Credit Risk Management Problems
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The document contains examples of calculating probabilities of default for bonds and credit portfolios using various inputs like probability of default, loss given default, recovery rates, bond yields, risk free rates, and firm value volatility. The key calculations shown include probability of 1, 2, or more bonds defaulting in a portfolio; cumulative default probability over multiple periods; implied default probability from bond-Treasury yield spreads; and default probability estimation using Merton model inputs like firm value, debt, and equity volatility.
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2. It includes problems calculating NPV for projects such as factories, machines, and ships where the cash flows include costs, revenues, operating costs, refit costs, and salvage value over multiple periods.
3. The last examples calculate the amount of annual savings needed to buy a boat in 5 years and the annual annuity payment an individual can expect based on investing a present value over their life expectancy.
Time value of money
- The document discusses time value of money concepts like present value, future value, rates of return, and compound interest.
- It provides examples of calculating future and present values for lump sums, annuities, and cash flows using different interest rates compounded annually and periodically.
- The key difference between an ordinary annuity and annuity due is whether the first payment is received at the beginning or end of the period.
Jm 4th edition_solutions_manual
This document contains solutions to end-of-chapter questions from the textbook "Fundamentals of Investments" by Jordan and Miller. The solutions summarize key concepts around risk, return, and the historical performance of different asset classes over long periods of time. Specific calculations include average returns, risk premiums, standard deviations, probabilities associated with normal distributions, and comparisons of arithmetic versus geometric returns.
Time value of money
The document discusses various time value of money concepts including future value, present value, perpetuities, and annuities. It provides examples of calculations for future and present value of a single sum, as well as present value calculations for perpetuities and annuities. Uneven cash flows are discussed as being the sum of present values of regular cash flows. Key steps in solving time value problems are identified as drawing the timeline, identifying the cash flows, determining what value is being calculated, and using the appropriate formula.
Assignment 3 Assignment 3 is due after you complete Lessons 9 to.docx
Assignment 3
Assignment 3 is due after you complete Lessons 9 to 11. It is worth 20% of your final grade.
Prepare your responses to these assignment problems in a word processing file; put financial data in a spreadsheet file. As you complete the assignment problems for each lesson, add your responses to these files.
Do not submit your answers for grading until you have completed all parts of Assignment 3.
Note: In assignments, show all calculations to 4 decimal places.
Lesson 9: Assignment Problems
9.1 The Constant-Growth-Rate Discounted Dividend Model, as described equation 9.5 on page 247, says that:
P0 = D1 / (k – g)
A. rearrange the terms to solve for:
i. g; and
ii. D1.
As an example, to solve for k, we would do the following:
1. Multiply both sides by (k – g) to get: P0 (k – g) = D1
2. Divide both sides by P0 by to get: (k – g) = D1 / P0
3. Add g to both sides: k = D1 / P0 + g
(8 marks)
9.2 Notation: Let
Pn = Price at time n
Dn = Dividend at time n
Yn = Earnings in period n
r = retention ratio = (Yn– Dn) / Yn = 1 – Dn/ Yn = 1 - dividend payout ratio
En = Equity at the end of year n
k = discount rate
g = dividend growth rate = r x ROE
ROE = Yn / En-1 for all n>0.
We will further assume that k and ROE are constant, and that r and g are constant after the first dividend is paid.
A. Using the Discounted Dividend Model, calculate the price P0 if
D1 = 20, k = .15, g = r x ROE = .8 x .15 = .12, and Y1 = 100 per share
B. What, then, will P5 be if:
D6 = 20, k = .15, and g = r x ROE = .8 x .15 = .12?
C. If P5 = your result from part B, and assuming no dividends are paid until D6, what would be P0? P1? P2?
D. Again, assuming the facts from part B, what is the relationship between P2 and P1 (i.e., P2/P1)? Explain why this is the result.
E. If k = ROE, we can show that the price P0 doesn’t depend on r. To see this, let
g = r x ROE, and ROE = Yn / En-1, and
since r = (Yn – Dn) / Yn , then D1 = (1 – r) x Y1 and
P0
=
D1 / (k – g)
P0
=
[(1 – r) x Y1] / (k – g)
P0
=
[(1 – r) x Y1] / (k – g), but, since k = ROE = Y1 / E0
P0
=
[(1 – r) x Y1] / (ROE – r x ROE)
P0
=
[(1 – r) x Y1] / (Y1 / E0 – r x Y1 / E0)
P0
=
[(1 – r) x Y1] / (1 – r) x Y1 / E0), and cancelling (1 – r)
P0
=
Y1 / (Y1/E0) = Y1 x (E0 / Y1) = E0
So, you see that r is not in the final expression for P0, indicating that r (i.e., retention ration or, equivalently, dividend policy) doesn’t matter if k = ROE.
