Financial Economics I – Lecture 1 Comprehensive Study Notes

Instructor & Course Logistics

• Prof. Nathanael Vellekoop (“Prof V.”)

  • Position: Assistant Professor in Economics

  • Research: Household finance & macroeconomics

  • Office: Max Gluskin House, Room 222

  • Walk-in office hours: Tuesdays 2-3 pm

  • Email: eco358.Vellekoop@utoronto.ca

  • Generally available before & after lectures

• Students

  • Mainly 3rd-year Economics majors

  • Instructor asked for other majors / exchange students to identify themselves

  • Verify that prerequisites are satisfied

  • Expected upper-level behaviour:

  • Arrive on time, come prepared (read chapter, slides, do exercises)

  • Use electronics solely for class

  • Take opportunities to speak publicly

• Assessment Scheme

  • MobLab: 5 %

  • Midterm 1 (90 min): 30 %

  • Midterm 2 (90 min): 30 %

  • Final Exam (2 h): 35 %

• Textbook

  • Berk, DeMarzo, & Stangeland, “Corporate Finance”, 5ᵗʰ Canadian Ed. (2020)

  • Older editions acceptable but "at your own risk"

  • App suggestion: BookBird for buying/selling used texts

• Weekly Schedule (excerpt)

  • 12 Sep: Tools (Ch. 3-4)

  • 19 Sep–26 Sep: Interest Rates & Bonds (Ch. 5, 6+6A)

  • 3 Oct: Valuing Stocks (Ch. 7)

  • 10 Oct: Risk & Return – Concepts (Ch. 10)

  • Midterm 1: Topics 1-4 (exact date TBA)

  • 17 Oct–31 Oct: Portfolio Theory & CAPM (Ch. 10-11)

  • Midterm 2: Topics 5-7 (TBA)

  • 14 Nov: EMH & Behavioral Finance (Ch. 7.5; 13 + videos)

  • 21 Nov–5 Dec: Options, Valuation, Course Recap (Ch. 14-15)

  • Tutorials numbered T1–T11 accompany most weeks

  • Reading Week: 7 Nov

• Exam Coverage Clarifications

  • Section 3.6 (“Price of Risk”) taught in Lecture 5, on Midterm 2

  • Sections 3.7, 4.6, 4.10 not tested

• Administrative Notes for Next Week

  • Modified online classes (details forthcoming)

  • Topic: Interest Rates & Bonds

  • TA office hours begin

  • Tutorials this Wed/Thu/Fri

Lecture 1 Toolkit Overview

• Core Topics
  A. Valuation Principle, Cash-Flow Valuation, & NPV
  B. Law of One Price & Arbitrage
  C. Perpetuities & Annuities

A. Valuation Principle & Net Present Value

• Manager vs. Investor

  • Same analytical tools: value projects by their cash-flows

• Key Questions

  • Up-front costs → what prices to assign?

  • Future benefits → incorporate time

  • Uncertain benefits/costs → incorporate risk

  • Multiple alternative projects → choose via valuation

• Two Fundamental Corporate Functions

  1. Valuing assets (real & financial)

  2. Managing assets (acquire/sell)

• Valuation Principle (text p. 67)

  • Market price in a competitive market determines value

  • Evaluate benefits & costs at market prices

  • Decision adds value if \text{PV(benefits)} > \text{PV(costs)}

• Time Value of Money Example

  • Certain cash-flows:

  • Cost: \$100{,}000 today

  • Benefit: \$105{,}000 in 1 yr

  • Demonstrates that money today ≠ money in future

• Interest-Rate Conventions

  • Risk-free rate r_f

  • Interest-rate factor: (1+r_f)

  • Discount factor: \dfrac{1}{1+r_f}

• NPV Decision Rule
  \text{NPV} = \text{PV(benefits)} - \text{PV(costs)}

  • Choose project with the highest positive NPV

  • Economically equivalent to receiving the NPV in cash today

• Illustrative NPV Table (abbreviated)

  • Projects: Sell Now, Scale Back, Continue Ops, Hire Manager

  • Each line shows today’s flow, 1-yr flow, computed NPV

  • Highest NPV wins (specific dollar results in slide)

• Hire-vs-Sell Example (Table 3.2)

  • Combine operations of hiring & external borrowing vs. immediate sale

  • Shows constructing equivalent cash-flows to compare alternatives

Calculating PV, FV, & NPV

• Simple Interest vs. Compound Interest

  • Simple: earn interest on principal only

  • Compound: earn interest on principal and accumulated interest

• Multi-Period Compounding Example (10 % p.a.)

  • Deposit: \$1{,}000

  • Compute balances under both schemes for 7, 20, 75 years (exercise on slide)

• General Present-Value Formula
  PV0 = \sum{t=0}^{n} \dfrac{Ct}{(1+rf)^t}

• Future-Value Equivalent
  FVn = \sum{t=0}^{n} Ct \,(1+rf)^{n-t}

• NPV Decision Example

  • "Would you pay \$5,000 for this cash-flow stream at 7 %?"

