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# 16.29 The value of a company’s equity is $4 million and the volatility of its equity is 60%. The... 1 answer below » 16.29 The value of a company’s equity is$4 million and the volatility of its equity is 60%. The debt that will have to be repaid in two years is \$15 million. The risk-free interest rate is 6% per annum. Use Merton’s model to estimate the expected loss from default, the probability of default, and the recovery rate (as a percentage of the no-default value) in the event of default. Explain why Merton’s model gives a high recovery rate. (Hint: The Solver function in Excel can be used for this question.) 1 In theory, a credit rating is an attribute of a bond issue, not a company. However, in many cases all bonds issued by a company have the same rating. A rating is therefore often referred to as an attribute of a company.

2 See E. I. Altman, “Financial Ratios, Discriminant Analysis, and the Prediction of Corporate Bankruptcy,” Journal of Finance 23, no. 4 (September 1968): 589–609.

3 Clearly Type I errors are much more costly to the lending department of a commercial bank than Type II errors.

4 In the United States, the claim made by a bond holder is the bond’s face value plus accrued interest.

5 See E. I. Altman, B. Brady, A. Resti, and A. Sironi, “The Link Between Default and Recovery Rates: Theory, Empirical Evidence, and Implications,” Journal of Business (November 2005): 2203–2228. The correlation is also discussed in publications by Moody’s Investors Service. It finds that the correlation between the average recovery rate in a year and the non investment-grade default rate is about 0.5.


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I really enjoyed how you listed all of the reasons to build passive income streams as well as the framework. You also made an interesting point about freelance writing on how the more skilled writers want to keep posts for their own website. Good insight because freelance writing is something I’ve been looking into for income recently. Also, it’s amazing what you’ve been able to accomplish with your blog over the past 6 years. It’s so motivational to see the success of Financial Samurai. I’m not in a place to afford any consulting, but, I wish I could pick your brain or get mentored by a successful blogger such as yourself…Not trying to blow smoke lol. It would just be so great to have someone who’s done it provide guidance around the direction of the blog, ways to earn, and on the general concept. Always enjoy your posts. Thanks for sharing :)

-The second brother has set up his stall in a very busy market place. It required some more starting investment but the returns were even more rewarding. On days like 31st December and 1st January, he easily earns 40,000 rupees. He is also very active on Facebook. Social media marketing helps a lot. Zomato rating of his stall is 3.9, and clearly, his focus on quality and customer satisfaction has paid off. Average monthly income is somewhere between 1 lac to 1.5 lac rupees.
If you have extra time with you over weekends or after your job, you can freelance and take small projects. There are many websites like elance.com , odesk.com or freelancer.com where you can earn money by working on projects. There are thousands of people in India who are working full time on these kind of freelancing websites and believe me, they are earning in lakhs. Look at it as a serious way of making money and not just a time pass activity.
I guess the people who bash this book would prefer to read a financial book by someone like Jane Bryant Quinn. How many people have made a fortune or any money at all following her advice? I rest my case.Or perhaps these bashers think the Road to Wealth is a college degree and work 9-5, 40 hours per week for 40 years and think that their employer will take real good care of them right? WRONG! Or perhaps these bashers feel the real key to wealth is to invest your 401 (k) money in your companies stock or you rate your wealth by your stock options huh? Ask employees invested in Lucent, Compaq or Enron how good they feel about retirement considering whats "left" in their company 401 (k) plan or by the value of their stock options (those who haven't been downsized that is).Robert Allens book is a excellent book for anyone who wants to reach permanent and rapid wealth. He teaches you how to invest with index funds and create cash flow with covered calls and options.He shows you how to 86 your job and start your own business through Network Marketing. He talks about the internet and licensing; real estate, discount mortgages and tax lien cerficates and then he shows you how to put it all together.Whats not to like about this book?I also recommend Who Stole the American Dream.For those who are happy with mediocity, keep your J-O-B *Which stands for just over broke) and read Jane Bryant Quinns book.
If you need cash flow, and the dividend doesn’t meet your needs, sell a little appreciated stock. (or keep a CD ladder rolling and leave your stock alone). At the risk of repeating myself, whether you take cash out of your portfolio in the form of “rent”, dividend, interest, cap gain, laddered CD…., etc. The arithmetic doesn’t change. You are still taking cash out of your portfolio. I’m just pointing out that we shouldn’t let the tail wag the dog. IOW, the primary goal is to grow the long term value of your portfolio, after tax. Period. All other goals are secondary.
Can you expound on the use of publicly-traded REITs as a passive income source? I’m 31 years old. No children. No wife. No dependents. (I am the closest thing to Ebenezer Scrooge you’ll ever see). My monthly expenses amount to less than $2,000 per month (most of which go to pay student loans) . I have a decent job making over$55K per year. I also have a $60K inheritance coming my way in a few weeks. I am absolutely crazy about achieving absolute financial independence, which for me would require a passive income of over$2000/month to cover my living expenses. I could achieve that in a mere couple of years if I were to save excessively and dump my savings (and inheritance) into a Mortgage REIT via the stock market, most of which are shelling out above 10% returns in dividend payments. Is this a good strategy for me? Or am I being too hasty and assuming too much risk?
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P2P lending is the practice of loaning money to borrowers who typically don’t qualify for traditional loans. As the lender you have the ability to choose the borrowers and are able to spread your investment amount out to mitigate your risk. The most popular peer to peer lending platform is Lending Club. You can read our full lending club review here: Lending Club Review.
This brings us back to the baby boomers. Will the boomers display the same pattern since our current data represents the behavior of prior generations? Consensus opinion suggests they may not benefit from the same amount of social capital as the prior generation. However, there is evidence — driven by the size of their demographic cohort — to suggest that much of the existing pool of financial capital will be concentrated with the baby boomers.

