38. Calculating Loan Payments. You need a 30-years, fixed-rate mortgage to buy a new home for $250,000. Your mortgage bank will lend you the money at a 6.8 percent APR for this 360-month loan. However, you can only afford monthly payments of $1,200, so you offer to pay off any remaining loan balance at the end of the loan in the form of single balloon payment. How large will this balloon payment have to be for you to keep your monthly payments at $1,200?

54. Calculating Annuities. You have recently won the super jackpot in the Washington State Lottery. On reading the fine print, you discover that you have the following two options: a. You will receive 31 annual payments of $175,000, with the first payment being delivered today. The income will be taxed at a rate of 28 percent. Taxed will be withheld when the checks are issued.

b. You will receive $530,000 now, and you will not have to pay taxes on this amount. In addition, beginning one year from this annuity will be taxed at 28 percent. Using a discount rate of 10 percent, which option should you select?

65. Calculating Annuity Payments. Your friend is celebrating her 35th birthday today and wants to start saving for her anticipated retirement at age 65. She wants to be able to withdraw $110,000 from her savings account on each birthday for 25 years following her retirement; the first withdrawal will be on her 66th birthday. Your friend intends to invest her money in the local credit union, which offers 9 percents interest per year. She wants to make equal annual payments on each birthday into the account established at the credit union for her retirement fund. a. If she starts making these deposits on her 36th birthday and continues to make deposit until she is 65 (the last deposit will be on her 65th birthday), what amount must she deposit annually to be able to make the desired withdrawals at retirement?

b. Suppose your friend has just inherited a large sum of money....

...Chapter4
1.
If you invest $1000 today at an interest rate of 10% per year, how much will you have 20 years from now,
assuming no withdrawals in the interim?
SOLUTION:
n
PV
FV
PMT
Result
20
2.
i
10
1000
?
0
FV =6,727.50
a.
If you invest $100 every year for the next 20 years, starting one year from today and you earn interest
of 10% per year, how much will you have at the end of the 20 years?
b. How much must you invest each year if you want to have $50,000 at the end of the 20 years?
SOLUTION:
n
PV
FV
PMT
Result
a. 20
10
0
?
100
FV = 5,727.50
b. 20
3.
a.
b.
c.
d.
e.
i
10
0
50,000
?
PMT = 872.98
What is the present value of the following cash flows at an interest rate of 10% per year?
$100 received five years from now.
$100 received 60 years from now.
$100 received each year beginning one year from now and ending 10 years from now.
$100 received each year for 10 years beginning now.
$100 each year beginning one year from now and continuing forever.
SOLUTION:
n
i
PV
FV
PMT
Result
a. 5
10
?
100
0
PV = $62.09
b. 60
10
?
100
0
PV = $.3284
c. 10
10
?
0
100 ordinary
PV = $614.46
d. 10
10
?
0
100 immediate
PV = $675.90
e. Perpetuity
10
?
0
100 ordinary
See below
e. PV = $100 = $1,000...

...Solutions to Textbook Answers Chapter 1 Introduction
Solutions to questions
1. Finance involves three main areas—corporatefinance, financial institutions and markets, and investments—that are closely related and complementary. For example, in corporatefinance the central issues are how to acquire and employ or invest funds. To acquire funds a financial manager must deal with financial institutions, so some knowledge of the operations of financial institutions and markets is essential. Similarly, corporatefinance involves investments because decisions have to be made about which assets should be acquired by a business. Given the close relationship between these three areas of finance, it is impossible to discuss one of them without some discussion of the others. In investment decisions , managers consider the amount invested in the assets of the business and the composition of that investment. Managers of the business are therefore involved in the task of choosing, usually from a long list of available projects, those that are to be undertaken. In addition to decisions about the amount and composition of investments, managers have to decide how to finance them. These are financing decisions . This will involve generating funds internally or raising funds from sources external to the business. Financing...

