GC

Time Value of Money - Lecture Notes

Module Outline

  • Weeks 1-8 (03/02/2025 - 28/03/2025):
    • Time Value of Money
    • Risk and Return
    • Balance Sheet
    • Income Statement
    • Cash Flow Statement
    • Capital Structure
    • Valuation
    • Payout Policy
  • Easter Break (31/03/2025 - 25/04/2025)
  • Weeks 9-10 (28/04/2025 - 09/05/2025):
    • Corporate Governance
    • Efficient Market and Behavioural Finance
  • Week 11 - Revision lecture (16/05/2025)
  • Textbook: Principle of Corporate Finance by Richard A. Brealey, Stewart C. Myers, Franklin Allen, Alex Edmans

Exam Structure

  • Two-hour in-person exam
    • Section A: Two numerical questions
    • Section B: Two essay-type questions
  • Answer ONE question from Section A (70 marks)
  • Answer ONE question from Section B (30 marks)

Intended Learning Outcomes

  • Understanding money and investments
  • Present Value (PV) and Net Present Value (NPV)
  • Perpetuity
  • Internal Rate of Return (IRR)

Make Money vs Manage Money

  • Kiyosaki (2001): Should money work for people, not the other way around.
  • Warren Buffett: "If you don’t find a way to make money while you sleep, you will work until you die."
  • Business school topics include: money, macroeconomics, microeconomics, accounting, finance, marketing, logistics, etc.
  • Traditional education focuses on becoming an employee, rarely on managing money.

Global Wealth Distribution

  • Over $1M:
    • 45.8% of global wealth ($191.6T)
    • Held by 1.1% of the global population
  • $100K - $1M:
    • 39.1% of global wealth ($163.9T)
    • Held by 11.1% of world adults
  • $10K - $100K:
    • 13.7% of global wealth ($57.3T)
  • Less than $10K:
    • 1.3% of total wealth ($5.5T)
    • Held by 55.0% of the population

How Rich People Get Richer

  • Three types of assets:
    • Money-producing assets:
      • Generate cash inflow for the owner (real cash, not paper profit).
    • Money-consuming assets:
      • Consume cash (real cash, not paper loss or gain).
    • Non-cash flow assets:
      • No real cash inflow or outflow (not paper gain or loss).
  • Wealthy people primarily own money-producing assets.
  • How to become richer:
    • Reduce money-consuming assets.
    • Accumulate money-producing assets (investors).
    • Create money-producing assets (entrepreneurs).
    • Investing good non-cash flow assets (traders and investors).

Some Misunderstandings

  • Stock market ≠ Casino
    • Is it too risky? What about your job?
    • The chance of a country (China, the US) declaring bankruptcy?
    • Credit ratings: USA (AA+, AAA); APPL (AA+, AAA); MSFT and J&J (AAA)
  • "I don't like doing investments myself"
    • Bank deposit - what type of assets?
    • Inflation rate: US 2.9%; UK 2.5%. Real interest rate?
    • Can you do better? (S&P500 annual return 10% for the last century)
    • Compound effect, 10,000, 30% annual return

Money Has Time Value

  • One pound today is not one pound tomorrow.
    • Example: £20K now or next year?
  • Money today is more valuable than tomorrow.
  • Why? Interest rate.
  • What happens when you deposit money into a bank account?

Interest Rate: Three Levels

  • Required Return:
    • Minimum rate of return an investor expects for taking on a certain level of risk.
  • Opportunity Cost:
    • Potential return an investor sacrifices by choosing one investment over another.
  • Discount Rate:
    • Rate used to determine the present value of future cash flows.
  • Example:
    • 100 \times (1+4\%) = 104
    • 100 = \frac{104}{(1+4\%) }
  • Risk = Opportunity Cost = Next Best Alternative
  • Life is about making choices; choosing one means giving up another.
  • Higher risk, higher required return, higher discount rate, lower present value.

Investment Preference

  • Consider two investment options with different inflow patterns over 3 years, both requiring an outflow of 50,000.
  • Investment I: 20,000 each year for 3 years.
  • Investment II: 40,000 in year 1, and 9,000 in years 2 and 3.

Which Investment Do You Prefer?

  • Face value:
    • Investment I pays back: 60,000
    • Investment II pays back: 58,000
  • Investment II pays 20,000 more in the 1st year
  • Potential to reinvest the extra 20,000 (e.g., get 5% from a savings account, or more if clever).
  • The timing of when the money is received matters, because you could be reinvesting the money to get higher returns.

Investment Preference with Reinvestment

  • Assume an opportunity to invest extra funds at a sure 10% per year.
    • Investment I: 66,200
    • Investment II: 67,300
  • The timing of when you get the money is important, as well as how much you get.
  • Money has a time value: the earlier, the better!

Is Either Investment Worth Putting 50,000

  • At the 10% opportunity rate:
    • Investment I: 66,200
    • Investment II: 67,300
    • Invest in 10%: 50,000 \times 1.1^3 = 66,550
  • At the 5% opportunity rate:
    • Investment I: 63,050
    • Investment II: 62,550
    • Invest in 5%: 50,000 \times 1.05^3 = 57,881
  • The results are called the “Accumulated Value” of future cash flows.

Present Value (PV)

  • Accumulated Value (AV) properly takes into account:
    • Investor’s opportunity rate
    • The time value of money
    • Amount of cash flows
  • Using AV for business decisions is inconvenient.
  • More useful to find out the “worth” of future cash flows in today’s dollars.
  • Compare this “Present Value” directly with the initial investment.