India started recovery in 2013–14 when the GDP growth rate accelerated to 6.4% from the previous year's 5.5%. The acceleration continued through 2014–15 and 2015–16 with growth rates of 7.5% and 8.0% respectively. For the first time since 1990, India grew faster than China which registered 6.9% growth in 2015.[needs update] However the growth rate subsequently decelerated, to 7.1% and 6.6% in 2016–17 and 2017–18 respectively,[144] partly because of the disruptive effects of 2016 Indian banknote demonetisation and the Goods and Services Tax (India).[145] As of October 2018, India is the world's fastest growing economy, and is expected to maintain that status for at least three more years.[146]
I wish I had more time to put into real estate. Given the run up since 2012, I may even be interested in selling my condo that I currently rent out. I need to get it appraised to really see what it’s worth, but I think conservatively it’s gone up ~50%, although rent is probably only up ~10% or so. I am bullish on rents going up in the future… mostly in line with inflation, or perhaps even slightly faster due to constricted credit and personal income growth which should provide a solid supply of renters. At this point, I just don’t want to manage the property. I’ll probably look into a property manager as my time is likely worth turning it into a nearly passive investment.

This equation implies two things. First buying one more unit of good x implies buying {\displaystyle {\frac {P_{x}}{P_{y}}}} less units of good y. So, {\displaystyle {\frac {P_{x}}{P_{y}}}} is the relative price of a unit of x as to the number of units given up in y. Second, if the price of x falls for a fixed {\displaystyle Y} , then its relative price falls. The usual hypothesis is that the quantity demanded of x would increase at the lower price, the law of demand. The generalization to more than two goods consists of modelling y as a composite good.

## Even if you don’t possess a particularly unique talent, speaking English is a skill in itself – and one that many people are keen to learn. Online language schools like www.lingoda.com offer flexible virtual teaching work, making it possible to coach English from the comfort of your own home. If you’re looking to make extra money without working long shifts or taking the time to master a new skill, cashing in on your existing skillset is the ideal solution.

I found this to be a fascinating and most helpful book. It was so motivating I'm already working on three new streams of income, and about to start a fourth. Forget net worth! Cash flow is much more important, particularly if you're retired. Only one slight criticism of the book. It's a bit dated, but those few parts make little difference to its overall value. If you're currently struggling with how you're going to survive after you retire, try Allen's approach. It will open your eyes.
Portfolio income can come from multiple sources – interest/bond coupons, stock dividends, financial strategies including derivatives and capital growth.  Each offers some cash flow and some also offer potential capital gain with some risk from liquidity and volatile prices.  In this low-yield environment, many investors rely too heavily on cash flows and to pursue this are venturing further into riskier areas than they’d normally consider.

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# Troubleshooting¶

## Symbol aliases¶

SymPy treats symbols with different assumptions as different symbols even if they have the same name. To reduce this confusion, Lcapy assumes that symbol names are not aliased. It achieves this by maintaining a list of defined symbols for each circuit. However, it is unaware of symbols created by SymPy.

