8. A Piper Cherokee is flying at 4000 ft standard altitude at 105 mph. The wing has a rectangular planform (shape) with a span of 30 ft and a chord of 5.33 ft. Assuming that the turbulent boundary layer grows as on a smooth plate and a completely turbulent boundary layer flow, determine: (a) The boundary layer thickness at the downstream edge of the wing. (b) The total skin friction drag coefficient of the wing. (c) The total skin friction drag of the wing in pounds.

9. Repeat the analysis for Prob. 8 assuming that the boundary layer is laminar.

Discuss three major differences between a “traditional” church and a new paradigm church. Use real-world examples to illustrate your points

What is the significance of the Christian Divergence (split between the Roman Catholic Church and Eastern Orthodox Church)? Discuss its consequences for the west and the world at large.

Opportunity or temptation?

Journal of Case Studies

Introduction

Their facility was just too small. Steady growth had them bursting at the seams. Finally, after years of searching, they thought that a suitable location finally had been found, a location that might garner enough support to win membership approval when it came time to vote. Capacity, turmoil, turnover, a bad economy, limited budget, and aged physical plant were all constraints that had held back Hope Community Church (HCC). But there were good reasons that its name was Hope. One was that its leadership core was made up of people who were of strong faith and strong will. Leadership believed that constraints were nothing more than speed bumps that could be overcome. Turmoil and turnover had already been overcome. The bad economy was subsiding and, at least regarding monthly operations, the church budget was no longer an issue. The final constraints, capacity and structural integrity of the church building continued to be problematic and underscored the need to relocate the church.

Sometimes, things are beyond repair or are no longer suitable for their intended purpose, but facing the need for change can be a difficult challenge. HCC's church sanctuary had some serious structural problems. So, for many years, a church building committee had been in search of a better facility or building site. More than once it was thought that a suitable "new" location or facility had been found, but each time a fatal flaw had been discovered. Finally, the church building committee had found what seemed to be an affordable acreage on which they could build. Now church members had to make the decision as to whether or not to buy the new site. Still, it was not without potential problems. But hopefully, church members would not consider any of them to be major when it came time for them to vote. Should the church membership vote yes on its opportunity to purchase the land for construction of a new church, or, vote no and continue to meet in the current facility, and once again ask its building committee to start over in its quest for a new building site?

The thought of moving to a new location touched emotions on both sides of the issue. One group of church members had strong personal attachments and memories that were inextricably tied to the old sanctuary. For many of these long term members who favored remodeling and making do with the current facility, moving was out of the question. The oldest active member of the church, and perhaps the church's most loved member, was a stoic advocate for remaining with the status quo as she had been married in the old sanctuary decades ago and had no desire to move. She had a strong following, and it was no secret that she was not excited about the possibility of the church relocating. In fact, her opinions were so well known that there was concern among the church leaders that moving to a new location could so offend her and other long term members that they might leave the church.

However, other members thought that remaining in the current facility was untenable. This group, that included much of church leadership, was more concerned with adequacy and stewardship than nostalgia. They openly expressed their opinions that it was past time to abandon tradition and move on. To them, throwing more money at the small, deteriorating church sanctuary seemed an unreasonable thing to do. Would remaining in the current facilities strangle church growth? The opinions of these two groups would heavily influence the upcoming membership vote as to whether or not to buy new property.

Bursting at the Seams

Serving a farm community of about 3,000 people in beautiful southern Colorado, particularly among young families, HCC had experienced steady growth, and church attendance had doubled over the past five years. During that same time period, tithes and offerings had grown from $185,000 to $250,000 annually. Now, often with more than 80 percent of its seats occupied, HCC's current facility was both literally and figuratively bursting at the seams.

Built in the early 1900s, the church sanctuary had served many years as the center for both fellowship and spiritual gatherings. Since the pictures that had been taken that showed a hitching post where worshipers could tie their horses, the structure had been updated many times. Gone were the old coal burning stoves, as well as their old, dangerous gas replacements; they had been replaced with safer more fuel efficient gas burning furnaces. Gone were many of the old single pane windows; they had been replaced with energy-saving double pane windows. Bathroom facilities had been dramatically improved as had the kitchen facilities and furnishings.

