CB

Time Value of Money: An Introduction

Time Value of Money: An Introduction

Learning Objectives

  • Identify the roles of financial managers and competitive markets in decision making.

  • Understand the Valuation Principle and its application in identifying decisions that increase the value of a firm.

  • Assess the effect of interest rates on today's value of future cash flows.

  • Calculate the value of distant cash flows in the present and current cash flows in the future.

  • Notation

    • r = interest rate

    • PV = present value

    • FV = future value

    • C = cash flow

    • n = number of periods

Introduction to Financial Decision Making

  • Every decision in finance has future consequences affecting the firm's value, typically balancing costs and benefits.

  • Example: Apple's decision in 2015 to enter the wearable technology market with the Apple Watch.

  • Another example: Amazon's $13 billion acquisition of Whole Foods in 2017, incurring ongoing costs but providing revenues and bolstering Prime memberships.

  • A decision is beneficial if the total value of benefits exceeds costs.

  • To compare costs and benefits occurring at different times, we convert them into common terms, typically cash today.

3.1 Cost-Benefit Analysis

Role of the Financial Manager

  • Financial managers are tasked to make decisions that maximize the value of the firm for its investors.

  • A fundamental principle: Good decisions have benefits exceeding costs.

  • Real-world opportunities are complex, requiring input from various management disciplines to quantify costs and benefits.

Expert Areas Influencing Decision Making

  • Marketing: Assessing revenue increases from advertising.

  • Economics: Analyzing demand changes from price adjustments.

  • Organizational Behavior: Studying impacts of management changes on productivity.

  • Strategy: Evaluating responses to competitors' price changes.

  • Operations: Estimating production costs after improvements.

Quantifying Costs and Benefits

  • Value of benefits must exceed the costs to enhance firm value.

  • Concrete examples help compare costs with immediate cash values.

  • Scenario: Jewelry Manufacturer's decision to trade 400 ounces of silver for 10 ounces of gold.

    • Cash value calculation:

    • Current silver price: $25/ounce
      ext{Cost} = 400 ext{ ounces} imes 25 = 10,000

    • Current gold price: $1900/ounce
      ext{Benefit} = 10 ext{ ounces} imes 1900 = 19,000

    • Net benefit:
      19,000 - 10,000 = 9,000

  • The decision nets the jeweler $9,000, enhancing the firm's wealth.

Role of Competitive Market Prices

  • Competitive markets have standardized prices; decisions should not change based on personal beliefs.

  • Example: Jeweler can sell gold received and buy silver back, realizing a profit regardless of preference.

  • Market price establishes the value of goods in financial markets.

  • Concept Check question: If crude oil trades competitively, would an oil refiner value it differently than an investor?

3.2 Market Prices and the Valuation Principle

Application of the Valuation Principle

  • Clear decisions arise from easy evaluation of costs and benefits based on market prices.

  • Valuation Principle

    • The value of a commodity or asset for a firm/investors is derived from competitive market pricing.

    • Cost-benefit evaluations should use market prices for decisions that enhance firm value.

Example Scenario

  • Operations manager opportunity: Acquire oil and copper for $25,000 with existent market values.

    • Current prices: Oil at $90/barrel, Copper at $3.50/pound.

    • Valued benefits:

    • 200 ext{ barrels of oil} imes 90 = 18,000

    • 3000 ext{ pounds of copper} imes 3.5 = 10,500

    • Net value of opportunity:
      18,000 + 10,500 - 25,000 = 3,500

    • Positive outcome recommends taking the deal.

Law of One Price & Arbitrage

  • Law of One Price: In competitive markets, identical cash flows must have the same price.

  • Arbitrage: Trading identical goods to exploit price differences for profit with no risk.

  • Arbitrage Opportunity: Scenario allowing profit without investment or risk.

  • Example: Global prices of McDonald's Big Mac showcase local variances but lack arbitrage due to local purchasing restrictions.

3.3 Time Value of Money and Interest Rates

Importance of Time in Financial Decisions

  • Most financial decisions incur upfront costs while generating future benefits, necessitating time consideration.

  • To accurately measure costs and benefits, the principle of time value of money is applied.

  • Time Value of Money: Reflects disparity between current and future cash values; $1 today is more valuable than $1 in one year due to potential investment earnings.

Interest Rate Concept

  • The interest rate defines the exchange rate of money today versus money in the future, determining cash flow values.

  • Example: Investment opportunity at a cost of $100,000 returning $105,000 in one year exemplifies cash flow evaluation through interest rates.

  • Necessary calculations include determining the present value of future earnings through discounting methods.

Present Versus Future Value

  • Present Value (PV): Cash flow value today.

  • Future Value (FV): Cash flow value in a future period.

    • Key Calculations

    • PV = rac{C}{(1+r)^n}

    • FV = C(1 + r)^n

Discount Rate and Discount Factor

  • The discount rate signifies the market rate for cash flow valuation, critical for calculating opportunity costs.

  • Discount factor computes today's value of future cash flow, demonstrating the diminishing present value of money over time.

3.4 Valuing Cash Flows at Different Points in Time

Rules of Valuing Cash Flows

  1. Comparison Rule: Only cash flows at identical points in time are comparable.

  2. Compounding Rule: Calculating FV necessitates compounding cash flows using interest rates.

  3. Discounting Rule: Determining present values requires discounting future cash flows appropriately.

Timelines in Financial Analysis

  • Timeline: A linear representation of cash flow timing, essential for organizing and solving financial issues.

  • Differentiate between inflows and outflows by assigning signs: Inflows are positive, while outflows are negative.

Example Problem

  • Savings bond offering $15,000 in 10 years at 6% market rate. Present value calculated as:
    PV = rac{15,000}{(1.06)^{10}} = 8,375.92

Summary & Key Equations

  • Evaluating decisions necessitates valuing incremental costs and benefits, ensuring benefits outweigh costs.

  • Competitive markets provide tools for fair price valuation.

  • Calculate cash flows via compounding and discounting, applying the three rules of cash flow valuation.

Key Terms

  • Present value (PV): Value of a future cash flow calculated in present terms.

  • Future value (FV): Value of cash flow moved forward in time[ \text{FV} = C(1 + r)^n ]

  • Interest rate: Market rate for cash exchanges.

  • Discount factor: Present valuation of future dollar amounts.

  • Discount rate: Rate for converting future cash flows to present values.

Concept Check Questions

  1. What constitutes a good investment decision?

  2. How do market prices serve financial managers?

  3. What is the significance of arbitrage in market pricing?

  4. Why should cash flows received at different times not be combined directly?

  5. What is the rationale for compounding and discounting cash flows?

Problems and Exercises

  1. Honda Motor Company's rebate analysis.

  2. International shrimp transaction valuation based on exchange rates.

  3. Examining alternatives between cash bonuses and stock options.

  4. Interest rate impact assessments on loans and savings.

  5. Case studies on financial decision making and valuation principles.