Check that changing r from .8 to .6 does not change your answer in part A of this question by re-calculating your result using r = .6.
(10 marks)
9.3 You are considering an investment in the shares of Kirk's Information Inc. The company is still in its growth phase, so it won’t pay dividends for the next few years. Kirk’s accountant has determined that their first year's earnings per share (EPS) is expected to be $20. The company expects a return on equity (ROE) of 25% in each of the next 5 years but in the six ...
Financial institutions and markets solutions
This document summarizes a homework assignment on analyzing bonds and interest rates. It includes questions about calculating bond yield to maturity, the effect of interest rate changes on bond prices, duration, and other bond valuation concepts. Sample questions are provided along with step-by-step solutions and explanations. Relationships between bond maturity, discount rates, and prices are explored through examples.
Assignment 3Assignment 3 is due after you complete Lessons 9 t.docx
Assignment 3
Assignment 3 is due after you complete Lessons 9 to 11. It is worth 20% of your final grade.
Prepare your responses to these assignment problems in a word processing file; put financial data in a spreadsheet file. As you complete the assignment problems for each lesson, add your responses to these files.
Do not submit your answers for grading until you have completed all parts of Assignment 3.
Note: In assignments, show all calculations to 4 decimal places.
Lesson 9: Assignment Problems
9.1
The Constant-Growth-Rate Discounted Dividend Model, as described equation 9.5 on page 247, says that:
P0 = D1 / (k – g)
A.
rearrange the terms to solve for:
i. g; and
ii. D1.
As an example, to solve for k, we would do the following:
1. Multiply both sides by (k – g) to get: P0 (k – g) = D1
2. Divide both sides by P0 by to get: (k – g) = D1 / P0
3. Add g to both sides: k = D1 / P0 + g
(8 marks)
9.2
Notation: Let
Pn = Price at time n
Dn = Dividend at time n
Yn = Earnings in period n
r = retention ratio = (Yn– Dn) / Yn = 1 – Dn/ Yn = 1 - dividend payout ratio
En = Equity at the end of year n
k = discount rate
g = dividend growth rate = r x ROE
ROE = Yn / En-1 for all n>0.
We will further assume that k and ROE are constant, and that r and g are constant after the first dividend is paid.
A.
Using the Discounted Dividend Model, calculate the price P0 if
D1 = 20, k = .15, g = r x ROE = .8 x .15 = .12, and Y1 = 100 per share
B.
What, then, will P5 be if:
D6 = 20, k = .15, and g = r x ROE = .8 x .15 = .12?
C.
If P5 = your result from part B, and assuming no dividends are paid until D6, what would be P0? P1? P2?
D.
Again, assuming the facts from part B, what is the relationship between P2 and P1 (i.e., P2/P1)? Explain why this is the result.
E.
If k = ROE, we can show that the price P0 doesn’t depend on r. To see this, let
g = r x ROE, and ROE = Yn / En-1, and
since r = (Yn – Dn) / Yn , then D1 = (1 – r) x Y1 and
P0
=
D1 / (k – g)
P0
=
[(1 – r) x Y1] / (k – g)
P0
=
[(1 – r) x Y1] / (k – g), but, since k = ROE = Y1 / E0
P0
=
[(1 – r) x Y1] / (ROE – r x ROE)
P0
=
[(1 – r) x Y1] / (Y1 / E0 – r x Y1 / E0)
P0
=
[(1 – r) x Y1] / (1 – r) x Y1 / E0), and cancelling (1 – r)
P0
=
Y1 / (Y1/E0) = Y1 x (E0 / Y1) = E0
So, you see that r is not in the final expression for P0, indicating that r (i.e., retention ration or, equivalently, dividend policy) doesn’t matter if k = ROE.
Check that changing r from .8 to .6 does not change your answer in part A of this question by re-calculating your result using r = .6.
(10 marks)
9.3
You are considering an investment in the shares of Kirk's Information Inc. The company is still in its growth phase, so it won’t pay dividends for the next few years. Kirk’s accountant has determined that their first year's earnings per share (EPS) is expected to be $20. The company expects a return on equity (ROE) of 25% in each of the next 5 years but in the sixth year they expect ...