Still, it was about a 100 year old wood and stucco structure sitting on dry rotted sill plates supported by a deteriorating rock and concrete foundation. In hindsight, the foundation had not been tall enough; the freezing and thawing that accompanied the melting snows of spring had eventually taken their toll, and little by little, the structure had slowly begun to sink. Some temporary mitigation had been provided by jacking up the building and inserting railroad ties under the floor joists, but maintenance costs continued to rise. From the steeple to its foundations, the church building had problems. Certainly if enough money were thrown at the structural problems, they could be solved. However, even if that were done, it would still just be an old building that the congregation had outgrown. And, remediation costs could be even greater than the costs of building a new structure. Rebuilding, on site, made little financial or practical sense, but some members of the congregation were still reluctant to move for sentimental reasons.

Both the city lot, 50' wide x 150' long, and the building were just too small. Membership was growing across all age groups, and finding a seat to attend church services had become problematic. Upon entering the packed facilities and surveying the lack of available seating potential, new congregants sometimes just turned around and left, never to be seen again. Hopefully, they found a church home in one of the other city churches that had excess capacity.

There were no church facilities for HCC's adult Sunday school. Classes had to be held in two rented rooms in a building half a block away, accessed by a rough graveled alley complete with mud puddles whenever it rained or snow melted. Sunday school for the church's swelling children ministry was held in yet another building. It was a too small 1960s vintage Housing and Urban Development (HUD) type house that also inadequately housed the church's administrative staff. Though needed, there was no youth ministry. There just was no place for them to meet. The church library was an old closet, and, not a very big one. There were no rooms for gatherings of the church's servant leadership team, elders, deacons, or women's ministry. There wasn't even room for the pastor to have an office. His office was in his home, about five miles from the church. In addition, what little bit of off-street parking that could be found did not come close to serving the needs of attending church members. Many members parked on the streets and in driveways of consenting owners. As the church continued to expand, these needs would not only increase but also constrain growth.

One possible partial solution that had been considered but rejected was to just increase the number of church services. Membership did not want to lose touch with other members who chose to attend the "other" service, and the small but dedicated praise and worship team did not want to commit to leading an additional weekly service. HCC was a small nondenominational church. While leadership certainly made efforts to interact with other church leaders, it was without the benefit of the organized network and knowledge base typical of larger denominations. Though there also was no evidence that they did so, had they felt the need for it, leadership might have gleaned some additional support regarding the need to relocate or build from information available through sources such as The Alban Institute (http://albiston.com).

Searching for a Solution

These problems certainly had not escaped the attention of church leadership. Eight years ago, the church had purchased highway acreage on the outskirts of town. It then slowly accumulated funds with which to build. It had made a good start and had accumulated about $110,000 when the church mission team identified an urgent need to support a TEARS (true evangelism always requires sacrifice) missionary dream in a third world country. Money was needed to provide housing, food, education, and spiritual training for impoverished single parent children including many girls who might otherwise become trapped in the horrors of human trafficking. Consistent with church goals, the membership enthusiastically voted to invest most (about $70,000) of its building fund in the effort to help save some of a third world country's young from despicable lives. The rest of the fund would be invested in a remodel of the sanctuary to address structural problems.

Several years later, after growing its building fund, the church building committee again started making plans to build on the site on the outskirts of town. Not long into the process, a problem was discovered. A government change in building codes now would require the church to fund acceleration/deceleration lanes to the adjacent highway, and that was expected to increase the cost of building by $500,000.

Five hundred thousand dollars would more than exhaust all of HCC's building funds and leave it unable to start construction. After considerable discussion, the decision was made. Church leadership recommended, and the church membership approved, that the acreage be resold. It was, and the church harvested a substantial profit of about $200,000. The profit enhanced the building fund and paved the way for a new search for a larger existing facility or a cost effective building site.