  • Approach: discount each flow, sum, compare to \$5,000

Internal Rate of Return (IRR)

• Definition

  • Discount rate r_{\text{IRR}} such that NPV = 0 given the cash-flow pattern

  • Useful when PV known but required return unknown

• Jessica’s Venture Example

  • Initial outlay: \$1 million

  • CF₁ = \$100 k, grows at 4 % perpetually

  • Solve 0 = -1{,}000{,}000 + \sum_{t=1}^{\infty} \dfrac{100{,}000 \times 1.04^{t-1}}{(1+r)^{t}}

  • Algebraically reduces to 0 = -1{,}000{,}000 + \dfrac{100{,}000}{r-0.04} (assuming r>0.04)

  • Therefore r_{\text{IRR}} = 0.14 (≈14 %)

B. Law of One Price & Arbitrage

• Arbitrage

  • Simultaneous buy/sell of similar goods in different markets to profit from price differences

  • Arbitrage opportunity: profit without risk & without initial investment

  • Normal market: no arbitrage opportunities exist

• Law of One Price (LOOP)

  • Identical goods must trade for the same price in all competitive markets

  • Example bond: Pays \$1{,}000 risk-free in 1 yr, r_f = 5\%

  • No-arbitrage price = \dfrac{1000}{1.05} = 952.38

• Arbitrage Scenarios

  1. Bond priced too low (e.g., \$940):

  • Today: Borrow 940 from bank at 5 %, buy bond

  • In 1 yr: Receive 1,000, repay bank 940\times1.05 = 987, pocket 13 risk-free

  1. Bond priced too high (e.g., \$960):

  • Today: Short-sell bond for 960, invest proceeds at bank 5 %

  • In 1 yr: Investment grows to 960\times1.05 = 1008, purchase bond back at maturity for 1,000, keep 8 risk-free

• No-Arbitrage Pricing Rule
  \text{Price(Security)} = PV(\text{all future cash-flows})

  • Any deviation → arbitrage → forces price back to PV

• Inferring Market Rates from Prices

  • Bond price given: 929.80, pays 1,000 in 1 yr

  • Solve 929.80 = \dfrac{1000}{1+rf} \Rightarrow rf = \dfrac{1000}{929.80} - 1 \approx 7.56\%

• Relationship with NPV

  • In a normal market, NPV{buy} = 0 and NPV{sell} = 0 for traded securities
    NPV{buy} = PV(cash-flows) - \text{Price} NPV{sell} = \text{Price} - PV(cash-flows)

C. Special Cash-Flow Streams: Perpetuities & Annuities

• Definitions

  1. Perpetuity: Constant cash-flow C each period forever

  2. Annuity: Constant cash-flow C each period for n periods

  • Growth extension: payments grow at constant rate g per period

• Present-Value Formulas

  • Perpetuity (level): PV_0 = \dfrac{C}{r}

  • Annuity (level): PV_0 = \dfrac{C}{r}\Bigg[1 - \dfrac{1}{(1+r)^n}\Bigg]

  • Growing perpetuity: PV0 = \dfrac{C1}{r-g} (requires r>g)

  • Growing annuity: PV0 = \dfrac{C1}{r-g}\Bigg[1 - \Big(\dfrac{1+g}{1+r}\Big)^n\Bigg]

• Endowment Example (Level Perpetuity)

  • Desired annual stipend: \$100 k, first payment in 1 yr

  • Expected return: 4 %

  • Donation required: PV = \dfrac{100{,}000}{0.04} = 2{,}500{,}000

• Endowment with Growth (Expenses ↑ 2 %/yr)

  • C_1 = 100{,}000,\ r = 0.04,\ g = 0.02

  • PV = \dfrac{100{,}000}{0.04-0.02} = 5{,}000{,}000

• Lottery Choice Example (Annuity vs. Lump Sum)

  • Option (i): 30 payments of \$1 M starting today → treat as an annuity-due:
    PV{due} = (1+r)\times PV{ordinary}

  • Option (ii): \$15 M today

  • Using r = 8\%, compute & compare (exercise)

• Proof Sketches

  • Slides derive formulas by multiplying PV by (1+r) and subtracting series

Ethical, Practical, & Pedagogical Notes

• Emphasis on market prices as objective valuation metric

• Arbitrage arguments underscore importance of competitive markets; real-world frictions (transaction costs, funding constraints) can prevent instantaneous price correction

• Time-value calculations form the analytical basis for capital budgeting, personal finance decisions (loans, retirement), and macro-financial policy evaluation

Connections & Look-Ahead

• Section 3.6 (Price of Risk) amplifies valuation into risk-adjusted discounting → scheduled Lecture 5

• Perpetuity/annuity framework re-appears in bond pricing (fixed coupons) & equity valuation (dividend discount model)

• CAPM (Lecture 8) will provide a theory of required return r in risky settings