Introduction to Finance

Discover the fundamentals of finance with a comprehensive exploration of time value of money and discounting. This tutorial begins by explaining why future cash flows are less valuable than present ones, illustrating this with an extreme example. It then delves into compound interest calculations using a numerical example of saving £10,000 at a 10% annual rate over five years. The video further demonstrates how to calculate the present value of future incomes and extends this to finding the present value of a stream of cash flows with varying discount rates. Subscribe to @AxiomTutoringCourses for more insightful finance tutorials.

Learn to simplify complex financial calculations in this video. Discover how to streamline geometric series summation to determine present value efficiently, even with multiple fixed cash flows and discount rates over extended periods. Subscribe to @AxiomTutoringCourses for more comprehensive finance lessons.

In this tutorial, we explore perpetual payments: constant cash flows with an infinite horizon. We derive the perpetuity formula using the limit of the annuity formula as time approaches infinity, yielding C/R. Key application conditions and relation to annuities are discussed. Subscribe to @AxiomTutoringCourses for more comprehensive finance lessons.

Learn how to calculate your monthly mortgage payments with this comprehensive guide. We break down the process step-by-step, starting with a mortgage principal of 1 million pounds and an annual interest rate of 6%. You'll discover how to adjust the annual percentage rate for monthly payments and determine the total number of periods. The video explains how to use the annuity formula to find the exact monthly payment amount. Furthermore, it details how to calculate the principal and interest components of any specific monthly installment, using the 61st payment as a practical example. This essential knowledge will help you understand your mortgage amortization thoroughly. Subscribe to @AxiomTutoringCourses for more finance tutorials.

In this comprehensive tutorial, we explore how to leverage present value, future value, and annuity formulas to effectively plan for savings and retirement consumption. The video walks you through a detailed example of a 30-year-old salaried worker, demonstrating calculations for total accumulated savings at retirement and the annual consumption possible over 20 years post-retirement. We then tackle a scenario where a specific retirement spending goal is set, calculating the required savings at retirement and the necessary annual savings percentage from salary. This detailed breakdown will equip you with the financial planning tools needed to manage your savings and consumption expectations after retirement. Subscribe to @AxiomTutoringCourses for more essential financial and mathematical tutorials.

Learn how to calculate the present values of annuities and perpetuities with constant growth. This video explains how to handle cash flows that increase at a steady rate while still applying a constant discount rate. We demonstrate the manual method of discounting individual cash flows and then show how to derive and apply generalized formulas for both annuities and perpetuities with growth. Understand the key assumption that the discount rate must be greater than the growth rate for the perpetuity formula to converge. Subscribe to @AxiomTutoringCourses for more financial tutorials.

This video tutorial explains how to calculate the present values of annuities and perpetuities when cash flows are growing at a constant rate. We cover both the manual method of discounting individual cash flows and the derivation of generalized annuity and perpetuity formulas for growth scenarios. Learn the crucial condition where the discount rate must exceed the growth rate for perpetuity calculations. Explore the nuances of constant growth in financial modeling. Understand how to apply annuity formulas with growth and the simplified perpetuity formula. Discover why unsustainable growth rates necessitate a return to manual calculation for initial periods. Subscribe to @AxiomTutoringCourses for more financial tutorials.

This video introduces the concept of arbitrage, clarifying that it differs from mere investing or buying low and selling high. Arbitrage exploits mispricing in assets, often generating risk-free profit by effectively producing value from nothing. You'll learn why mispricing occurs, such as when fundamental financial principles are violated. The tutorial then demonstrates how to construct a simple arbitrage portfolio through a practical example involving differing discount rates, illustrating how to achieve a positive cash flow with zero initial net investment. The video details an example where a two-year discount rate is lower than a one-year rate, violating the fundamental principle that a dollar today is worth more than a dollar tomorrow. This specific mispricing allows for the construction of an arbitrage portfolio by borrowing at the cheaper two-year rate and simultaneously lending at the higher one-year rate. This strategy results in a guaranteed future profit without any initial cash outlay. Alternatively, the video shows how to achieve an immediate positive cash inflow at time zero without any future repayment obligations. The discussion consistently emphasizes that genuine arbitrage stems from asset mispricing, not simply an increase in asset value over time. Subscribe to @AxiomTutoringCourses for more insights into financial concepts.