Renewed Hope

Unfortunately, such sites proved to be scarce. Church membership had a strong desire to build within the city limits, but few undeveloped parcels of adequate size remained. Those that did remain were owned by the city's school board, other government agencies, or farmers who did not want to subdivide their holdings. Time and again, over a period of years, the church's building committee investigated possible sites only to discover "show stopping" flaws. Some sites were too expensive; some were too small. Some, with existing structures, did not provide the needed space or could not be cost effectively remodeled. Others were too remote, or too far outside the city limits.

After several years of fruitless searching, in a private conversation with a public minded elderly land owner of an unlisted property, a building committee member discovered a possible site. It wasn't ideal; by now it was known that those sites either did not exist or were prohibitively priced. But the price on this parcel seemed right. At $110,000, the cost would only consume about one third of the church's building funds; there would still be money left over for construction of an economical metal building. So, after assurances that it would be a bargain purchase by a trusted realtor who had written the contract and who had long been an active church member, and one of its Sunday school teachers, church leadership acted decisively to lock in the opportunity to purchase the new parcel.

The church had lost out on other opportunities when those had become publicly known. Sometimes it had been "outbid". On one occasion, approval of a sale to the church had been nixed by regulatory board members who favored a non-church use for land over which the board had control. There was concern that this parcel also might get snatched away from the church by a higher bidder, if the owner's asking price became public knowledge. Hence; acting with approval of the church leadership team, HCC church pastor, Keith Wickman, signed a contract to buy the land and authorized $5,000 of earnest money as a down-payment towards its purchase.

One advantage of this parcel was that it was more than big enough for church needs. In total, it was about twenty acres; most of it was on a steep hillside or in a flood plain and not suitable for construction. However, about six acres were suitable for building, so space would not be a problem. The church would have more than enough land for building not only to meet its current needs but also for those of the foreseeable future. And unlike some other parcels that had been considered, where it was not clear that the church could get approval to build, on this land zoning was not a problem. So, that was another advantage of this land; there should be no problems getting necessary governmental approval to build the church. Yet another advantage was that the land had already been legally subdivided, so reselling some of the land was a possibility should the church need to raise additional funds. In fact, a one acre parcel even had commercial zoning dating back to a time when it had once been used as a meat processing plant. Besides affordable cost, among its advantages was that the acreage was within the city limits. It was in an area that so far had not yet experienced much development. But, as would be revealed in an upcoming meeting, that lack of development seemed to be destined to change.

Troubling Concerns

The contract had been carefully written to protect church members' interests (e.g. to recover its earnest money if the church voted not to complete the purchase). Before the church could close on the contract, in accordance with its bylaws, it had to obtain a two-thirds majority approval of church membership by a vote of its congregants. Prior to the vote, Pastor Wickman, mailed church members a letter that expounded upon the land's good qualities. In addition, during church services Pastor Wickman announced that following church services, the church building committee would host two weekly meetings to allow church members to raise questions regarding the possible acquisition.

The meetings were lightly attended; only a handful of church members stuck around to participate, and only a few questions were asked. One of the questions asked, was about access to the property. It was said that there was an existing 10-12' wide paved road that led to the property. Only two homes, ones that had existed for many years, were nearby; both had constructed additions that were within five feet of the pavement and probably encroached on the city right of way. Another building committee member, who was also a city school teacher, did not hesitate to add that those structures no doubt would be condemned when the city began construction of two new schools at an unspecified future date.

Asked if there was another access road, it was revealed that there was an undeveloped forty foot easement that led to the land. When questioned as to how much it would cost to improve the easement to meet government standards, a committee member responded that the committee did not know and could not find out until after the purchase was completed. When asked why that was so, it was said that the city's building department members refused to discuss the matter with the church building committee because the church was not the legal owner of the property.

When asked about utilities, building committee members revealed that electricity had already been installed but city water had not been extended to the property. Asked as to the cost to bring city water to the property lot line, again the building committee did not know; the city's building department refused to discuss such issues with the church building committee because the church was not the property owner.

