Financial Economics and Financial Mathematics Flashcards

Flashcards covering basic concepts, financial laws, annuities, inflation, compounding, loans, and investment criteria from the Financial Economics and Financial Mathematics lecture notes.

What is Financial Capital?

Value of an asset at the moment it becomes available.

What does interest rate represent?

Return demanded for renouncing to consume now, in exchange for a promise of future consumption.

What are the two components of any interest rate?

Risk-free interest rate and Risk premium.

Define Financial Operation.

Intertemporal exchange of capital.

Define Financial Law.

Model for valuing (moving) money over time.

Define Financial Equivalence.

Correspondence between two financial capitals under a given financial law.

Define Capitalization.

Moving money forward in time; determining the final value equivalent to a certain initial value.

Define Discounting.

Moving money back in time; determining the initial value equivalent to a certain final value.

List Capitalization Laws.

Simple Interest and Compound Interest.

List Discounting Laws.

Simple Rational Interest, Simple Commercial Interest and Compound Interest.

Capitalization - Simple Interest Definition

The capitalization of a given initial amount using a simple interest rate means that said interest rate will only apply to that initial amount.

Capitalization - Simple Interest. Formula

CT = C0 * (1 + I * T), where: CT = Final capital, C0 = Initial capital, I = Interest rate, T = Maturity

Discounting - Simple Rational Interest Formula

C0 = CT / (1 + I * T)

Discounting - Simple Commercial Interest Formula

C0 = CT * (1 − I * T)

What is the difference between SCI vs SRI

SRI: Interest is calculated on the initial capital. SCI: Interest is calculated on the final capital (taking interest for financing capital)

Capitalization - Compound Interest Definition

The capitalization of a given initial amount using a compound interest rate means that said interest rate will not only apply to that initial amount, but also to the interests received during the life of the operation.

Capitalization - Compound Interest Formula

CT = C0 * (1 + I)^T, where: CT = Final capital, C0 = Initial capital, I = Interest rate, T = Maturity

Discounting - Compound Interest Formula

C0 = CT / (1 + I)^T

Define Annuities

A periodic stream of financial capitals (payments).

Annuities classification by the number of payments

Temporal (limited number of payments) and Perpetual (infinite number of payments).

Annuities classification by the period in which the first payment falls

Immediate (first payment occurs in the first period) and Deferred (first payment occurs after the first period).

Annuities classification by the moment in which payments are made in each period

In advance (payments are made at the beginning of each period) and In arrears (payments are made at the end of each period).

Annuities classified by the amount paid

Constant (all payments represent the same amount) and Variable (at least one payment involves a different amount).

Annuity Valuation

Involves establishing the financial equivalence between that annuity and one single financial capital.

Present Value (PV) of an annuity

The single financial capital today which is equivalent to that annuity.

Final Value of an annuity

The single financial capital at the time of the last payment which is equivalent to that annuity.

The relationship between nominal interest, real interest and inflation formula

1 + IR = (1 + IN) / (1 + II), where: IR = Real Interest, IN = Nominal Interest, II = Inflation

What is the effect of Nominal interest vs effective interest?

Effect of the compounding frequency on the final AMOUNT

What is the effect of Nominal interest vs real interest?

Effect of inflation on the final PURCHASING POWER

General Formula for Capitalization – Compound Interest

CT = C0 * (1 + Ik)^(k*T) where: CT = Final Capital, C0 = Initial Capital, k = Number of compounding per year, lk = Nominal interest rate, Ik = Effective interest rate over the term, T = Maturity date

Formula to calculate the Equivalent interest rates

Given two effective interest rates, Ik and Ik′, the capital generated by each of them after T years will be: 1+𝐼𝑘′ = (1 + 𝐼𝑘 )^(𝑘/𝑘′) − 1

General formula for the premuture redemptions

Principal yet to be amortized and value of the debt is: 𝑃ℎ = 𝐶 · (1 + 𝐼𝑝)^(𝑁−ℎ) − 1 / 𝐼𝑝 · (1 + 𝐼𝑝)^(𝑁−ℎ) ; 𝑉ℎ = 𝐶 · (1 + 𝐼𝑚)^(𝑁−ℎ) − 1 / 𝐼𝑚 · (1 + 𝐼𝑚)^(𝑁−ℎ)

The loan single payment for principal and periodic payment of interest structure is

This has the structure of a coupon bond.

French System - amortize the principal and pay interest

In this case, all installments are the same (e.g., mortgages)

Loans premature redemption Gain on redemption formula

𝑉ℎ > 𝑃ℎ and Gain on redemption: 𝑉ℎ − 𝑃ℎ

Net Present Value (NPV) method:

Select those projects with a positive NPV.

What happens in payback method

Choosing those projects for which the payback is equal or less than a previously chosen ceiling.

Internal Rate of Return (IRR):

Discount rate which would make the project’s NPV equal to zero.

IRR method:

Accept those projects whose IRR is greater than the Opportunity Cost of Capital

Opportunity Cost of Capital

The return we forego by investing in a given project instead of investing in the market (assuming the same level or risk).