This video introduces bonds as a financial asset used by firms and institutions to borrow money. We explore the fundamental elements of a bond, including face value, coupon rate, and maturity. The discussion also covers spot rates and how they are used as discount rates for each period until maturity. You will learn how to calculate the price of a bond by understanding its cash flows and applying the appropriate discount rates based on the payment structure. Subscribe to @AxiomTutoringCourses for more educational content.

Calculating the Internal Rate of Return (IRR) can be challenging, especially for projects with multiple cash flows, often necessitating complex calculations or software. This video introduces simplified methods to approximate the IRR, offering alternatives to manual polynomial solving or reliance on Excel. We detail the trial and error approach and then present a more efficient linear approximation technique that can be easily calculated. The video also highlights important caveats for IRR, including its underlying assumptions and potential issues like multiple IRRs or no IRR when cash flows fluctuate in sign. Ultimately, understand why IRR remains a useful benchmark for evaluating investment projects, even with its inherent limitations. Learn how to approximate IRR using trial and error, adjusting the discount rate until the Net Present Value (NPV) approaches zero. A more practical linear approximation method is then presented, involving selecting two discount rates that yield positive and negative NPVs, respectively. By drawing a straight line between these points, an approximate IRR is found where the line intersects the horizontal axis. This method offers a straightforward calculation without advanced tools. However, the effectiveness of IRR relies on the assumption that NPV always strictly declines as the discount rate increases, which typically occurs when all negative cash flows precede positive ones. When cash flows alternate between positive and negative signs, multiple IRRs or even no IRR can exist. Despite these complexities, IRR provides a valuable benchmark for investment decisions. It helps determine project viability by comparing the IRR to the actual discount rate, indicating a positive NPV when the real discount rate is lower than the IRR. Subscribe to @AxiomTutoringCourses for more finance tutorials.

This video introduces the Internal Rate of Return (IRR), a crucial method for investment appraisals. Learn how IRR is defined as the discount rate that sets a project's Net Present Value (NPV) to zero. The video demonstrates calculating NPV with various discount rates to narrow down the IRR's range. Discover why exact IRR calculations often require specialized tools like Excel, as it involves solving complex polynomial equations. See an example where the precise IRR for a cash flow stream is determined. Subscribe to @AxiomTutoringCourses for more finance tutorials.

This video introduces the payback period, a key investment appraisal method. It's defined as the time required to recover your initial investment based purely on cash flows, without any discounting involved. The video demonstrates this calculation with a detailed example of a three-year project, showing how to determine the exact point at which the initial capital is reclaimed. Learn how to calculate it to the nearest month, such as 2 years and 4 months in the given scenario, assuming linear cash flows for precise calculation. The discussion emphasizes that this method does not incorporate discounting. Subscribe to @AxiomTutoringCourses for more finance tutorials.

This video delves into calculating the payback period, an investment appraisal method. It demonstrates how to determine the time it takes for an initial investment to be recovered through cash inflows, using practical examples. We explore the key assumptions and significant disadvantages of the payback period, such as its disregard for future cash flows and the time value of money. While less commonly used than NPV, this method remains relevant for short projects or when liquidity is a primary concern. Understand its application and limitations in investment decisions. Subscribe to @AxiomTutoringCourses for more finance tutorials.

In this video, we explore how to calculate bond prices by considering varying maturities, coupon rates, and spot rates. We'll use a simplified face value of 1000 pounds for all bonds and demonstrate the process with concrete examples, showing how to discount future cash flows to their present value. Learn how different spot rates and coupon rates significantly impact a bond's final price. This tutorial also covers a shortcut for calculating bond prices when spot rates are flat, utilizing annuity formulas for efficiency. Subscribe to @AxiomTutoringCourses for more financial tutorials.

In this video, we explore the concept of bond duration and its relationship to bond price sensitivity. We'll delve into how changes in yield to maturity affect bond prices and introduce duration as a measure of this sensitivity. Using two example bonds with different coupon rates, we'll calculate their prices at a given yield and then observe the price changes when the yield shifts slightly. This practical illustration will highlight how coupon rates influence a bond's price volatility. We then introduce MacCaulay duration, a metric that quantifies this sensitivity by time-weighting cash flows. We'll demonstrate the calculation of MacCaulay duration for both example bonds and compare their values. Understanding MacCaulay duration helps investors assess which bonds are more susceptible to fluctuations in market interest rates. Subscribe to @AxiomTutoringCourses for more financial education.

