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# Important information about Present Value Analysis

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Present Values. Compute the present value of a \$100 cash flow for the following combinations of discount rates and times:
1. r = 8 percent, t = 10 years.
2. r = 8 percent, t = 20 years.
3. r = 4 percent, t = 10 years.
4. r = 4 percent, t = 20 years.

Future Values. Compute the future value of a \$100 cash flow for the same combinations of rates and times as in problem 1.

Calculating Interest Rate. Find the interest rate implied by the following combinations of present and future values:

Present Value Years Time period
\$400 11 \$684
\$183 4 \$249
\$300 7 \$300

Loan Payments. If you take out an \$8,000 car loan that calls for 48 monthly payments at an APR of 10 percent, what is your monthly payment? What is the effective annual interest rate on the loan?
(using the excel PMT function)

Amortizing Loan. You take out a 30-year \$100,000 mortgage loan with an APR of 6 percent and monthly payments. In 12 years you decide to sell your house and pay off the mortgage. What is the principal balance on the loan?

Amortizing Loan. Consider a 4-year amortizing loan. You borrow \$1,000 initially, and repay it in four equal annual year-end payments.

1. If the interest rate is 8 percent, show that the annual payment is \$301.92.
2. Fill in the following table, which shows how much of each payment is interest versus principal repayment (that is, amortization), and the outstanding balance on the loan at each date.

Bond Yields. A bond with face value \$1,000 has a current yield of 7 percent and a coupon rate of 8 percent. What is the bond's price?

Bond Pricing. A 6-year Circular File bond pays interest of \$80 annually and sells for \$950. What are its coupon rate, current yield, and yield to maturity?

Bond Prices and Yields.

1. Several years ago, Castles in the Sand, Inc., issued bonds at face value at a yield to maturity of 7 percent. Now, with 8 years left until the maturity of the bonds, the company has run into hard times and the yield to maturity on the bonds has increased to 15 percent. What has happened to the price of the bond?
2. Suppose that investors believe that Castles can make good on the promised coupon payments, but that the company will go bankrupt when the bond matures and the principal comes due. The expectation is that investors will receive only 80 percent of face value at maturity. If they buy the bond today, what yield to maturity do they expect to receive?

A project has a cost (projected outflow of (\$14,000) in year 0.
This project has the following projected inflows in years 1-5:
Year 1 \$ 2,000
Year 2 \$ 4,000
Year 3 \$ 7,000
Year 4 \$ 7,000
Year 5 \$ 7,000

Ø When is the pay back? (Year / months):

Ø If this firm has a payback policy of 3 years, will this project meet that criteria?:

Consider the data on the following two mutually exclusive projects under consideration by the Stephen Company:

Year

Project A

Project B
0

-30,000

-60,000
1

10,000

20,000
2

10,000

20,000
3

10,000

20,000
4

10,000

20,000
5

10,000

20,000
The cost of capital is 14%.
Given this information, calculate the following values for each project using the time value tables in the text:
Ø NPV
Ø IRR (Round to the nearest whole percentage.)
Ø Profitability index
Ø Payback period

#### Solution Preview

Present Values. Compute the present value of a \$100 cash flow for the following combinations of discount rates and times:
1. r = 8 percent, t = 10 years.
2. r = 8 percent, t = 20 years.
3. r = 4 percent, t = 10 years.
4. r = 4 percent, t = 20 years.

PV = FV/(1 + i)n where PV is the present value
FV is the future value
i is the interest rate
n is the period
1. PV = 100/(1 + 0.08)10
PV = 46.32
2. PV = 100/(1 + 0.08)20
PV = 21.45
3. PV = 100/(1 + 0.04)10
PV = 67.56
4. PV = 100/(1 + 0.04)20
PV = 45.64

Future Values. Compute the future value of a \$100 cash flow for the same combinations of rates and times as in problem 1.

FV = PV (1+i)n where PV is the present value
FV is the future value
i is the interest rate
n is the period

1. FV = 100(1 + 0.08)10
FV = 215.89

2. FV = 100(1 + 0.08)20
FV = 466.10

3. FV = 100(1 + 0.04)10
FV = 148.02

4. FV = 100(1 + 0.04)20
FV = 219.11

Calculating Interest Rate. Find the interest rate implied by the following combinations of present and future values:

Present Value Years Time period
\$400 11 \$684
\$183 4 \$249
\$300 7 \$300

400 = 684/(1 + i)11
(1 + i)11/11 = (1.71)1/11

i = 5.00

183 = 249/(1 + i)4
(1 + i)4/4 = (1.3607)1/4

i = 8.00

300 = 300/(1 + i)7
(1 + i)7/7 = (1)1/7

i = 0.00

Loan Payments. If you take out an \$8,000 car loan that calls for 48 monthly payments at an APR of 10 percent, what is your monthly payment? What is the effective annual interest rate on the loan?
(using the excel PMT function) please refer to excel file.

Effective annual interest rate
= (1 + 0.10)12 - 1 = 10.47%
12

Amortizing Loan. You take out a 30-year \$100,000 mortgage loan with an APR of 6 percent and monthly payments. In 12 years you decide to sell your house and pay off the mortgage. What is the principal balance on the loan? please refer to excel file.

79,089.55

Amortizing Loan. Consider a 4-year ...

