b1. F = Pert, which assumes continuous compounding, says that the Future value (F) of an amount (P) invested today at an annual rate (r), expressed as a decimal for the time (t) in years, is given by the function. EXAMPLE: invest $100 at the annual rate of 5 1/2% for 6 years and 3 months and you should get back (at the end of the time), F = $100e(0.055)(6.25) = $100e(0.3438) = $100(1.4102) = $141.02. Some auto dealerships are advertising, “72 months, no interest, no payments” However, on the maturity date you have to pay the whole amount owed. If you are even a minute late, then you owe all the interest you avoided, too. You want a $50000 auto for which, after down payment, you qualify for a $40000 loan as advertised. Six percent per annum will be assessed if you are late paying. What total amount will you owe if you are late?

b2. Alternatively, if a borrower tells you that he needs a loan for 6 years and 3 months and will pay you an annual rate of 5 1/2% for the loan, but will only give you $141.02 back at the end of the loan term, you should only loan him $100 today. Here is a loan proposition more in line with current rates. A borrower agrees to pay you 4.5% annually for 3 years and 3 months. At the end of the term he will make a balloon payment of $9000 to repay the loan and interest. What amount (P) does the formula P = F/ert indicate you should loan this prospect?

I tried to go off of the example provided but I don't know where the 1.402 comes from in the first example. Please give detailed feedback. I am trying to understand, just having a difficult time.

1) A 10-year corporate bond has a coupon rate of 6% with annual payments. If interest rates rise to 8% on similar bonds, then what is the value of the bond in the marketplace?

2) A 10-year corporate bond has a coupon rate of 6% with quarterly payments. If interest rates rise to 8% on similar bonds, then what is the value of the bond in the marketplace?

3) A 100-year corporate bond has a coupon rate of 6% with annual payments. If interest rates drop to 4% on similar bonds, then what is the value of the bond in the marketplace?

4) A 100-year corporate bond has a coupon rate of 6% with monthly payments. If interest rates drop to 4% on similar bonds, then what is the value of the bond in the marketplace?

5) A 30-year annual bond is offered at 6%. After that the buyer of the bond sells the bond to someone else, but in between interest rates rose to 6.5%. Why is the first buyer of the bond upset with what the second buyer of bond is willing to pay?

6) A 10-year corporate bond has a coupon rate of 6% with annual payments. If the current value of the bond in the marketplace is $900, then what is the Yield-to-Maturity (YTM)?

7) A 100-year corporate bond has a coupon rate of 6% with semi-annual payments. If the current value of the bond in the marketplace is $400, then what is the Yield-to-Maturity (YTM)?

8) How much do you pay for a zero coupon government bond that has a term of 30 years, an interest rate of 6%, and a par value of $1000.

9) A taxable bond has a yield of 6% and a municipal bond has a yield of 4.6%. If you are in a 23% tax bracket, which bond do you prefer?

10) A taxable bond has a yield of 8% and a municipal bond has a yield of 6%. If you are in a 23% tax bracket, which bond do you prefer?

The distribution of pregnancy lengths of a certain mammal is known to be right skewed with a population mean of 170 days and a population standard deviation of 100 days.

a. Suppose four random samples with different sample size are drawn from this distribution and the sample mean for each is calculated. The same means were 145,169.8,183.3,175. Match the appropriate sample size below with each sample mean, using the Law of Large Numbers.

Sample Size 2..... Sample Mean =
Sample Size 20.... Sample Mean =
Sample Size 50.... Sample Mean =
Sample Size 200... Sample Mean =


b. Suppose we repeatedly take samples of size 100 from the population distribution, calculate a sample mean each time, and plot those sample means in a histogram. The histogram we created would be an example of a  --- sampling distribution variable population distribution . According to the central limit theorem, the histogram would have a shape that is approximately  --- right skewed normal left skewed , with mean  (give a number) and standard deviation  (give a number). The standard deviation of the statistic under repeated sampling is called the  --- standard error absolute error deviation absolute deviation . The middle 95% of the histogram we created lies between  and  (give numbers for both blanks with the smaller number listed first).


c. Suppose we draw one sample of size 100 from the population distribution of animal pregnancy lengths.
(Round to 2 decimal places)
I. Calculate a z-score for a sample mean of 175.2.
II. Calculate a z-score for a sample mean of 152.
III. Is it more likely that we would observe a sample mean of 175.2 or 152?  --- equally likely 152 175.2
Justify your answer to III in one sentence.

Differential Rail Pricing Employed by a UK Rail Company: A Case Study in Price Discrimination

Introduction

The discussion is about Virgin Trains and its joint venture with the Stagecoach Group. The focus will be on the Virgin Trains East Coast line which operates between London and Edinburgh. East Coast has a market share of “just over 30 per cent” of the public transport market including airlines which are also in competition with the railways The discussion will focus on Virgin’s ability to vary its pricing between peak and off peak periods of the day. It also has the technological ability to charge different prices according to how far in advance the passenger is booking.

Discussion

Virgin has managed to successfully increase the number of passenger journeys by exploiting their dominant market power through price discrimination. Business travellers pay more for their rail tickets while leisure travellers tend to pay less because they can be more “flexible with their travel plans" The offer of cheap fares has been used to fill the trains during off peak periods.

Price discrimination has been used by Virgin to segment the travel market so that revenue can be maximised. There is a difference between the peak (commuting) period where the price elasticity of demand is inelastic and the off peak (leisure) period where price elasticity is price elastic .. Under price discrimination, the monopolist rail company assumes that some business travellers are willing to pay a price above a level where marginal cost equals marginal revenue. The monopolist rail company (Virgin-Stagecoach) seeks to “maximise revenue and generate excess profit” . It is for this reason that the monopolist does not want to charge a single price. Instead, they will segment the market and charge more to consumers who are willing to pay extra to travel at the peak period.

Virgin will want to maximise its load factor, which measures its ability to sell all of the available seats on the train . The train operation is a fixed cost and operates regardless of whether there are no passengers or whether the train is full. There will still be fuel and staffing costs which do not vary according to the number of passengers. It is necessary for Virgin to sell as many train tickets as possible to offset its costs. Demand theory suggests that additional demand can be generated from lower prices. If a passenger wants a train ticket 3 months in advance then they can purchase one for a low price. This is because there are many seats available and Virgin wants to make sure that they achieve a sufficient level of sales. Once a sufficient level of rail sales has been obtained then they can charge a higher price to later ticket bookers.

Answer the following Questions

Mention the first two degrees of price discrimination? What degrees of price discrimination are practiced by the UK Rail Company?

How is price discrimination beneficial to the monopolisr UK railt?

Is the concept of elasticity in any way related to price discrimination? Explain diagrammatically drawing references from the case?

1. Two firms a and b have identical price earnings ratio. We know that A’s stock price is trading at $200/share; net income amounts to $20 billion a year; and the number of shares of A outstanding amounts to 2 billion. On the basis of this information we conclude that B’s earnings yield amounts to:

   	a.	10.0%
   	b.	5.0%
   	c.	4.0%
   	d.	0.5%

How does an effective price floor affect buyers and sellers? Why does the government enact price floors? Explain.