Summary For The Final

Notes from Chapter 1 – 3 - These are the notes, which I prepared for myself after taking the quizzes. This would help me to review before the final test.

Glass Steagall Act

– Congress passed an act in 1933, which said that commercial banks must not carry out the activities performed by the investment banks.

LIBOR interest rate problems –

For example if the problem has LIBOR base points as 89 and interest rate at 4.19%

We need the calculate the LIBOR interest rate – 4.19 + 0.89 = 5.08%

Conversion price from bonds to shares

Conversion of any security is done in the order of higher to lower, for example bonds to common stock.

Example problem – Face value of a bond = 1000, # of shares = 40 & bond was sold at discount of $78
Conversion price = 1000/40 = 25 [ Always calculated on face value]

Preferred Stock –

In the order they come before common stock.

Cumulative Preferred Stock – If a company cannot pay dividends for some years, and when announce dividends in a particular year they will have to pay dividends for all the missing years and they need to pay dividends to preferred stock holder before they can pay to the common stock holders.

Bonds

Interest is always paid on the face value.
Example FV – 1000, 10% and selling at discount price of $900.
Interest = 0.1*1000 = $100

Rights of bondholder and limitations of the issuer are on the bond indenture

Deferred Coupon bonds – Sold at deep discount, premium or at par and pay no interest for several years and pay a higher interest rate later.

Under writing process –

Some terms used
Over hanging – Security is selling slowly and investment bankers may make loss in order to get rid of the security.

Over Subscribed / Out the window – Security sold very quickly and investment bankers might have made some profit.

Under pricing IPO[ Initial public offering] – Investment bankers work will be easier.

US Bills / Notes / Bonds

Bills - < 1year
Notes - 1 - 10 years
Bonds > 10years

Problems with Rights On and Rights Off

Rights On

Value of the right = (stock price – subscription free) / N + 1
N – Number of rights

Rights off / Ex rights

Value of the right = (stock price – subscription free) / N
N – Number of rights

If number of rights are not given then you have to calculate if outstanding shares and additional share
N = outstanding shares / additional shares

Types of Common Stock

A – Dividends are equal or greater that B
B – More votes per share

Problem with number of votes

Class A – 982 shares
Class B – 76 shares and each gets 17 votes per share

So total number of votes = 982 + 17 * 76 = 2274

If a person has 786 shares of class A, he has 796/2274 = 35% of the votes

Chapter 4 – 5

Measure of risk is standard deviation or variance.

Standard deviation [s] = Sqrt (Variance)

Co-relation co-efficient [r] = Covariance i,j / si * sj

Slope of the capital market line = Rt – Rf / st

Rt – Expected return on tangent portfolio, Rf – Risk free interest rate

Example problem – Rt = 18.9%, Rf = 7.3%, Standard deviation = 0.21
Slope of the market line = 18.9 – 7.3 / 21 = 0.55

Combined b of the portfolio = fraction A* bA + fraction B* bB + ……….

Covariance from risk observation problem

Expected return of A 4.3, Expected return of B 4.58
Two joint observation
A, B = 3.15,6.92
A,B = 4.04,6.23

N1 = [3.15-4.3]*[6.92-4.58] = -2.691
N2 = [4.04-4.3]*[6.23-4.58] = -0.429

Covariance = N1 + N2 / 2 = -1.56 , If you have more observation you need to do the same calculations and divide number of observations.

Expected % return [r] = b [Rm – Rf] + Rf

*** What return on a portfolio is predicted by the CML line if the portfolio has standard deviation of .3, tangency portfolio has standard deviation of .25, risk free rate of return as .06 and expected return on the tangency portfolio as 0.18

[[0.18-0.06 ] * 0.3 /0.25] + 0.06 = 0.204

Ration of risk premium to covariance problems

Risk premium = Ri – Rf

Risk premium / covariance = Rt – Rf / Variance

Problems with dividends and initial stock price and later stock price

Individual return = final stock price + dividend – initial stock price / initial stock price

