4. investment

Investment

Big Question

• Determinants of Investment

  • Fundamental question: What are the key factors influencing investment decisions?

Lecture Overview

• Objective: Understand Investment

• Specific Questions:

  1. What is the value of investment over time?

  2. How do firms make investment decisions?

Big Picture on Investment

• Investment as a Driver: Investment is a critical component that drives productivity in the economy.

  • Output per worker is denoted as $Y/L$

  • Capital per worker is denoted as $K/L$

  • Source: Macmillan Learning, ©2023

Types of Investment

• Capital Stock (K): Refers to the total amount of capital available in the economy at a given point in time.

• Investment Function:

  • Investment results in an increase in the capital stock (K).

  • Defined as a flow of new purchases or acquisitions of capital assets that add to the existing stock of capital.

Macroeconomic Investment

• Key Trade-off: Investment entails a crucial trade-off between present costs and future benefits.

• Objective: Assess the value of future benefits in relation to present costs.

• Comparison of Values: Requires evaluation of worth at different temporal points.

• Methodologies Used:

  • Compounding: Process of determining the future value of an investment based on current value and interest rates.

  • Discounting: Process of determining the present value of future cash flows.

• Focus on firm-level investment analysis, which can also apply to broader scenarios involving initial costs for future cash flows.

Evaluating Investment Decisions

• Compound Interest:

  • Defined as interest calculated on the initial principal and also on the accumulated interest from previous periods. Therefore, it grows exponentially.

  • Example:

  • Assume a deposit of $Y_0 = 1000$ at an interest rate $r = 10\%$ for $t$ periods:

    • Year 1: Invest $1000$ at 10% → Earned: $100$ → Total: $1100$

    • Year 2: Earn 10% on $1100$ → Earned: $110$ → Total: $1210$

    • Year 3: Earn 10% on $1210$ → Earned: $121$ → Total: $1331$

  • General Formula for the value of the deposit at year $t$ is:
    $Y<em>t = Y</em>0(1 + r)^t$

  • Where:

  • $r$ = real interest rate

  • $Y_t$ in base year dollars reflects purchasing power.

  • If using $i$, $Y_t$ reflects nominal dollars.

The Power of Compound Interest

• Nominal Values: Represent actual dollar amount currently held.

  • Calculated using nominal interest rate $i$ in the compounding formula.

• Real Values:

  • Adjusted for inflation.

  • Calculated using real interest rate $r$ in the compounding formula.

• Importance of Real Values: Real values highlight purchasing power—the actual capacity of money to buy goods and services.

Real vs Nominal Interest Rates

• Business Investment Characteristics:

  • Typically, involves an up-front cost alongside anticipated future cash flows.

• Evaluation of Costs and Benefits:

  • Need to convert future benefits into present values since receiving $500$ in the future is not equivalent to receiving $500$ today, due to potential investment returns over time.

  • Opportunity Cost: Represents the potential earnings forgone from compounding interest if principal is not invested today.

• Present Value Concept:

  • Present Value (PV) signifies the current worth of a series of future cash flows.

  • Discounting: Process of converting future nominal values to their present equivalent values.

  • Present value of cash flow in year $t$, $CF<em>t$ in terms of year 0 is represented as: $CF</em>0 = \frac{CF_t}{(1+i)^t}$

  • Use nominal interest rates for discounting when inflation is present.

Evaluating Investment Decisions Process

1. Convert Future Cash Flows: Transform future benefits into present value using the discounting formula (PV). Adjust for future costs, such as depreciation, by subtracting these from benefits for that period and convert net benefits to present value.

2. Cost vs Benefit Comparison: Compare the present value of future net benefits/cash flows to the initial investment cost (C).

3. Investment Evaluation Rule: Pursue investment opportunities if C < PV.

At Home Practice

• Investment Decision Question: Would you consider investing today $950$ in a project that yields $1000$ next year at different interest rates?

  • Interest Rates: 4%, 5%, 6%

  • Calculating Present Value (PV): Steps are to adjust cash flows to the same present time and then compare costs to benefits.

• Investment Decision Evaluation:

  • For 4%: Yes, since PV > Initial Cost.

  • For 5%: Yes, since PV > Initial Cost.

  • For 6% or higher: No, since Initial Cost > PV.

Additional Practice Problem

• Initial Investment: If your initial investment is $1825$ today, determine applicable interest rates for receiving $1000$ next year plus another $1000$ in two years.

  • Analysis: Evaluate by performing calculations for each interest scenario presented, establishing thresholds for investment decision making based on present values compared to initial costs.