Present Value (PV) continued

  • The rate of return r is called the discount rate, hurdle rate, or opportunity cost of capital.
  • NPV = PV - Investment

Net Present Value (NPV)

  • Discounted Cash Flow (DCF) formula:
  • PV0 = \frac{C1}{1+r} + \frac{C2}{(1+r)^2} + \frac{C3}{(1+r)^3} + … + \frac{C_t}{(1+r)^t}
  • NPV0 = -C0 + \sum{t=1}^{T} \frac{Ct}{(1+r)^t}
  • \sum{t=1}^{T} \frac{Ct}{(1+r)^t} is the summation of all the future cash flows discounted back to the current period.
  • -C_0 is the initial investment.

Additional Variables

  • NPER is the number of periods
  • RATE is the interest rate per period
  • PMT is the periodic payment
  • PV is the present value
  • FV is the future value

Calculating Present Value (Excel Example)

  • Timeline: Now, 1, 2, 3 (years)
  • Cash-flow stream: 0, $100, -$150, $300
  • Discount rate: 10%
  • Present value: 192.34
  • In Excel: =NPV(B3,C2:E2) (where B3 is the discount rate and C2:E2 are the cash flows)

NPV Example: NIKE Plant Investment

  • NIKE plans to invest 75 million to build a new shoe manufacturing plant.
  • The new plant will generate annual returns of 25 million over the next five years.
  • Discount rate: 10%
  • Should NIKE proceed with building this plant?
  • PV_0 = \frac{25}{1 + 0.1} + \frac{25}{(1 + 0.1)^2} + \frac{25}{(1 + 0.1)^3} + \frac{25}{(1 + 0.1)^4} + \frac{25}{(1 + 0.1)^5}
  • PV_0 = 94.77
  • NPV_0 = -75 + 94.77 = 19.77
  • NIKE should invest because the NPV is positive.

Perpetuity

  • Perpetuities are bonds with no obligation to repay the principal, but offer a fixed income each year to perpetuity.
  • Financial concept where a cash flow is theoretically received forever.

Perpetuity - Example

  • If the discount rate is 10%, what is the present value of a perpetual bond with an annual interest payment of 1 million

Perpetuity Discussion Points

  • If you had this perpetual bond, would you sell it for 10 million
  • Is there a problem with the formula for calculating the present value of perpetual bonds?

Perpetuity - Initial Investment

  • Initial investment: 1,000, with 100 interest payment each year forever. The PV of the future payment for the next 20 years is only worth 851 today.

Perpetuity - Loughborough University Example

  • A successful alumnus wishes to endow a Professor of Finance at Loughborough University with the initial payment occurring at the end of the first year.
  • Interest rate: 2%
  • Aim: Provide £100,000 a year in perpetuity.
  • How much should be set aside today?

Three Points of NPV

  • The NPV rule recognizes that a dollar today is worth more than a dollar tomorrow.
  • NPV depends solely on the forecasted cash flows from the project and the opportunity cost of capital.
  • Because present values are all measured in today’s dollars, you can add them up: NPV(A+B) = NPV(A) + NPV(B)

Internal Rate of Return (IRR)

  • A project’s internal rate of return (IRR) is the discount rate that makes the NPV of the project equal to zero.
  • NPV = 0 = -CF0 + \frac{CF1}{1+IRR} + \frac{CF2}{(1+IRR)^2} + … + \frac{CFt}{(1+IRR)^t} + … + \frac{CF_T}{(1+IRR)^T}

Internal Rate of Return (IRR) - Example

  • Purchase a machine tool for 4,000.
  • The investment will generate 2,000 and 4,000 in cash flows for two years, respectively.
  • What is the IRR on this investment?

Internal Rate of Return (IRR) - Rule

  • The IRR rule is to accept an investment project if the opportunity cost of capital is less than the IRR.
  • If the cost of capital is less than the IRR, then the project has a positive NPV.
  • If it is equal to the IRR, the project has a zero NPV.
  • If it is greater than the IRR, it has a negative NPV.

IRR and NPV Relationship

  • Graph showing the relationship between NPV and discount rate.
  • IRR is the point where NPV = 0.

Calculating the IRR (Excel Example)

  • Timeline: Now, 1, 2, 3
  • Cash flows: -160, $100, -$150, $300
  • IRR = 17.89%
  • In Excel: =IRR(B2:E2)

Stock Investment Question

  • If an investor invests in the stock of a company that is widely recognized as an excellent company, could it be a bad investment?
  • It’s not what you buy, it’s how much you pay!

Stock Overvaluation Question

  • An investor invests in an overvalued stock, and the stock price falls back shortly thereafter (paper loss).
  • Belief: "This is a high-quality company; if the company's profits continue to grow in the next few years, the stock price will rebound, and she will turn losses into profits in the future, so she decides to hold on the stocks firmly."
  • Do you agree with the above point of view?

Stock Prices

  • Stock prices reflect the market's expectations for the future.
  • Did you buy into rational or irrational expectations?

Market Summary

  • Example: PetroChina Company Limited (SHA: 601857) stock price over time.

Future Cash Flows and Discount Rates

  • Expectations of future cash flows are constantly changing.
  • Discount rates are changing, and hence the discounted future cash flows.
  • Both the numerators and denominators are changing.
  • Success depends on grasping a constantly changing future!

Reading

  • Principle of Corporate Finance:
    • Part One: Chapter 2 and Chapter 5