...Chapter4
15. For discrete compounding, to find the EAR, we use the equation:
EAR = [1 + (APR / m)]m – 1
= .0719, or 7.19%
EAR = [1 + (.07 / 4)]4 – 1
EAR = [1 + (.16 / 12)]12 – 1
= .1723, or 17.23%
= .1163, or 11.63%
EAR = [1 + (.11 / 365)]365 – 1
To find the EAR with continuous compounding, we use the equation:
EAR = er – 1
EAR = e.12 – 1 = .1275, or 12.75%
23.
Although the stock and bond accounts have different interest rates, we can draw one time line, but we
need to remember to apply different interest rates. The time line is:
0
1
Stock
Bond
$800
$350
360
361
...
660
…
$800
$350
$800
$350
$800
$350
$800
$350
C
C
C
We need to find the annuity payment in retirement. Our retirement savings ends at the same time the
retirement withdrawals begin, so the PV of the retirement withdrawals will be the FV of the
retirement savings. So, we find the FV of the stock account and the FV of the bond account and add
the two FVs.
Stock account: FVA = $800[{[1 + (.11/12) ] 360 – 1} / (.11/12)] = $2,243,615.79
Bond account: FVA = $350[{[1 + (.06/12) ] 360 – 1} / (.06/12)] = $351,580.26
So, the total amount saved at retirement is:
$2,243,615.79 + 351,580.26 = $2,595,196.05
Solving for the withdrawal amount in retirement using the PVA equation gives us:
PVA = $2,595,196.05 = C[1 – {1 / [1 + (.08/12)]300} / (.08/12)]
C = $2,595,196.06 / 129.5645 = $20,030.14...

...Practice Problem Set – 1 ( The following problems are from CorporateFinance by Ross, Westerfield, and Jaffe – Tenth edition, McGraw-Hill / Irwin – ISBN 978-0-07-803477-0 ) 1. Audrey Sanborn has just arranged to purchase a $ 550,000 vacation home in the Bahamas with a 20 percent down payment. The mortgage has a 6.1 percent stated annual interest rate, compounded monthly, and calls for equal monthly payments over the next 30 years. Her first payment will be due one month from now. However, the mortgage has an eight-year balloon payment, meaning that the balance of the loan must be paid off at the end of year 8. There were no other transaction costs or finance charges. How much will Audrey’s balloon payment be in eight years ? Your job pays you only once a year for all the work you did over the previous 12 months. Today, December 31, you just received your salary of $ 65,000, and you plan to spend all of it. However, you want to start saving for retirement beginning next year. You have decided that one year from today you will begin depositing 5 percent of your annual salary in an account that will earn 10 percent per year. Your salary will increase at 4 percent per year throughout your career. How much money will you have on the date of your retirement 40 years from today ? A 15-year annuity pays $ 1,500 per month, and payments are made at the end of each month. If the interest rate is 12 percent compounded monthly for...

...Chapter 06
Discounted Cash Flow Valuation
Multiple Choice Questions
1. An ordinary annuity is best defined by which one of the following?
A. increasing payments paid for a definitive period of time
B. increasing payments paid forever
C. equal payments paid at regular intervals over a stated time period
D. equal payments paid at regular intervals of time on an ongoing basis
E. unequal payments that occur at set intervals for a limited period of time
2. Which one of the following accurately defines a perpetuity?
A. a limited number of equal payments paid in even time increments
B. payments of equal amounts that are paid irregularly but indefinitely
C. varying amounts that are paid at even intervals forever
D. unending equal payments paid at equal time intervals
E. unending equal payments paid at either equal or unequal time intervals
3. Which one of the following terms is used to identify a British perpetuity?
A. ordinary annuity
B. amortized cash flow
C. annuity due
D. discounted loan
E. consol
4. The interest rate that is quoted by a lender is referred to as which one of the following?
A. stated interest rate
B. compound rate
C. effective annual rate
D. simple rate
E. common rate
5. A monthly interest rate expressed as an annual rate would be an example of which one of the following rates?
A. stated rate
B. discounted annual rate
C. effective annual rate
D. periodic monthly rate...

