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

1. Equivalent Units Calculation

2. Cost per Equivalent Unit

Financial Balance Sheet Formulas

• Working Capital (WC) = Accounts Receivable + Stock - Accounts Payable
• Net Short-Term Debt = Banking ST Debt - Cash
• Net Assets = WC + Net Fixed Assets
• Net Liabilities = Net ST Debt + Long-Term Debt + Equity
• Financial Margin (%) = Equity + Long-Term Debt - Net Fixed Assets

Working Capital (WC) Metrics

• AMP Collecting = (Average Receivables / Revenue) × 365
• 1 Day Revenue = Revenue / 365
• Purchases = Stock1 - Stock0 + Cost of Sales (COS)
• AMP Payment = (Average Payables / Purchases) × 365
• 1 Day Purchases = Purchases / 365
• AMP Stock = (Average Stock / COS) × 365
• 1 Day COS = COS / 365
• PMMF = AMP Collecting + AMP Stock - AMP Payment

Cash Flow Analysis

• CFO (Cash Flow from Operations) = Net Profit + Amortization - Increase in WC (WC1

Vocabulary Builder: 35 Essential Words

A

1. Agonized

Manifesting, suffering, or characterized by great physical or mental pain.

2. Ample

Large and accommodating.

3. Assent

The expression of approval or agreement.

B

4. Befall

(Of something bad) happen to someone.

C

5. Chariots

A two-wheeled horse-drawn vehicle used in ancient warfare and racing.

6. Conceive

Become pregnant with (a child). Form or devise (a plan or idea) in the mind.

7. Cordial

Friendly, warm.

D

8. Dews

Moisture condensed from the atmosphere, especially at night, and deposited in the form of small drops upon any cool surface.

9. Divine

Of, from, or like God or a god.

10. Doe

Female deer.

F

11. Foe

An enemy or opponent.

G

12. Gossamer

Used to refer to something very light, thin, and insubstantial or delicate.... Continue reading "Vocabulary Builder: 35 Essential Words with Definitions" »

Property Tax and Assessment Calculations

A home has an assessed value of $430,000.

Calculating Portioned Assessment

Calculate the total portioned assessment for the property if the portioned percentage is 45%:

• $430,000 × 0.45 = $193,500

Municipal and Education Tax

The mill rate for the Municipal tax is 24 mills on the portioned assessment:

• $193,500 × (24 / 1,000) = $4,644

In addition to the Municipal tax, there is an Education tax of $3,870 and a provincial tax credit of $700. The total tax calculation is:

• $4,644 + $3,870 - $700 = $7,814

Calculating Gross Debt Service Ratio (GDSR)

George is considering purchasing a home. He earns a gross income of $44,400 annually. His monthly costs include:

• Heating: $140
• Property Taxes: $200
• Mortgage Payment: $940

To calculate... Continue reading "Practical Math Problems for Finance and Geometry" »

Financial Market Scenarios: Fixed Income and Derivatives

Sildavia: Term Structure and Yield Curve Construction

In Sildavia's financial market, we assume the existence of a series of zero-coupon bonds and conventional bonds. Each bond type presents specific traits:

• Zero-Coupon Bonds: Defined by spot rates and coupon interest rates.
• Conventional Bonds: Defined by specific characteristics (data assumed to be provided in an accompanying table).

Based on the provided data, the objective is to construct the TSIR (Term Structure of Interest Rates) and the Yield Curve for both kinds of bonds.

Moravia: Calculating Forward Rates

Considering the TSIR shown in Table 1, calculate the corresponding forward rates (r_t).

Furthermore, if the market involves an inverted

Parity and Set Theory Proofs

1. Direct proof: odd + even is odd

Statement: If x is an odd integer and y is an even integer, then x + y is odd.

Proof: Suppose x = 2k + 1 and y = 2l for integers k, l. Then
x + y = 2k + 1 + 2l = 2(k + l) + 1, which is of the form 2·(integer) + 1, hence odd. ∎

2. Contrapositive proof: even implies next is odd

Theorem: If n is an even integer, then n + 1 is odd.

Proof by contraposition: The contrapositive is: If n + 1 is not odd (i.e., even), then n is not even (i.e., odd). Suppose n + 1 is even. Then n + 1 = 2k for some integer k. Thus n = 2k − 1 = 2(k − 1) + 1, which is odd. Therefore the contrapositive is true, and so the original implication holds. ∎

3. Proof by contradiction: even implies next is odd

Theorem:

This document outlines the steps to calculate production costs, including equivalent units and costs for work-in-progress (WIP) and finished goods.

1. What does boot mean?
2. How to determine the basis of taxable and non-taxable stock dividends?
3. How to determine if a gain is long-term or short-term?
4. How does capital gain/loss netting work?
5. What is the tax rate of regular long-term capital gain? [0%, 15%, 20%]
6. Individual taxpayers can deduct net capital loss (short-term or long-term) up to $3,000 per year.
7. The maximum tax rate for collectibles is 28%; the maximum tax rate for unrecaptured Section 1250 gain is 25%.
8. How to determine amount realized? How to determine amount realized when there is debt assumption?
9. What is unrecaptured Section 1250 gain? How to calculate it?
10. What is the basis of gifts? How to determine the holding period of a gift?
11. How to determine the adjusted basis?
12. How to determine realized