 till 2011, it then declines from the year 2011 to year 2012 and then increased back again in 2012 till 2014. In Exhibit 14 the valuation of Sun Microsystems was calculated using cash flows estimates. Sun Microsystems operating income is calculated by EBIT using a tax rate of 35% and that then indicates the NOPAT. Then the next step is that we calculated the net working capital by adding the net receivables and the inventory and other current assets then we subtracted account payable and other current liabilities which is taken from Exhibit 11.
The Net Working Capital (NWC) has an average of sales of 10.12% of net revenue which is found from Exhibit 14. In addition, the PPE from Exhibit 14 was then used to calculate Net PPE. Then this change in net working capital was calculated by subtracting the Net PPE of 2009 from the Net PPE of 2010. After finding the change in Net Working Capital, the Free Cash Flows were then projected from years 2008 to 2014. To calculate the Free Cash Flows (FCF), the change in Net Working Capital and the change in capital expenditure was then subtracted from the NOPAT. In Q3.3 the approach taken was the multiples of comparable companies to get the terminal value which is 7,480.
c. What is your estimate of terminal value?
To calculate the terminal value of the company, one must then determine the perpetuity growth model and then the multiples of comparable companies. In Q3.2, the terminal value of 4,815 was calculated by dividing the perpetuity growth (444.35) by the WACC of 12.05% minus the growth rate of 2.82%.
d. What is the enterprise value of Sun Microsystems? What is the equity value?
Another method for valuation is the enterprise value for the acquirer to maintain at the levels of consideration as it will affect the bid price that a company will be willing to pay for the target firm. When deciding on the bid price, the buyer (Oracle) will perform an analysis of the future cash flows of the target (Sun Microsystems) as a stand-alone business. The effects of which will be if they have a higher enterprise value for the target then they would raise the bid price and will still undertake a positive net present value for investors. This stand-alone value will give a benchmark for businesses and shareholders to use when the decision making process occurs for the organization takeover.
The enterprise value in the DCF with perpetuity growth was calculated by adding the Net Present Value (NPV) of Free Cash Flow (FCF) and the net present value of the terminal value. In addition, to find the price per share of the equity value is was calculated as (enterprise value – debt + cash) to then be divided by the number of shares which are 739 which are found in Exhibit 9. The result of which will be a price per share of $7.40.
Then the enterprise value which is found in the DCF with the multiples was then calculated by adding the Net Present Value (NPV) of Free Cash Flows (FCF) and the present value of the terminal value. In addition, to find the price per share the equity was calculated from (the enterprise value – debt + cash) to for it then it to be divided by the number of shares which are 739 from Exhibit 9. The result will then be $9.44 price per share.
4.Conduct a compare companies or multiples analysis to value Sun. What economic fundamentals are reflected in the multiples?
The multiples used in valuation and the earnings of target company must show consistency to obtain the best price. The price to earnings multiple (price per share / earnings per share) can be employed during the calculation. This method considers estimating the equity and comparing it against the income. The company in this scenario is evaluated basing on its free cash flow. The revenue when used may mislead as it may illustrate presumptions about the capital structure of a firm. Several multiples which assimilate the capital structure of a firm have therefore, been used. This would help to evaluate the company in the same way that would be done by an acquirer. The price to earnings multiple fails to amalgamate the sales multiples, cash on hand, EBIT multiples, or EBITDA multiples of a firm.
Multiples of Comparable Companies
Comparable companies’ multiple is based on the assumption that firms whose assets are the same trade their goods and services at homogenous rates (Petitt & Ferris, 2013). Notably, a proportion which assimilates certain values for example, earnings would be same across companies in the same industry. The valuation of a company can thus, be attained by taking into account the figures of other firms in the form of an index which are comparable in size as well as products that operate in the same industry.
Sun is a firm which deals with hardware, business systems and utilities, storage and software such as Java, Solaris, and MySQL. A benchmark of companies which ae comparable to Sun Microsystems must be performed to execute a comparison analysis. See Exhibit 4 to gain a snapshot of the firms which offer tangible and intangible goods.
