Notes, abstracts, papers, exams and problems of Mathematics

1. Present Value of an Investment

15 Years Case

Present Value of the Investment = $4,900 [ (1/0.08) − (1/0.08(1 + 0.08)^15)] = $41,941.45

2. Effective Annual Rate (EAR)

EAR = (1 + (APR/m))^m − 1 If m becomes infinite, EAR = e^APR − 1

7% APR and quarterly compounding: EAR = (1 + (0.07/4))^4 − 1 = 7.19%

16% APR and monthly compounding: EAR = (1 + (0.16/12))^12 − 1 = 17.23%

11% APR and daily compounding: EAR = (1 + (0.11/365))^365 − 1 = 11.63%

3. Value of a Perpetual Stream of Payments

Present Value of the Perpetuity = (Payment/Interest Rate) Payment = $2,500, Interest Rate = 0.061

PV of the perpetuity at date t=14 is $2,500/0.061 = $40,983.61. Discounting it back to date t=7, we should have PV7 = $40,983.61/(1+0.061)^7 = $27,077.12.

4. Bond

Operationalizing Concepts

Operationalizing involves transforming abstract concepts into measurable and tangible factors. This is achieved by examining the behavioral dimensions, facets, or properties associated with the concept. For instance:

• Achievement Motivation: Measured by observing behaviors like the inability to relax or constantly thinking about work, even at home.

Structured Observation

Structured observation is the systematic recording of predetermined behavioral patterns of individuals, objects, and events. Examples include:

• Personal Observation: Mystery shopping, pantry audits
  • Advantages: Clarifies questionnaire doubts, captures non-verbal cues.
  • Disadvantages: High cost, time-consuming, geographical limitations, potential for response

) What is the difference between PEST, PESTEL, STEEPLE, and SLEPT Analysis?

16.) What are a corporation's dynamic capabilities and why is it important to be aware of them as part of the strategic management process?

17.) Different internationalization strategies are normally compared based on two main dimensions. What are these two dimensions and why were they originally chosen by companies to compare their internationalization strategies?

18.) How can a company create competitive advantage in its most basic form?

19.) What are sources of competitive advantage?

20.) What is the next step after you have conducted a PEST Analysis? How do you use such an Analysis?

21.) In class we discussed four basic levels of internationalization. Name and compare... Continue reading "International Business and Global Competitiveness: Key Concepts and Strategies" »

PASIVE 

Essential Math Formulas and Concepts

Volume of Shapes

(a) Cube:

• Formula: V = s³ (where s is the length of a side)
• Example: A cube with side length 4 cm

V = 4³ = 64 cm³

(b) Cylinder:

• Formula: V = πr²h (where r is the radius and h is the height)
• Example: A cylinder with radius 2 cm and height 6 cm

V = π(2²)(6) = 24π cm³ (approximate value)

Surface Area of Shapes

(a) Cube:

• Formula: SA = 6s² (where s is the length of a side)
• Example: A cube with side length 3 cm

SA = 6(3²) = 54 cm²

(b) Cone:

• Formula: SA = πr(r + √(r² + h²)) (where r is the radius and h is the height)
• Example: A cone with radius 5 cm and height 8 cm

SA = π(5)(5 + √(5² + 8²)) = 129.74 cm² (approximate value)

Stem and Leaf Plot

(a) Mean:

• Example: Data: 5, 7, 8, 9, 10, 12, 15

Mean = (5 + 7 + 8... Continue reading "Essential Math Formulas and Concepts: A Quick Reference" »

Cost of the Building: Land+Construction

When was the building bought? YTD amort.construction 2020 / construction P&L --> it has been amortized x years until 2020

At which price did the company sell the building? ((Land + Construction) - YTD amort.constr) + Profit from selling

useful life of the building? construction / construction P&L

Occupancy: 33%. VERY LOW !! ===> 70 rooms x 600 ADR x occupancy x 365 days = 5.059.000 €

F&B Menu: 7 € ==> VERY LOW & doesn't match with an 600 ADR !! [(80% of 100 people for lunch) + (80% of 100 people per Dinner) ] * Menu Price * 365 days = 409.000 €
F&B Breackfast: 18€/person. Reasonable with 600 ADR 80% of 1,5 clients x 33% occupancy * 70 rooms * 365 days * Breackfast Price... Continue reading "Hotel Financial Analysis and Recommendations" »

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... Continue reading "Calculating Stock Prices and Weighted Average Cost of Capital (WACC)" »

Geometry

Angles

Adjacent angles - that have a common vertex and side, but no common interior points

Angle - formed by two rays with a common endpoint called the vertex

Complementary angles - whose measures add up to 90°

Congruent angles - that have the same measure

Supplementary angles - two angles whose measures add up to 180°

Vertical angles - the nonadjacent angles formed by two intersecting lines

Lines

Midpoint - the point that divides a segment into two congruent segments

Parallel lines - in a plane that never meet

Perpendicular lines - that intersect at 90° angles

Transversal - a line that intersects any two or more other lines

Triangles

Triangle Inequality Theorem - the sum of the lengths of any two sides of a triangle is greater than the length... Continue reading "Essential Geometry and Algebra Glossary" »

Statistics: Key Concepts and Methods

1. Statistics is a collection of methods for planning experiments, obtaining data, and then organizing, summarizing, presenting, analyzing, interpreting, and drawing conclusions.

2. Statistical methods consist of a series of procedures for managing, analyzing, and collecting qualitative and quantitative research data.

3. A population includes all objects of interest, whereas a sample is only a portion of the population.

Example: The population could be all students of a postgraduate program, and a representative sample of this population could be 400 students from different studies of the program.

Understanding Variables in Statistics

4. A variable is any characteristic, number, or quantity that can be measured... Continue reading "Key Concepts and Methods in Statistical Analysis" »