## Symbol assumptions¶

There can be difficulties with symbol assumptions when working with SymPy. By default SymPy creates symbols with few assumptions, for example,

>>> from sympy import Symbol
>>> R1 = Symbol('R')
>>> R1.assumptions0
{'commutative': True}

On the other hand, by default, Lcapy assumes that symbols are positive (unless explicitly defined otherwise). For example,

>>> from lcapy import symbol
>>> R2 = symbol('R')
>>> R2.assumptions0
{'commutative': True,
'complex': True,
'hermitian': True,
'imaginary': False,
'negative': False,
'nonnegative': True,
'nonpositive': False,
'nonzero': True,
'positive': True,
'real': True,
'zero': False}

Since R1 and R2 have different assumptions, SymPy considers them different symbols even though they are both defined with the same name R.

Note, every real symbol is also considered complex although with no imaginary part. The proper way to test assumptions is to use the attributes is_complex, is_real, etc. For example,

>>> t.is_real
True
>>> t.is_complex
False

## Zero substitution¶

Be careful with zero substitutions. For example, consider
>>> x = symbol('x')
>>> (x * (s + 1 / x)).subs(x, 0)
0

In general it is safer (but slower) to evaluate a limit at zero.

>>> x = symbol('x')
>>> (x * (s + 1 / x)).limit(x, 0)
1

Another approach is expand the expression to avoid the division:

>>> x = symbol('x')
>>> (x * (s + 1 / x)).expand().subs(x, 0)
1

## Computation speed¶

Lcapy can be slow for large problems due to the computational complexity of the algorithms. If speed is important, it is better to substitute symbolic values with numerical values.

The results from slow computations are cached to improve the speed.


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# How do you align equations parts vertically?

I have read many other solutions but this situation seems unique.

\documentclass{exam}
\usepackage{multicol}
\usepackage{amsmath}
\begin{document}
\begin{questions}
\question Simplify the following:
\begin{multicols}{4}
\begin{parts}
\part $8^\frac{2}{3}$
\part $\dfrac{16^{\frac{2}{3}}}{16^{\frac{1}{6}}}$
\part $9^\frac{1}{3}\cdot 9^{-\frac{5}{6}}$
\part $\left(25^{\frac{1}{3}}\right)^{\frac{3}{2}}$
\end{parts}
\end{multicols}
\end{questions}
\end{document}

-

The heights of the four part letters is different, because the different heights of the formulas. The following example defines \vphantomB with an invisible box of the greatest height of part (b):

\documentclass{exam}
\usepackage{multicol}
\usepackage{amsmath}
\begin{document}
\begin{questions}
\question Simplify the following:
\begin{multicols}{4}
\def\vphantomB{\leavevmode\vphantom{$\dfrac{16^{\frac{2}{3}}}{}$}}
\begin{parts}
\part \vphantomB $8^\frac{2}{3}$
\part $\dfrac{16^{\frac{2}{3}}}{16^{\frac{1}{6}}}$
\part \vphantomB $9^\frac{1}{3}\cdot 9^{-\frac{5}{6}}$
\part \vphantomB $\left(25^{\frac{1}{3}}\right)^{\frac{3}{2}}$
\end{parts}
\end{multicols}
\end{questions}
\end{document}

-

you can use the package enumitem instead:

documentclass{exam}
\usepackage{amsmath}
\usepackage[inline]{enumitem}
\begin{document}
\begin{questions}
\question Simplify the following:

\begin{enumerate*}[label*=(\alph*),itemjoin={\hfill}]
\item $8^\frac{2}{3}$
\item $\dfrac{16^{\frac{2}{3}}}{16^{\frac{1}{6}}}$
\item $9^\frac{1}{3}\cdot 9^{-\frac{5}{6}}$
\item $\left(25^{\frac{1}{3}}\right)^{\frac{3}{2}}$
\end{enumerate*}
\end{questions}

\end{document}

-
In this solution, if you have too many items, there is no vertical alignment betwen the items in different lines. – Bernard Apr 24 '14 at 12:01


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bplapply stalling upon error with large data objects
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0
Entering edit mode
Aaron Lun ★ 28k
@alun
Last seen 5 hours ago
The city by the bay

I stumbled across some strange behaviour of bplapply when a large data object is passed to FUN and an error is also raised within FUN:

library(BiocParallel)
bigmat <- matrix(rnorm(1e7), nrow=50)

.recount_cells <- function(x, incoming)
{
stop("YAY")
return(x)
}

system.time(bplapply(1:2, FUN=.recount_cells, incoming=bigmat,
BPPARAM=SerialParam())) # Finishes instantly
system.time(bplapply(1:2, FUN=.recount_cells, incoming=bigmat,
BPPARAM=MulticoreParam(2))) # Killed after several minutes

This doesn't happen if I set bigmat <- 1, nor if I remove the stop call in .recount_cells. In those situations, both of the bplapply calls above execute in a timely manner.

