Notes, summaries, assignments, exams, and problems for Mathematics

Stock Valuation and WACC Examples

Problem 1: Constant Dividend Growth

Thomas Brothers is expected to pay a $0.35 per share dividend at the end of the year (D1 = $0.35). The dividend is expected to grow at a constant rate of 6% a year. The required rate of return is 13%. What is the stock’s current price?

P0 = D1 / (r – g) = 0.35 / (0.13 - 0.06) = $5.00

Problem 2: Current Stock Price with Constant Growth

A stock just paid a dividend of D0 = $1.50. The required rate of return is r = 10%, and the constant growth rate is g = 4.0%. What is the current stock price?

P0 = D0(1+g) / (r – g) = 1.50(1 + 0.04) / (0.10 - 0.04) = $26.00

Problem 3: Expected Stock Price in One Year

Using your answer for problem 2, what is the expected stock price in one year...

Practicing material for Quiz #5 – Discrete Probability Distribution SOLUTIONS

1. The manager of a baseball team has determined that the number of walks, x, issued in a game by one of the pitchers is described by the probability distribution given below.

1. This pitcher issues as few as 0 walks and as many as 5 walks in a game.

1. Determine the following probabilities

i. P(x = 2) = 0.15

ii. P(x > 4) = 1 – 0.10 = 0.90

iii. P(x > 5) = 0

iv. P(2 < x < 4) = 0.15+0.45+0.15 = 0.75

1. Calculate the mean for this discrete probability distribution, µ = 2.85 walks

µ = Sxp(x) = 0(0.05) + 1(0.10) + 2(0.15) + 3(0.45) + 4(0.15) + 5(0.10) = 2.85

1. The average, over time, of walks issued in a game by one of the pitchers is 2.

Capital Intensity

Automation is a system, process, or piece of equipment that is self-acting and self-regulating. It substitutes labor-saving capital equipment and technology for labor. Automated manufacturing processes typically require high volumes, and costs are high. Fixed automation produces one type of part or product in a fixed sequence. Flexible automation can be changed to handle various products. Industrial robots and automated service processes.

Chapter 2 Process Analysis

DMAIC = Define, Measure, Analyze, Improve, and Control.

Process Analysis

A firm cannot gain competitive advantage with faulty processes! Processes can be analyzed and improved using certain tools and techniques. Process analysis is the documentation and detailed understanding...

Unit 6: Costing and Production Systems

1. Production Systems

The two common cost accumulation systems are job order costing and process costing. The election to use one or the other of these systems depends primarily on the nature of the product and the manufacturing process by which it is created. Process production and job-order production are the extreme possibilities when considering the heterogeneity of products. The difference between order accounting and section accounting is the aim of the cost system, and the difference between process costing and job costing is the method to assign the cost to products.

1.1. Job Order Costing System

Job order costing suits the processes where it is necessary to assign costs to a specific amount of production...

Descriptive and Inferential Statistics

Descriptive Statistics

Descriptive statistics involve organizing, summarizing, and presenting data. This can include using:

• Graphs
• Frequencies
• Tables

Inferential Statistics

Inferential statistics involve drawing conclusions from data.

Example: Fitness Center Data Analysis

A fitness center wants to know the average time clients exercise each week.

Key Concepts:

• Population: All clients in the fitness center
• Sample: A group of clients from the fitness center
• Parameter: Population mean amount of time clients exercise each week
• Statistic: Sample mean amount of time clients exercise each week
• Variable (X): The amount of time one client exercises in the center each week
• Data: Values for X (e.g., 4 hours, 6 hours, 10 hours)

Important

Business Documents

Commercial documents, also called "proof," constitute the evidence of any business operation conducted by a company. Thus, each proof tests a type of transaction. It is known that any operation involves at least two parts. For each of them, it will have a different meaning (as discussed later: buyer or seller, debtor or creditor, or collector payer, etc.).

Small-Scale vs. Large-Scale Risk Aversion

The core idea is to understand the differences between how small and large changes in wealth affect risky gambles.

Diminishing marginal utility (risk aversion) primarily applies to large-scale gambles. This is because the utility function is sufficiently concave over lifetime changes in wealth. This concavity results in a higher utility for taking a certain outcome than for taking a gamble, even if the gamble has a higher expected return.

However, for small-scale gambles, the utility function is locally linear, yielding almost risk-neutral behavior. For wealthy individuals, the utility function is very weakly concave, leading to an asymptotically linear curvature. Thus, diminishing marginal utility cannot...

Which of the following is most likely an issuer bonds: HEDGE FUND

A bond issued by a city would most likely be classified as a: NON-SOVEREIGN GOVERNMENT BOND

A fixed-income security issued with a maturity at issuance of nine months is most likely classified: MMSECURITY

The price of a bond issued in the US by a British company and denominated in US dollars is most likely: CHANGE AS US INTEREST RATES CHANGE

Interbank offered rates are best described as the rates at which major banks can: BORROW UNSECURED FUNDS

A company issues floating-rates bonds. The coupon rates is expressed as the three-month Libor plus a spread. The coupon payments are most likely: LIBOR INCREASES

A 10-year bond was issued four years ago. The bond is denominated in US dollars,

Selecting Samples

A simple random sample of size n from a finite population of size N is a sample selected such that each possible sample of size n has the same probability of being selected.

A random sample of size n from an infinite population is a sample selected such that the following conditions are satisfied.

Point Estimation

By making the preceding computations, we perform the statistical procedure called point estimation. We refer to the sample mean x as the point estimator of the population mean m, the sample standard deviation s as the point estimator of the population standard deviation s, and the sample proportion p as the point estimator of the population proportion p. The numerical value obtained for x, s, or p is called the point...