The companies taken into consideration bearing in mind that Sun is a hardware firm are Advanced, Micro Devices, Apple, Dell, EMC, Hewlett-Packard (HP), Intel, International Business Machines (IBM), and NetApp. These companies had to sieved further to remain only with those who products and services are similar to Sun. These companies are Apple, Dell, Hewlett-Packard (HP), Intel, and International Business Machines (IBM). Advanced Micro Devices, EMC, and NetApp offer product lines and progression plans that are not the same as Sun Microsystems.
The comparable companies’ levered betas reflect a median of 1.12 for the entire industry, and a levered beta of 1.73 for Sun Microsystems (see Exhibit 9). Additionally, we figured out the unlevered beta by computing the debt to equity (D/E) ratio. We used a 35% tax rate (question 2), exhibiting a 9.35% median and a 1.58 unlevered beta for the entire industry. Whilst Sun Microsystems had a debt to equity (D/E) ratio of 25.44% and a levered beta of 2.13 hence, it is considered to be rather higher than the market. This indicates that the business is more perilous compared to the industry in which it operates. Therefore, this denotes the ideal ratio of debt to equity (D/E) that Sun Microsystems must achieve. We also computed the cost of equity by using the capital asset pricing model (CAPM). We substituted a risk-free rate of 2.82% and a market premium rate of 6% (as assumed in question 2). We further computed the debt to capital ratio as well as equity to capital ratio in order to attain the comparable companies’ weights of equity and debt both. We achieved this by using the information provided in Exhibit 9. We reasserted the optimum capital structure that needs to be attained by Sun Microsystems in order to be correspondent to the median of the industry. Each company’s bond rating is mentioned in Exhibit 9, therefore, we took the cost of debt from the corporate bond yields, which is provided in Exhibit 10 (in conformance with the bond ratings for each company).
Lastly, we calculated the WACC and reached a value of 9.50% as the industry’s median and a value of 12.05% for Sun Microsystems. It is therefore, evident that Sun Microsystems has a cost of capital that is much higher than that of the industry. This is reflected in the elevated rate of return that is expected to be received on capitalizing in Sun Microsystems (which denotes that firm is much distressful compared to the other competing companies that operate in the industry).
Finally, we computed the multiples using EBIT, EBITDA as well as Sales (provided in Exhibit 9).
Multiples Analysis
|
|
EBIT Multiple |
EBITDA Multiple |
Sales Multiple |
|
Sun Microsystems |
-1.41 |
-13.15 |
1.72 |
|
Median |
9.40 |
6.28 |
1.39 |
We integrated the multiples’ average values, as they are essential in computing Sun Microsystems’ implied enterprise value (EV).
For us to do the comparable companies analysis (CCA), we needed to figure out the average price per share. We determined that the foremost thing to do was use the average EBIT, EBITDA and Sales average values for the former two years (2007-2008) in order to form our information on documented historical data. Since the accessible data was only for the former two years, we decided to include the data for both years. In the excel sheet Q.4, we included the detailed computations of our calculations in order to find the average price per share, after which we reached an outcome of $13.06 as the average share price.
Economic Fundamentals
To compute the terminal value, we took the U.S. treasury’s earnings (for 10 years) and used it as the risk-free rate (which was substituted as the growth rate). To compute the average price per share needed for the comparable companies’ analysis (CCA), we computed the implied enterprise value (EV) using the averages of the multiples mentioned earlier. Knowing that this comparable companies’ analysis (CCA) would be used to set a benchmark for Sun Microsystems to be valued upon, we must keep in mind that this benchmark might possibly result in an inaccurate computation of the real worth of the company. This would be due to the main fact that some companies are in a considerably more fiscally sound and firm situation compared to our target firm (Sun Microsystems), such as Apple or Dell.