This video explores the concept of Yield to Maturity (YTM) for bonds. We learn that YTM is the universal discount rate needed to compare bonds with varying maturities and coupon rates, effectively representing the bond's internal rate of return. The tutorial demonstrates how to calculate YTM, showing that while it can be solved algebraically for short maturities, more complex calculations often require tools like Excel or online calculators. Understanding YTM provides a standardized way to assess the return on investment for different bonds. Subscribe to @AxiomTutoringCourses for more financial tutorials.

In this video, we explore the relationship between a bond's coupon rate and its UTS maturity. UTS maturity acts as a constant discount rate, simplifying cash flow calculations compared to using individual spot rates for each period. We examine three scenarios with a £1,000 face value bond, a 5% UTS maturity, and a three-year term, varying the coupon rate from 3% to 8%. This demonstration illustrates how coupon rates directly influence bond prices, leading to concepts like pricing at a discount, par, and a premium. Understanding this relationship can provide shortcuts and self-checking mechanisms for bond valuation problems. Subscribe to @AxiomTutoringCourses.

This video provides a detailed, step-by-step mathematical derivation of duration and modified duration, explaining their fundamental role in approximating bond price changes in response to yield to maturity fluctuations. It visually illustrates how modified duration acts as a linear approximation of the bond's price curve, highlighting the source of approximation error when yield changes are significant. The explanation walks through the calculus required to arrive at the modified duration formula and demonstrates why it's a practical tool for financial analysis, particularly as a first-order Taylor series expansion. Subscribe to @AxiomTutoringCourses for more in-depth financial mathematics and tutoring.

This video explains how to calculate the approximate change in a bond's price due to changes in its yield to maturity using modified duration. We'll review the concept of Macaulay duration and introduce modified duration as a linear approximation tool. Using a practical example, we demonstrate how to calculate modified duration and then apply it to estimate price changes. We'll also explore the accuracy of this approximation and when it becomes less reliable with larger yield shifts. Subscribe to @AxiomTutoringCourses for more finance tutorials.

Learn how to calculate Effective Annual Rate (EAR) for savings compounded at various intervals. Discover why EAR differs from quoted rates and how it's affected by compounding frequency. We explore daily, monthly, quarterly, semi-annually, and continuously compounding scenarios using clear examples. Find out the upper limit of EAR under continuous compounding.**

Learn the essential technique of immunization to protect your assets from changes in maturity. This video demonstrates how immunization works by calculating the impact of a yield to maturity shift on a firm's net asset value. We walk through a practical example, showing how to invest in zero-coupon bonds to offset potential losses and maintain financial stability. Discover the two key conditions required for successful immunization and understand why it's a dynamic strategy that needs regular rebalancing. Subscribe to @AxiomTutoringCourses for more financial insights.

This video explains the concept of forward rates in finance, building upon the understanding of spot rates. Spot rates are the current interest rates for various investment durations. The video demonstrates how to calculate future interest rates, known as forward rates, by considering alternative investment paths and ensuring they yield the same overall return. This principle is essential for avoiding arbitrage opportunities. We explore how to derive forward rates between different periods using a clear, generalized formula. Understanding this concept allows you to lock in future interest rates today, even though the actual future rates may differ. Visit AxiomTutoring.com for more financial education resources and subscribe to @AxiomTutoringCourses for similar content.

This video explains how to construct an arbitrage portfolio when a forward rate is mispriced. It begins by demonstrating how to calculate the fair forward rate using spot rates. When the given forward rate differs from the calculated fair rate, an arbitrage opportunity arises. The video then walks through the specific steps to build a portfolio that capitalizes on this discrepancy, ensuring zero net cash flow at the start and a guaranteed profit. It also touches on how to approach arbitrage if the forward rate is mispriced in the opposite direction. Visit AxiomTutoring.com and subscribe to @AxiomTutoringCourses.

This video delves into the mathematical derivation and interpretation of the Dividend Discount Model (DDM). We begin by exploring the concept that a stock's price is the discounted value of its future dividends and price. The video then progressively expands this formula, substituting future prices with their discounted dividend equivalents. This step-by-step expansion reveals a pattern that leads to the generalized DDM. Finally, we discuss the model's core implication: a stock's true value lies in its future dividend payments, not its fluctuating market price, aligning with long-term investment principles. Visit AxiomTutoring.com and subscribe to @AxiomTutoringCourses.