Asked about the remaining, unusable land, the committee indicated that part of it was a steep hillside. The rest was in a flood plain, had a stream running through it, and had settling ponds left over from the days when the meat processing facility had discharged effluent (waste water). Might there be Environmental Protection Agency cleanup costs associated with the settling ponds? Building committee members were amused at the question and could see no reason to expect that there might be. However, to protect against the remote possibility that a child might somehow wander astray and drown in one of the ponds, the church would probably need to enclose the ponds with a chain link fence. With that question, the first meeting came to a close, and the second meeting, a week later, resulted in no questions at all.

At the conclusion of the following week's sermon, Pastor Wickman encouraged members to remain for a business meeting to vote on the possible land purchase. He briefly reiterated that the church had entered into a contract to buy acreage on which to build its new church and gave a brief description of the parcel. He then asked church members if anyone had questions regarding the land purchase. A woman asked if it was known what it would cost to pave the easement to the land. Pastor Wickman reported that an estimate of $750,000 (far more than what the church had in its building fund) had just been obtained. It was also stated that it was unknown how much of that amount would be absorbed by the new schools and other developments and how much would be the responsibility of the church or when the church might be able to build on the land if it were acquired. It was also disclosed that both the church building committee and the church's Servant Leadership Team had voted in favor of the acquisition but that neither had done so unanimously. One member of each group voted against the acquisition, but Pastor Wickman did not provide reasons for the dissenting votes and no church member asked for an explanation. With these facts in hand, the church membership was asked to vote.

1. What is the finacial analysis?

2. Based on the reading, what can we recommend?

3. What could be the risks/challeges/solutions?

The Japanese market is on the verge of rising again, and the UK market is doing better than the US market in the current economic recovery. Therefore, as a US investor, John is contemplating investing in the Japanese and UK stock markets. Using the historical data, John has estimated the means, volatilities, and correlation of the US, UK, and Japanese stock markets as the following:
US UK Japan
Means 0.120 0.150 0.084
St. Dev. 0.150 0.240 0.220
Correlation matrix:
US UK Japan
US 1.000 0.500 0.266
UK 0.500 1.000 0.358
Japan 0.266 0.358 1.000
Assume that the risk-free rate is 4%. .
(a) Given the data above, what are the Sharpe ratios on the US portfolio and the UK portfolio? Given the correlation between US and UK above, should John add the UK portfolio to his US only portfolio?
(b) To see how robust his conclusion is on the issue of adding UK stocks to his portfolio, John wants to know the lowest expected return on UK stock can be in order to improve his Sharpe ratio from holding the two country stocks, given the correlations, volatilities and US Sharpe ratio. What is it? Show your reasoning and computations.
(c) What is the Sharpe ratio for the Japanese equity? Similar to (b), compute the lowest expected return for the Japanese equity. Are the differences between your answers to (b) and (c) surprising? Why or why not?

We consider the Boundary Value Problem :

u'(x)+u(x)=f(x), 0<x<1

u(0)-eu(1)=a

,a is real number kai f is continue in [0,1].

1. Find a a necessary and sufficient condition ,that Boundary value problem is solvabled.

2. Solve the Boundary value problem with a=0.

Their new task consisted of determining Entergy Corp.’s value in common stock, preferred stock, and bonds. With this information, they were to prepare a second seminar to explain the valuation process to the clients

Nicholas and Karina were able to obtain the following information in regard to Entergy Corp.’s long term obligations. The table indicates the first three first-mortgage bonds listed in the Annual Report.

Table 1

Nicholas and Karina concluded that the effect of increased concern in regards to any event risk, was to lower Entergy Corp.’s cost of bond financing. The following information was gathered through the use of Value Line Survey.

Entergy’s recent price was $38 per share with a P/E of 14.6 and a dividend yield of 4.8%. Its beta was .60.