5. Identify the synergies and conduct a sensitivity analysis to estimate the effect of synergies on enterprise value.
The potential synergies were the integration charges of $1.1 billion whereby, $750 million were incurred in 2010 and the remainder ($350 million) being incurred in 2011. A loss of $45 million in operating income was recorded. The loss is attributed to clients’ loss and delay in purchases.
The cost-cutting that would be experienced by Sun after the acquisition is staff reduction at around 20 to 25%. The company will also realize reduction in selling, general, and administrative expenses by 22 to 32%. Furthermore, licensing income, new products, besides “integrated application to-disk” service would result in an annual rise in operating profit by $900 million. As had been previously assumed, these synergies would be slowly increasing over a period of time that is, between 2011 and 2013, attaining its $900 million full capacity in 2013. See the spread sheet (Exhibit Q5.1) about the synergy sources effects.
The spreadsheet (see questions 5.1, 5.2, and 5.3) shows how Sun Microsystems are valued with synergies. Levered beta was obtained from question two in the spreadsheet. Unlevered beta was however, computed by conducting a subdivision of levered beta by multiples by D / E where D is the weight of debt and E is the weight of equity. The other figures which were obtained from question 2 are equity weight, debt weight, market risk premium, risk free rate, cost of equity, WACC, cost of debt, and tax rate. The growth rate equates to risk free rate. This is because there is a relationship between growth rate and risk-free rate. Hence, any changes which occur in risk free rate is correlated to changes in sustainable growth which is also applicable to stand alone computed for question three above. The figures for EBIT and EBIT multiple are obtained from question four. Market value of equity and book value of debt are obtained from exhibit nine in the spreadsheet. The market value of equity and book value of debt are added together to obtain the total value. Debt percentage is computed by dividing the book value of debt over total figure. The synergies obtained are used to find out the discounted free cash flow and free cash flows. More information about the steps to be followed as indicated below.
· EBIT and sales minus synergies were obtain from exhibit fourteen. EBIT minus synergies equates to operating income. Perpetuity growth for sales is computed by multiplying 2014 figure with 1+ growth rate.
· Initial loss in operating income is obtained from the textbook page 679 which is $45 million. The loss is a result of customer loss or / and deferred purchases.
· Integration charges are also obtained from page 679 leading to a total value of $1.1 billion whereby, $750 million was incurred in 2010 and the remaining in 2011.
· The operating profit is annually increasing by $900 million as highlighted by Madison that the synergies would rise gradually in three years beginning 2011. In 2011 therefore, the figure was obtained by taking $900 million and dividing by three years leading to $300 million. In 2012, $300 million was subtracted from $900 million to confirm any increase. The figures for 2013 as well as 2014 are obtained from page 679 which is $900 million.
· EBIT with synergies was calculated by taking EBIT without the synergies less loss in operating income less integration charges then, add rise in net operating profit. The formula was used for years 2010 to 2014.
· The taxes were computed by multiplying tax rate with EBIT. 2010 however, had negative EBIT leading to negative tax values, making it wise to replace with zero because negative taxes are not realistic.
· NOPAT is computed by taking EBIT with synergies less taxes. Perpetuity growth is computed by multiplying NOPAT for last year with 1+ the growth rate.
· Net PPE perpetuity growth and net working capital were computed by multiplying 2014 figure with 1+ growth rate. PPE and net working capital were gotten from question 3.1.
· The change in net working capital is New Year less prior year which applies to 2010 to 2014 and is same for perpetuity growth.
· Changes in capital expenditure are computed by taking 2010 PPE less 2009 PPE. PPE is seen as capital expenditure. This step is also followed when computing perpetuity growth.
· Free cash flows for 2010 to 2014 and for perpetuity growth are calculated by taking NOPAT less change in net working capital less change in capital expenditure. The spreadsheet shows that free cash flows are annually increasing.
· Discounted cash flow was computed by using both perpetuity growths including the multiples (see question 5.2 and 5.3 in the spreadsheet).Net present value was computed by using net present value function which consists of free cash flows and WACC from 2010 to 2014.
