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

Monthly Financial Data

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

CS 206 Spring 2016, Rutgers University

Prof. David Cash

March 27, 2016

General Advice for Exam Preparation

This preparation document is meant to help you prepare for Midterm 2. It does not contain any new problems or topics. Instead, it places everything we've covered in one place, and isolates some specific skills that will be tested in the exam.

Learning math (or, more specifically, learning problem-solving skills in order to do well on an exam) is a highly personal activity. But I can describe how I learn math, in the hope that my opinion will be useful.

To learn basic topics, like how to compute simple conditional probabilities, one can actively work through solved examples, especially the ones from class. While this is an important first step,... Continue reading "CS 206 Midterm 2 Preparation: Story Proofs and Probability Skills" »

Understanding Annuity Due

An annuity due is a series of equal payments made at the beginning of each period. Below are practical examples to help you master these calculations.

Example 1: Lease vs. Cash Purchase

You are buying a new vehicle and must decide between leasing or paying cash. The salesperson offers a cash price of $23,000 or a five-year lease with:

• Monthly payments of $300 (first payment due at signing).
• A buyout of $9,500 at the end of five years.

Since the first payment is made at the start, the lease requires 59 additional equal payments. Assuming a 6% annual interest rate compounded monthly (0.5% per month):

• BGN Mode: N = 60, I = 0.5, FV = $9,500, PMT = $300
• Result: CPT PV = –$22,638

Conclusion: The lease is the better deal because... Continue reading "Annuity Due Calculations: Financial Analysis and Examples" »

) 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" »

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" »

Discrete Math Concepts

Binary Relations

Cartesian Product

The Cartesian product of two sets A and B, denoted A × B, is the set of all ordered pairs (a, b) where a is in A and b is in B.

Example: If A = {0, 1}, the Cartesian product A × A is {(0,0), (0,1), (1,0), (1,1)}.

Properties of Binary Relations

A binary relation R on a set A can have several properties:

1. Reflexive: For all x ∈ A, (x, x) ∈ R.
2. Symmetric: For all x, y ∈ A, if (x, y) ∈ R, then (y, x) ∈ R.
3. Transitive: For all x, y, z ∈ A, if (x, y) ∈ R and (y, z) ∈ R, then (x, z) ∈ R.
4. Irreflexive: For all x ∈ A, (x, x) ∉ R.
5. Antisymmetric: For all x, y ∈ A, if (x, y) ∈ R and (y, x) ∈ R, then x = y.

Examples of Relation Properties

Consider a set A = {0, 1}.

• The relation R = A

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" »