Earnings Per Share

Quarterly Dividends Paid Per Share

FMS SECURITIES CASE B - Questions

1.) Entergy Corp. has $54,956,000 of preferred stock outstanding.

a.) Suppose its Series A, which has a $100 par value and pays a 4.32 percent cumulative dividend, currently sells for $48.00 per share. What is its nominal expected rate of return? It’s effective annual rate of return? (Hint: Remember that dividends are paid quarterly. Also, assume that this issue is perpetual.)

b.) Suppose a Series F, with a $100 par value and a 9.75 percent cumulative dividend, has a mandatory sinking fund provision. 60,000 of the 300,000 total shares outstanding must be redeemed annually at par beginning at the end of 2004. If the nominal required rate of return is 8.0 percent, what is the current (January 1, 2004) value per share?

2.) Now consider Entergy Corp.’s common stock. Value Line estimates Entergy Corp.’s 5- year dividend growth rate to be 6.0 percent. Assume that Entergy Corp.’s stock traded on January 1, 2003 for $22.26. Assume for now that the 6.0 percent growth rate is expected to continue indefinitely.

a.) What was Entergy Corp.’s expected rate of return at the beginning of 2003? Value Line estimate Entergy Corp.’s dividends to be $1.80 at the start of 2003.

b.) What was the expected dividend yield and expected capital gains yield on January 1,

2003? Describe the relationship between dividend yield and capital gains yield over time under constant growth assumptions.

3.) What conditions must hold to use the constant growth (Gordon) model? Do many “real world” stocks satisfy the constant growth assumptions?

4.) Suppose you believe that Entergy Corp.’s 6.0 percent dividend growth rate will only hold

5 years. After that, the dividend growth rate will return to Entergy Corp.’s historical 10-year

average of 7.5 percent. Note that D6 = D5 x 1.075. (Use to answer questions 4-8)

a.) What was the value of Entergy Corp.’s stock on January 1, 2003 (the end of 2002), if the required rate of return is 13.5 percent? Remember this value you calculate does

not have to agree with the market value of $22.26.

5.)

a.) What is the expected stock price at the end of 2003 (beginning of 2004) assuming

that the stock is in equilibrium?

b.) What is the expected stock price at the end of 2004 (beginning of 2005) assuming

that the stock is in equilibrium?

6.) What is the expected dividend yield, capital gains yield, and total return for 2003?

Hint: You need the expected January 1, 2003 price to compute.

7.) Suppose Entergy Corp.’s dividend was expected to remain constant at $1.80 for the next 5 years and then grow at a constant 6 percent rate. If the required rate of return is 13.5 percent, would Entergy Corp.’s stock value be higher or lower than your answer in Problem 4?

8.) Entergy Corp.’s stock price was $22.26 at the beginning of 2003. Using the growth rates given in the introduction to this question, what is the stock’s expected rate of

return?

9.) Based on the information provided in Value-Line Tables is the assumed 6 % growth rate reasonable? What has been the trend?

10.) Given Value-Line’s ROE estimated for 2005 through 2007 and at the projected

earnings and dividends per share for the same period.

1. Could those figures be used to develop an estimated long-run “sustainable” growth rate?

2. Does this figure support the 7.5 percent growth rate given in the problem?

Hint: Think of the formula g = br = (Retention ratio)(ROE)

the Brewster angle for a certain media boundary is 33°. what is th me critical angle for total internal reflection for the same boundary?

Hello! I have some questions related to using Ansys Fluent, I have read the instruction of Ansys Book , but I still do not understand clearly, can you help me? They are as the following:
1. When do we need to use pressure inlet for B.C for the inlet boundary and pressure outlet B.C for the outlet boundary?

2. Can we use pressure inlet B.C for the inlet boundary and outlet B.C for the outlet boundary in one fluid flow study (air flow, gas flow..)? The reason why I ask this question because I used to see on the internet written that if we use pressure inlet B.C for the inlet boundary, we are not recommended to use pressure outlet B.C for the outlet boundary, we are recommended to use velocity outlet B.C for the outlet boundary. Is it right or not?

3. Does the operating pressure in the operating condition effect the gauge pressure in the pressure outlet/ inlet ?

4. In the wall B.C, what does it mean if I choose the stationary wall or the moving wall? Sorry, I have read the instruction of ansys, but I still do not get it.

Thank you in advance! I will thumb you up!