· The methods which can be utilized to compute terminal value are perpetuity growth or comparable multiples. Discounted cash flow with perpetuity growth shows that Sun will probably grow throughout. The used growth rate (2.82%) equates to risk-fee rate. The figure is same as terminal value in discounted cash flow with perpetuity growth which was computed as 2014 free cash flow divided by WACC less growth rate. Moreover, discounted cash flow with multiple is computed as EBIT for 2014 multiplied by median multiple which is 9.40.
· Terminal value was divided by 1+ WACC power 5 showing the years from 2010 to 2014 to find out terminal value net present value. This applied to calculation of discounted cash flow with multiple methods and perpetuity.
· To get enterprise value, free cash flow net present value was added to terminal value net present value. Cash and debt were gotten from exhibit eleven. Equity is computed as enterprise value less debt adds cash. Total shares were gotten from exhibit nine and price per share is gotten by taking equity and dividing by shares outstanding.
· Both methods will lead to various prices per share. Discounted cash flow with perpetuity growth will lead to price per share which is $12.79 while discounted cash flow with price per share of multiples will lead to $16.32.
· Specific synergies would take place if oracle acquires Sun;
· Oracle will use Sun’s Java programming to form several applications.
· Sun’s MSQL will assist in adding widening customer base.
· Another added advantage is expansion of product lines as well as risks.
· Research and development and sales teams of both companies will be combined.
The below table shows the sensitivity analysis for the two approaches:
Stand-Alone Sensitivity Analysis:
Synergy Value Sensitivity Analysis:
The sensitivity analysis for the synergy values using the two methods, perpetuity growth method (PGM) and the exit multiple method (EMM) show a higher enterprise value then the stand-alone valuation preformed.
Summary of Results:
|
|
Enterprise Value |
Equity Value |
Price per share |
|
Stand-Alone (Base-Case) using the Perpetuity method |
3,653 million |
5,465 million |
$7.40 |
|
Stand-Alone (Base- Case) using the Multiples method |
5,161 million |
6,973 million |
$9.44 |
|
Synergy using the Perpetuity method |
7,632 million |
9,444 million |
$12.79 |
|
Synergy using the Multiple method |
10,238 million |
12,050 million |
$16.32 |
|
Comparable Company method |
|
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$13.06 |
|
Oracle’s offer price |
|
|
$9.50 |
|
Sun Microsystem (Current Share Price) |
|
|
$6.69 |
With respect to the above sensitivity analysis, it is notable that the Stand-Alone by use of perpetuity method led to an enterprise value of 3,653 million and an equity value of 5,465 million, eventually projecting a price of $7.40 per share which is close to the price per share of Sun Microsystems. When the multiple method for Stand-Alone was used we got $9.44 price per share which has a difference of only $2.75 ($9.44-$6.69). Therefore, the synergies valuation method was used to obtain the accurate results of share price. The synergy using perpetuity method which has an enterprise value of 7,632 million and an equity value of 9,444 million resulted in a $12.79 price per share. In addition, when using the multiple method for the synergy, the price per share of $16.32 shows a major difference between Sun Microsystems and Oracle’s offer price.
6. If a competing bidder appears, how high a price should Oracle be willing to offer?
|
Sun Microsystems Implied Offer Price |
Perpetuity Growth Method |
Exit Multiple |
Sun Microsystems Share Price |
|
DCF using the Standalone Value |
$7.40 |
$9.44 |
$8.42 |
|
DCF using the Synergy Value |
$12.79 |
$16.32 |
$14.55 |
|
Average CCA |
|
|
$13.06 |
|
Current Offer Price by Oracle |
|
|
$9.50 |
Oracle is presently proposing the shares for a value of $9.50 per share for Sun Microsystems. We have used the three different approaches (as portrayed in the table above) in order to ascertain the highest price that Oracle is inclined to pay. In the DCF using the standalone value with perpetuity growth method offered us a value of $7.40 per share. However, when we used the exit multiple method, we got a value of $9.44 per share. Conversely, in the DCF using the synergy value, the perpetuity growth method offered us a value of $12.79 per share while the exit multiple method offered us a value of $16.32 per share. The two values are higher than the price offered by Oracle (which is equivalent to $9.50 per share) in comparison to the DCF with the standalone value.