This video explores the term structure of interest rates, which visually represents spot rates against maturities. We'll examine the common shapes of this term structure, including upward sloping, flat, and downward sloping curves, and discuss that its form is dictated by market realities. The primary focus is on the expectation hypothesis, which posits that forward rates are unbiased predictors of future spot rates. This means that, on average, forward rates accurately forecast where spot rates will be in the future, implying that investing in short-term or long-term instruments should yield the same results. Visit AxiomTutoring.com and subscribe to @AxiomTutoringCourses.

This video provides a foundational understanding of stocks, also known as equity or shares, the most common financial instruments globally. We explore how publicly traded equities are invested on stock exchanges, distinguishing them from private equity. Discover what it means to be a shareholder and your entitlement to a proportion of a company's future profits, not its physical assets. Learn about the two main types of stocks: common and preferred, and understand the key difference between book value and market value. Visit AxiomTutoring.com and subscribe to @AxiomTutoringCourses for more educational content.

This video delves into the Liquidity Premium Theory, expanding upon the Expectations Theory by incorporating the concept of a liquidity premium. Investors prefer short-term savings due to easier access to funds, thus demanding a higher return for long-term commitments. This liquidity premium acts as an upward bias in forward rate calculations, suggesting that short-term and long-term investments are imperfect substitutes. Learn how this theory, alongside the Expectations Theory, explains various term structures, primarily predicting an upward-sloping yield curve under normal economic conditions, with downward slopes potentially signaling a recession. Visit AxiomTutoring.com for more resources and subscribe to @AxiomTutoringCourses for additional insights.

Discover the Market Segmentation Theory, which posits that short-term and long-term investment markets are entirely distinct, with no direct links between them. According to this theory, each maturity period constitutes a separate market. Spot rates for specific maturities are solely determined by the supply and demand within that particular market. This flexibility allows for a wide range of term structure shapes, including upward sloping, downward sloping, and relatively flat curves. It is considered the most adaptable among term structure theories. Learn more about finance and economics at AxiomTutoring.com. Subscribe for more educational content at @AxiomTutoringCourses.

This video introduces the fundamental steps for valuing common stocks, beginning with the concept of expected return for investors. We break down the expected return into its two key components: the dividend yield, representing return from dividends, and capital gain, reflecting the change in stock price. Learn how to mathematically express expected return and then rearrange the equation to determine the present value, or current price (P0), of a stock. This initial valuation model considers expected future dividends and prices, discounted by the expected return, and can be generalized across any time period. Visit AxiomTutoring.com for more resources and subscribe to @AxiomTutoringCourses for expert financial education.

This video explores the Gordon Growth Model, a key component of the dividend discount model. We delve into how a stock's value is intrinsically linked to its future dividends and the appropriate discount rate. The discussion focuses on scenarios where dividends grow at a constant rate, simplifying to a perpetuity with growth formula. We examine the underlying assumptions of the model, particularly the critical condition that the required rate of return must exceed the growth rate. The video also introduces the concept of multiple growth rates and how to approach stock valuation when a company experiences varying growth phases. Visit AxiomTutoring.com and subscribe to @AxiomTutoringCourses.

This video explains how companies grow by reinvesting their net income. We'll explore the concept of Return on Equity (ROE) as a measure of a firm's ability to earn money based on shareholder investments. Learn how net income can be distributed as dividends or retained earnings, and understand the significance of the plowback ratio in driving company growth. Discover the formula for calculating a firm's growth rate and its direct relationship to ROE and the proportion of earnings reinvested. Visit AxiomTutoring.com and subscribe to @AxiomTutoringCourses for more.

This video explains the concept of the present value of growth opportunities for a firm. We delve into how a company's decision to reinvest earnings versus paying them out as dividends impacts its valuation. Through a simple example, we compare the stock price of a firm with zero growth to one with growth, illustrating the valuation difference. This difference highlights the financial benefit of strategic reinvestment for future expansion. Visit AxiomTutoring.com and subscribe to @AxiomTutoringCourses.

In this video, we delve deeper into the relationship between a stock's price and its earnings, building upon previous discussions. We'll explore how the price is determined by earnings per share, the required rate of return, and the present value of growth opportunities. The video will then rearrange this formula to isolate and analyze the Price-to-Earnings (P/E) ratio. Discover how the P/E ratio indicates a firm's earnings and growth potential, and understand the distinction between growth stocks and value stocks based on this metric. Visit AxiomTutoring.com and subscribe to @AxiomTutoringCourses.