Seminar 2 guidelines
1. The document provides guidelines and examples for calculating bond prices and yields. It discusses how changing the discount rate impacts the present value and price of bonds with different coupon amounts.
2. Specific examples calculate bond prices for bonds with different maturities, coupon rates, and discount rates. It finds that bonds with smaller coupons see a greater percentage change in price when the discount rate changes.
3. The document also provides internet exercises on bond ratings and historical corporate bond yields. It asks readers to analyze changes in bond yields over time and how yields differ between rating categories.
Timevalueofmoney
The time value of money is the concept that money available at the present time is worth more than the identical sum in the future due to its potential earning capacity. This core principle of finance holds that, provided money can earn interest, any amount of money is worth more the sooner it is received. Time Value of Money is also sometimes referred to as present discounted value.
Decision analysis
This document discusses various techniques for decision making under uncertainty. It defines subjective and objective probabilities, and consistency requirements for probabilities. It describes the key elements of decision problems including alternatives, states of nature, payoff tables, and uncertainty. It defines three types of decision making environments: certainty, risk, and uncertainty. For decision making under risk, it discusses expected monetary value, expected opportunity loss, and expected value of perfect information as decision criteria. It provides examples to illustrate these concepts and techniques. Finally, it outlines several criteria that can be used for decision making under uncertainty including maximax, maximin, and minimax.
Compound interest and related problems in business mathematics
This document provides a lesson on compound interest and related business mathematics concepts. It includes examples of calculating compound interest, simple interest, annuities, sinking funds, and more. Formulas are provided for topics like future value, present value, effective interest rates, and calculating monthly loan payments. Resources are also listed for downloading additional material on entrepreneurship, economics, accounting and related topics.
TimeValueOfMoney.ppt
The document discusses the time value of money concepts of future value and present value for single sums and annuities. It provides examples of calculating future value and present value for single cash flows using formulas and a financial calculator. It also discusses the differences between ordinary annuities, where cash flows occur at the end of periods, and annuity dues, where cash flows occur at the beginning of periods.
Retirement Portfolio Financial Analysis - Graduate Project
The document describes an industrial/applied math masters project that investigates optimal retirement portfolio allocation through Monte Carlo simulation. It models three investment options - cash/money market, stocks, and bonds - under various allocation schemes. The results show that balancing stability and growth is important, as portfolios with too much imbalance toward higher-risk/return investments performed poorer overall. Specifically, a 75% stock/10% bond/15% cash allocation yielded the highest success rate and average ending balance.
Time value of money
This document provides an overview of time value of money concepts including simple and compound interest, future and present value, and annuities. Key points covered include:
- Compound interest earns interest on previous interest amounts as well as the principal, resulting in higher total returns over time compared to simple interest.
- Future value and present value formulas allow calculating the value of a single deposit or withdrawal at a future or present point in time using a given interest rate.
- Annuities represent a series of equal periodic cash flows, and formulas are provided to calculate the future and present value of ordinary annuities and annuities due.
Cost of Debt Capital problems kd
Cost of debt (i.e, debentures and long term debt) is defined in terms of the required rate of return that the debt, investment must yield to protect the shareholders interest. Hence, Cost of debt is contractual interest rate, adjusted further for the tax liability of the firm.
Cost of Debt Debentures are issued at par, at a premium and discount. Cost of Redeemable Debt
CFA LEVEL 1- Time Value of Money_compressed (1).pdf
This document focuses on End of Chapter questions and commonly asked questions under Quantitative methods (Time Value of Money ) . The mainly asked questions include :
-calculation and interpretation of Future Value and Present Value of a single sum of money , an ordinary annuity, annuity due, a perpetuity (PV only) and a series of unequal cash flows.
-demonstration of the use of timelines in modeling and solving time value of money
This is a very interesting topic!
Similar to Credit Risk Management Problems (20)
Assignment 3 Assignment 3 is due after you complete Lessons 9 to.docx
Assignment 3 Assignment 3 is due after you complete Lessons 9 to.docx
Assignment 3Assignment 3 is due after you complete Lessons 9 t.docx
Assignment 3Assignment 3 is due after you complete Lessons 9 t.docx
Compound interest and related problems in business mathematics
Compound interest and related problems in business mathematics
Retirement Portfolio Financial Analysis - Graduate Project
Retirement Portfolio Financial Analysis - Graduate Project
CFA LEVEL 1- Time Value of Money_compressed (1).pdf
CFA LEVEL 1- Time Value of Money_compressed (1).pdf
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Speaker:
Lyndsey Byblow, Test Suite Sales Engineer @ UiPath, Inc.
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