Moreover, the values of each method, the perpetuity method and the multiples method, were not accounted for autonomously because of the challenges faced (as stated earlier in question 2). Thus, in order to avert misrepresenting the real worth of Sun Microsystems, we decided to take the average of the two methods. Accordingly, to find out what the highest price Oracle might propose to Sun Microsystems, values ranging from $8.42 to $14.55 was given (marking the lowest and highest prices that Oracle may offer to Sun Microsystems). As portrayed, it is evident that share price derived through the comparable companies’ analysis (CCA) and the price offered by Oracle are both contained within the suggested range (prices are $13.06 and $9.50 respectively).
All in all, we decided that the optimum price that should be proposed by Oracle is $11.38. This value was computed by finding the average of all the prices represented above along with the amount that is offered by Oracle ((8.42+14.55+13.06+9.50)/4= $11.38).
7- What approaches and methods are used for valuation of Mergers and Acquisitions; their pros and cons, role of synergies in M&A valuation.
8- How the IT sector in general and software industry in particular has grown in last ten years, who are the major players, what are the key trends and future outlook. Please highlight a recent Merger and Acquisition transaction (other than Sun Microsystem) in the IT sector.
The growth in the IT sector can be looked at from various dimensions. One of this dimension is the number of new users; this can be looked at by looking at the number of internet users for the last ten years, as at December 2008 the figure stood at 1.5 billion representing 23.5% of the world population while currently the figure stands at above 55%. This has been pushed by the availability of portable gadgets such mobile phones (Ray, 2018).
The other dimension is in terms of innovations and technological changes, every system or even simple website has to make provision for social media. Mobile phones have become a substitute to computers and every company has to come up with mobile friendly or compatible versions in order to cut a niche in the market. Technology giants such as Samsung and Apple have in the period engaged in fierce competitions with new gadgets being released every year, the budget therefore has changed with research and development cost going up. Oracle has had to release new versions of the database from year 2007 when 11g was released to the current 18c.
The other dimensions is in terms of strategic alliances over the years, in the last ten years giants have fallen and new giants have come up, mergers and acquisitions have been common in the past 10 years with one of the largest being Verizon communications and Verizon wireless at a purchase price of over $130 billion. One of the most recent acquisitions was by Germany giant SAP where it acquired Qualtrics for $8 billion. Qualtrics is market survey software maker and before the take over the company had planned an IPO to raise $485 but the takeover deal was a better deal for the owners and the shareholders since the IPO would have taken the company valuation to around $6 billion.
Over the last few years, Amazon, Apple, Google and Samsung have dominated the market in various aspects such research, funding, capitalization and revenues. Other major players in the industry include Microsoft, Verizon and Facebook among others. Looking forward mergers and acquisitions are bound to increase with a common trend of venture capitalist coming in to develop IT companies and selling them later. Looking at most startups in the IT sector the main agenda is shifting from competing with the giants to capturing the attention of the giants for a possible acquisition or merger. In the near future there will be cut throat competitions from the giants with an effort to acquire small firms and form strategic alliances. I foresee scenario where the market is bound to turn to an oligopolistic market owing to the many mergers and acquisitions.