...CHAPTER 2
How to Calculate Present Values
Answers to Problem Sets
1. If the discount factor is .507, then .507*1.126 = $1
2. 125/139 = .899
3. PV = 374/(1.09)9 = 172.20
4. PV = 432/1.15 + 137/(1.152) + 797/(1.153) = 376 + 104 + 524 = $1,003
5. FV = 100*1.158 = $305.90
6. NPV = -1,548 + 138/.09 = -14.67 (cost today plus the present value of the
perpetuity)
7. PV = 4/(.14-.04) = $40
8. a. PV = 1/.10 = $10
b. Since the perpetuity will be worth $10 in year 7, and since that is roughly
double the present value, the approximate PV equals $5.
PV = (1 / .10)/(1.10)7 = 10/2= $5 (approximately)
c. A perpetuity paying $1 starting now would be worth $10, whereas a perpetuity starting in year 8 would be worth roughly $5. The difference between these cash flows is therefore approximately $5. PV = 10 – 5= $5 (approximately)
d. PV = C/(r-g) = 10,000/(.10-.05) = $200,000.
9. a. PV = 10,000/(1.055) = $7,835.26 (assuming the cost of the car does not
appreciate over those five years).
b. You need to set aside (12,000 × 6-year annuity factor) = 12,000 × 4.623 = $55,476.
c. At the end of 6 years you would have 1.086 × (60,476 - 55,476) = $7,934.
10. a. FV = 1,000e.12x5 = 1,000e.6 = $1,822.12.
b. PV = 5e-.12 x 8 = 5e-.96 = $1.914 million
c. PV = C (1/r – 1/rert) = 2,000(1/.12 – 1/.12e .12 x15) = $13,912
11....

...| Corporate Finance2 CreditsBU.231.620.62Thursday 6pm – 9pm, 10/18/2012--12/13/2012Fall2, 2012Columbia, Columbia Center, 218 |
Instructor
Shabnam Mousavi
Contact Information
Phone Number: (410)234-9450
E-mail Address: shabnam@jhu.edu
Office Hours
Monday/Thursday 10am-noon
Required Text and Learning Materials
(1) Berk, J. and P. DeMarzo. 2007. CorporateFinance. 2nd Edition. Pearson, Addison-Wesley with MyLab access. The ISBN is 0-13-295-040-5.
(2) Lecture Notes. The lecture notes will be posted weekly on Blackboard, before class.
(3) MyFinanceLab: All homework and quizzes are posted on MyFinanceLab. Instructions available at the end of this syllabus. Course ID: mousavi28617
Blackboard Site
A Blackboard course site is set up for this course. Each student is expected to check the site throughout the semester as Blackboard will be the primary venue for outside classroom communications between the instructors and the students. Students can access the course site at https://blackboard.jhu.edu. Support for Blackboard is available at 1-866-669-6138.
Course Evaluation
As a research and learning community, the Carey Business School is committed to continuous improvement. Therefore each student must complete the course evaluation as part of the continuous improvement process. Information on how to complete the evaluation will be provided near the end of the course.
Disability Services
Johns...

...Chapter4
29. Annuity Present Values What is the value today of a 15-year annuity that pays $500 a year?The annuity’s first payment occurs at the end of year 6. The annual interest rate is 12 percentfor years 1 through 5, and 15 percent thereafter.
(Ross, Stephen A.. CorporateFinance, 8th Edition. Irwin/McGraw-Hill, 112006. 4.8).
33. Growing Annuity Southern California Publishing Company is trying to decide whether to revise its popular textbook, Financial Psychoanalysis Made Simple. The company has estimated that the revision will cost $50,000. Cash flows from increased sales will be $12,000the first year. These cash flows will increase by 6 percent per year. The book will go out of print five years from now. Assume that the initial cost is paid now and revenues are received at the end of each year. If the company requires an 11 percent return for such an investment, should it undertake the revision?
(Ross, Stephen A.. CorporateFinance, 8th Edition. Irwin/McGraw-Hill, 112006. 4.8).
37 Calculating Annuity Present Values You want to borrow $45,000 from your local bank tobuy a new sailboat. You can afford to make monthly payments of $950, but no more. Assumingmonthly compounding, what is the highest APR you can afford on a 60-month loan?
(Ross, Stephen A.. CorporateFinance, 8th Edition. Irwin/McGraw-Hill, 112006. 4.8).
41. EAR versus APR You have...