I have encountered related problems with bplapply stalling even when there is no error being raised in FUN, but the above example is the simplest to reproduce on my system (Ubuntu, below). The same behaviour is observed with BiocParallel 1.7.5 and on a Mac OSX.

Anyway, here's my sessionInfo():

R version 3.3.0 Patched (2016-05-03 r70580)
Platform: x86_64-pc-linux-gnu (64-bit)
Running under: Ubuntu 14.04.5 LTS

locale:
[1] LC_CTYPE=en_GB.UTF-8       LC_NUMERIC=C
[3] LC_TIME=en_GB.UTF-8        LC_COLLATE=en_GB.UTF-8
[5] LC_MONETARY=en_GB.UTF-8    LC_MESSAGES=en_GB.UTF-8
[7] LC_PAPER=en_GB.UTF-8       LC_NAME=C
[11] LC_MEASUREMENT=en_GB.UTF-8 LC_IDENTIFICATION=C

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base

other attached packages:
[1] BiocParallel_1.6.3

loaded via a namespace (and not attached):
[1] parallel_3.3.0
biocparallel bplapply multicore • 760 views
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Entering edit mode

I don't yet have a solution but the problem can be seen in this non-parallel code

fun <- function(x) stop()
do.call("fun", list(matrix(rnorm(1e7), 50)))

which gets slower as the data get larger.

3
Entering edit mode
@martin-morgan-1513
Last seen 12 days ago
United States

The problem is that on error R creates a variable .Traceback that contains a text version of the call stack. Each element of the call stack has a text representation of the entire bigmat object. Fixing this requires a change to R (after svn revision r71040) and an updated BiocParallel (version 1.6.4 / 1.7.6).

0
Entering edit mode

Thanks. The MulticoreParam example now finishes up in 30 seconds, which is better. (Still a bit odd that it takes so long to just throw an error, though.) This also fixes the related problem that I referred to in my original post.

0
Entering edit mode

ok, now 1.6.5 / 1.7.7 might be a better solution.


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# Math Help - points of sruface closest to origin.

1. ## points of sruface closest to origin.

Problem :
Find the points on the surface $xy^2z^3=2$ that are closest to the origin.

I solved it for z:
$z=\sqrt[3]{\frac{2}{xy^2}}$.
and I said:
$f(x,y)=\sqrt[3]{\frac{2}{xy^2}}$
I stopped here.

2. For the solution using Lagrange multipliers see the attachment

check my arithmetic

3. Originally Posted by TWiX
Problem :
Find the points on the surface $xy^2z^3=2$ that are closest to the origin.

I solved it for z:
$z=\sqrt[3]{\frac{2}{xy^2}}$.
and I said:
$f(x,y)=\sqrt[3]{\frac{2}{xy^2}}$
I stopped here.
The square distance:

$D^2=x^2+y^2+z^2$

so:

$D^2=x^2+\frac{2}{xz^3}+z^2$

Which leaves you with the unconstrained minimisation of a function of two variables.

CB


text:
•
•

#### Article Title

Upper bounds for inverse domination in graphs

#### Abstract

In any graph $G$, the domination number $\gamma(G)$ is at most the independence number $\alpha(G)$. The \emph{Inverse Domination Conjecture} says that, in any isolate-free $G$, there exists pair of vertex-disjoint dominating sets $D, D'$ with $|D|=\gamma(G)$ and $|D'| \leq \alpha(G)$. Here we prove that this statement is true if the upper bound $\alpha(G)$ is replaced by $\frac{3}{2}\alpha(G) - 1$ (and $G$ is not a clique). We also prove that the conjecture holds whenever $\gamma(G)\leq 5$ or $|V(G)|\leq 16$.

ref_tag2021080205.pdf (138 kB)
Supplemental Reference List with DOIs

COinS

#### DOI

https://doi.org/10.20429/tag.2021.080205