Conclusion
It is recommended that Oracle acquires Sun Microsystems. Oracle will be able to add new products such as MySQL, Java, and Solaris to its portfolio. The acquisition will also weaken the competition among the two companies even though the nature of competition is indirect. The acquisition can however, create cannibalization on Oracle’s software. Nevertheless, the acquisition will grant Oracle an opportunity to increase its market shares by dealing with consumers at the lower-end of the market segment. On the other hand, the WACC of Sun Microsystems is 12.05%, reflection that investing in the company is appealing but comes with a high-risk level. The methods which were used to arrive at the best price which Oracle should offer Sun’s shares were discounted cash flow and multiple valuation method. Discounted cash flow estimates the stand-alone of Sun Microsystem by using WACC, equity value, and enterprise value. As illustrated by the spreadsheet, the enterprise value of $3,653 million and $5,465 million equity value led to $7.40 share price. Notable, the difference between the obtained share price and the original share price of $6.69 was little. The little difference is because the enterprise value was calculated using terminal value, leading to conclusion, that the values emanate from the future. In relation to discounted cash flow, the investment is future and not present focused. The final price per share was at a range $8.42 to $14.55. The changes in the IT sector as well as software industry has been assessed in terms of internet users, innovation, and strategic alliances. Overall, the IT sector has realized immense growth over the last decade. In conclusion, Oracle should Acquire Sun Microsystems as the benefits outweigh the costs.
References
Brigham, E., & Ehrhardt, M. (2013). Financial management: Theory and practice. Mason, Ohio: South-Western.
Comptia. (2018). IT industry outlook. Retrieved from https://www.comptia.org/resources/it-industry-trends-analysis
Kumar, B. (2012). Mega mergers and acquisitions: Case studies from key industries. Basingstoke: Palgrave Macmillan.
Nicalao, H. (2012). Sun acquisition by Oracle. New York, N.Y.: Crypt Publishing.
Petitt, B., & Ferris, K. (2013). Valuation for mergers and acquisitions. Upper Saddle River, N.J.: FT Press.
GEO 200 In-Class Activity
Name _________________________________________________
In-class activity 4: Earth – Sun Relationships
Introduction
Solar radiation that enters the Earth-Atmosphere system is the primary source of energy for nearly every atmospheric process on Earth. The unique relationship between the Earth and Sun is what causes the seasons, controls the length of days, and organizes the basis for keeping track of time. An understanding of this relationship is essential when learning about atmospheric processes on Earth.
Basic Earth-Sun Geometric Relationships
The earth’s orbit around the sun is elliptical, varying the distance between the earth and sun throughout the year. While the average distance between the earth and the sun is approximately 150 million kilometers (93 million miles), the actual distance at any given time fluctuates by as much as 5 million kilometers (3 million miles). The earth is nearest the sun (perihelion) during the Northern Hemisphere’s winter (January) and is farthest from the sun (aphelion) during the Northern Hemisphere’s summer (July).
The sun’s rays are close to parallel to each other as they stream toward earth, so if the earth’s axis of rotation was perpendicular to the plane of the ecliptic, the sun’s most direct rays would always be received at the Equator. In this case, there would be no seasons.
Seasons occur due to the tilt of Earth’s axis of rotation. The axis is an imaginary line that connects both poles, and it is tilted at an angle of 23.5 relative to the plane of the ecliptic, the plane on which the Earth revolves around the Sun. Since the axis of rotation is always oriented in the same direction (pointing toward the North Star), different latitudes receive direct solar radiation at different times throughout the year.
Due to its rotation, half of the Earth is always receiving some portion of Sunlight, known as the circle of illumination. However, the tilt of the Earth’s axis also controls daylength. During June, the Northern Hemisphere is tilted toward the Sun and experiences longer daylengths. During December, the Northern Hemisphere is tilted away from the Sun and experiences shorter daylengths.
The Arctic Circle (66.5N) and the Antarctic Circle (66.5S) outline the polar regions of our planet. The area within each circle experiences 24 hours of daylight on its June Solstice (Summer in the Northern Hemisphere; Winter in the Southern Hemisphere); likewise, the December Solstice (Winter in the Northern Hemisphere; Summer in the Southern Hemisphere) brings 24 hours of darkness. During both Equinoxes (Vernal in March and Autumnal in September), daylength is 12 hours at all latitudes across the globe.
Solar Declination
The seasonal temperature changes are controlled by the amount of direct radiation received at the surface. As a result of the tilt of the axis and the curvature of the Earth, some latitudes receive direct radiation while other latitudes receive radiation at an oblique angle. When radiation strikes an object at an oblique angle, the energy is distributed over a larger area and is less intense.