Some additional problems

Q1

P r
Stock a - 0.37 7
Stock b - 0.12 6
Stock c - 1 –(0.37+0.12) =0.51 5

Rp [Portfolio return ] = Pa * ra + Pb * rb + Pa * ra
=5.86%

Q2

Amount r
Stock a - $700 5
Stock b - $822.6 6.6

Pa = 700 / 1522.6 = 0.4597
Pb = 822.6/1522.6 = 0.54

Rp = 0.4597 * 5 + 0.54 * 6.6 = 5.8642

Return earned on the portfolio = 5.8642 * 1522.6 / 100 = 89.3

Chapter 7 – 8

Track portfolio binomial model

Vu = delta * S + B (1 + Rf)

Vu = Risk neutral expected future value
S = value of the underlying asset
Delta = # of units or shares of under lying asset
B = # of dollars in risk free

V = delta * S + B where V is the current value of the tracking portfolio

Risk Neutral Valuation

Vu = (P Vuu + (1 - P) Vud) / ( 1 + Rf )

P & ( 1- P) are the risk neutral probabilities.

P = 1 + Rf – d / u – d

notes.tiff

Some problems from Quiz 4

Question

A firm considers investing $243 in a new factory. Cash flows two years from now depend on the economy. At the full capacity those cash flows product the following –

2 good year $809
1 good year and 1 bad year $489
2 bad years $-119
A market portfolio produces a risk probability of .5 for upward and risk free rate is 12%.
What is the value of an option to scale production back to 50%at no cost if unfavourable conditions occur in year 1.

I am understanding the question as follows

809

Vu
489
243

Vd
-119

Vu = .5 * 809 + .5*489 / 1.12 = 579.48
Vd = .5*489 + .5*-119 / 1.12 = 165.2

Vo = .5 * 579.48 + .5*165.2 / 1.12 = 332.44

Now cutting production by 50% when unfavorable

809

Vu
244.5
243

Vd
-59.5

Vu = .5 * 809 + .5 *489/1.12 = 579.46
Vd = .5 *244.5 + .5-59.5/1.12= 82.58

Vo = .5 579.46 + .5*82.58/1.12=295.55

Value of the option = 295.55-332.44 = -36.89

Question

Q A firm considers investing $105 in a new factory. Cash flows two years from now depend on the economy. At full capacity, those cash flows produce the following pattern.
If there are two good years, the cash flow is $896.
If one good year is followed by one bad year, the cash flow is $533.
If one bad year is followed by a good year, the cash flow is the same. That is the pattern recombines.
Finally, if two bad years occur, the cash flow is $12.
A market portfolio produces a risk neutral risk probability of 0.6 for upward transitions and the annual risk free rate is 3%.
The firm has an option to double capacity under good economic conditions. What is the most that option could be worth initially if the cost to double the facility in year 1 equals the same dollar amount as its original cost?

896 / 1792

-105
Vu
533 / 1066
-105

Vd
12

Vu = .6 * 1792 + .4*1066/ 1.03 = 1457.86 – 105 = 1352.86
Vd = .6*533 + .4*12 / 1.03 = 315.15

Vo = .6 * 1352.86 + .4*315.15 / 1.03 = 910.46

With out option

Vu = .6 * 896 + .4*533/ 1.03 = 728.93
Vd = .6*533 + .4*12 / 1.03 = 315.15

Vo = 547

Options worth = 910.46 – 547 =363

Question

Q. Total capacity of your copper mine is 148313 pounds a year for each of the next two years. Current forward copper prices are $0.51 a pound for a 1-year contract and $0.66 a pound for a 2-year contract. Extraction costs are $.15 a pound and the annual risk-free rate for each of the two years is 6%. Determine the present value of the expected cash flows (assume end of year payments for the copper).

Y1 = 148313(.51-.15) = $ 53,392.68
Y2 = 148313(.66-.15) = $ 75,639.63

Present Value = 53,392.68/1.06 + 75,639.63 / 1.06^2 = 117,689.45