#### Solution Summary

This solution is comprised of a detailed explanation to calculate the present values, the bond price, and the NPV, payback, and IRR of the projects.

\$2.19
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## Budgeting and Financing Problems

Darren is 45-year old Caucasian male who is currently in career counseling due to a host of issues that has eventually led to his unemployment for the past year. He is a well-educated man that he has lived in cities all his life, growing up in Chicago and moving to New York and Houston for university and graduate school.respectively. After completing his architecture studies, he lived and worked in LA for a decade after which he moved to Portland, Oregon. As a landscape architect, the primary issue he had in his previous job is his difficulty in getting along with others in a structured environment, especially with his supervisor. He admits that this is a pattern, made the worse recently as while he is currently unemployed, he is also in the process of divorcing his wife and fighting for the custody of their son. Darren's interests are creative and singular pursuits like photography, and digital design. Concurrently, he receives financial help from his parents but feels that their help in all aspects of his life is never enough. SO far as his counseling has gone, he has taken a number of instruments to assess his interests and personality type.

Presenting problem

The presenting problem refers to the manner by which the client presents or introduces the issues he or she has to the therapist. The issue here is that clients are not necessarily sure about what to say because they themselves are confused about why they act or feel in certain ways so that the problem the client presents is not usually the true issue, made much worse if the client is embarrassed or afraid to face painful truths. In Darren's case, one of the presenting problems that has come to my notice is his current situation - he appears to be in the middle of a difficult divorce and as such, it is a very stressful time for him - fighting for custody as an unemployed father depending on his own parents for financial support does not bode well for his chances at getting custody of his child. Additionally, there is the problem that he says that he has issues with the supervisor. It could be that because of his personality type, structured environments are just not for him - so the supervisor is not his problem, the system of his employment is.

Stage 1

Stage 1 is all about exploring the problem - making sense of what is presented. In this case, the intake and the proceeding sessions center on talk to mesh out the details that matter, to establish roles and trust and to construct a secure pattern of talk and communication in the therapist-client relationship. Personally, to develop rapport, it would be good to encourage talk and to establish in the client that my intent is only to help him. The measures of confidentiality, of trust - they have to be established here side by side with a non-judgmental and an emphatic stand. Also, by employing active listening skills and interjecting when needed as well as disclosing bits and pieces of my own experience here and there to encourage talk and the notion of relativity and trust, I believe that stage 1 can be effective. Lastly, it will be important for me to employ an informal setting, listing down information and asking questions that relate to the main topic of the discussion so as to encourage the construction of relevant meaning making on the client's part. Thus, I will encourage Darren to talk freely, and ensuring that he does so by encouragement, by active listening. This will all be used to explore his relationship with his soon to be ex-wife, his child, his supervisors and colleagues.

Stage 2

Stage 2 is all about Understanding. This stage is the primary section of the therapy and takes up half the time of the therapy itself. The idea is to truly delve into the main emergent patterns and issues so as to create a clear picture of what's going on. Based on the exploration stage, I will more than likely focus on Darren's employment history as well as the impact of his personal issues on his employment experience. It appears to me that Darren's creative and non-settling personality is all about unique, creative and independent ways of living and doing in dynamic and fast-paced environments. A structured workplace to Darren is difficult and stifling - especially since he has to answer to others which in a way can dampen creativity and limit the experience of artistry and authorship. Additionally, it appears that Darren feels abandoned and 'left alone' by those whom he considers his family - as it is, even if his father supports him financially, he feels all of that is not enough in terms of support provided. Here, I would encourage him to share information about his childhood experiences to further explore that angle - this is a cathartic release for him as well as an important information source in context for me. It is always important to talk about things from Darren's perspective and then rephrasing that from the perspective of another individual in the recalled situation aside from Darren himself.

Stage 3

Stage 3 is all about Action - this stage is a quarter of the entire therapy focused solely on what should be done after the therapy for the purpose of putting Darren through the challenges in his career. While it is clear his personal issues (divorce, child custody, parental conflict) are among the main source of his troubles, another is his lone artist nature - the need for creativity and the inability to handle situations that stifle that lone artist persona. It is important, I believe, for Darren to come to realize his personality type and the kind of work settings that are ideal for him. Having come to a conclusion that creative independence with support is what he needs, then such a work situation is what he should strive to have. Only can such a work situation encourage Darren to settle and to stop from moving from one city to the next where the since of being anchored by a respectable job can help out in his divorce and custody issues. He also needs to at least strive at moving on from his passivity, something essential in improving his interpersonal skills, communication skills and moving on from the feelings of sadness and desperation that has seemed to permeate in his life in the past year.

Word Count: 1,083
Resources:
(Book)
• Evans, G. (n.d.) The Three-Stage Framework of a Helping Encounter. Books for Dummies.
• Hill, C. & O'Brien, K. (1999). Helping Skills: Facilitating Exploration, Insight and Action. American Psychological Association.
(Web)
• Modes of Helping - http://www.sagepub.com/upm-data/18616_chapter3.pdf
• Presenting Problem - http://changingminds.org/disciplines/coaching/process/presenting_problem.htm
• Psychotherapy Process (Exploration) - http://drum.lib.umd.edu/bitstream/1903/1540/1/umi-umd-1331.pdf

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