The latitude at which the Sun is directly overhead at noon is the solar declination. The solar declination for the June Solstice is 23.5N (Tropic of Cancer), and 23.5S (Tropic of Capricorn) for the December Solstice. During both Equinoxes, the solar declination is at the Equator (0). The solar declination changes every day as the Earth revolves around the Sun, but is constrained between the Tropics.
1. List the date and the solar declination for each position.
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Date |
Solar Declination |
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Summer Solstice
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Autumnal Equinox
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Winter Solstice
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Vernal Equinox
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2. Label the diagram below with the appropriate date for each position.
3. In the diagram below, what is the date?
4. Using the diagram above, describe the day or night length from the Arctic Circle to the North Pole.
5. What percentage of the Earth is illuminated at noon December 21 (or at any time)?
6. How many hours of daylight does the South Pole receive on March 21?
7. How many hours of daylight does the South Pole receive on June 21?
8. Which latitude(s) experience the GREATEST seasonal change in daylight hours? (In other words, do any areas on the globe change from completely dark to completely lit over the year? Where does this happen?)
9. What would happen if the earth’s axis of rotation was NOT tilted at a 23.5° angle?
10. Give the numerical latitude and cardinal direction for the 5 major lines of latitude.
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Arctic Circle
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Tropic of Cancer
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Equator
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Tropic of Capricorn
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Antarctic Circle
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Solar Angle
In addition to the solar declination, it is useful to understand some related geometric terms: zenith angle: the angle between a point directly overhead and the Sun at solar noon, and solar angle: the angle of the Sun above the horizon at solar noon. These angles are important because they determine the amount of insolation (incoming solar radiation) potentially received at the surface of the Earth.
To determine the zenith angle at a particular location, calculate the number of degrees of latitude separating the solar declination and the location in question. If the declination or latitude is in the southern hemisphere, it will be a negative value. The zenith angle should always be positive; therefore, you should report the absolute value of the zenith angle.
Example: zenith angle = (location latitude) – (solar declination)
At Alexandria, VA (39N) on January 20 (solar declination: 20S)
Zenith angle = 39 - (-20)
Zenith angle = 59
At Sao Paulo, Brazil (23S) on January 20 (solar declination: 20S)
Zenith angle = -23 - (-20)
Zenith angle = -3
Absolute value zenith angle = 3
The solar altitude angle is calculated by subtracting the absolute value of the zenith angle from 90. As the solar declination progresses, the zenith angle decreases and the solar altitude increases. At solar noon at the latitude of the solar declination, the zenith angle is 0 and the solar altitude angle is 90. The zenith angle and the solar altitude angle are significant because the Sun’s rays are much more intense where they strike the Earth directly (zenith angle of 0 and a solar altitude of 90) (Figure 3.3).
Figure 3.3: Zenith angle (A) and solar altitude angle (B) for 30N on December 21.
11. First, calculate the zenith angle for Alexandria, VA (39N), St. Petersburg, Russia (60N), and Sydney, Australia (33S) on the following dates. Show your work, and then check your work before you proceed with the solar angle table.
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Alexandria |
St. Petersburg |
Sydney |
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March 21
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June 21
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September 21
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December 21
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12. Now, using your answers from the table of zenith angles, calculate the solar angle for Alexandria, VA (39N), St. Petersburg, Russia (60N), and Sydney, Australia (33S) on the following dates. Show your work.
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Alexandria |
St. Petersburg |
Sydney |
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March 21
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June 21
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September 21
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December 21
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13. Graph your solar altitude angle results for Alexandria, St. Petersburg, and Sydney on a line graph. Your x-axis should be time of year, and your y-axis should be solar altitude angle. A line graph requires that you connect the plotted data with a line, per each location, so you will have 3 different lines. Make sure that you follow the rules of making graphs and supply a name for the graph, and correct units and labels for each axis.
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Answer the following questions using your graph.
14. Which location likely receives the most insolation during June?
15. Which location is probably the warmest during December?
16. In which month does Sydney likely receive the most insolation?
8
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