Lecture Notes: Labor Market Indicators, Present Value, Bonds, Stocks, and GDP (Comprehensive Summary)
Labor Market Indicators and Upcoming Reports
- ADP employment report (Automated Data Processing) is a major labor-market indicator released on the first Wednesday of each month. It provides payroll data from a large portion of US payrolls (the speaker notes it could be over a third, though the exact percentage is to be looked up).
- The July report: actual payrolls were 7,200,000 vs forecast of 7,400,000 (lower than expected), and the number was the same as the prior month in some discussions.
- Market interpretation: when data come in below forecast, stock markets tend to fall as it signals weaker-than-expected labor-market performance; when data beat forecasts, markets rally. If data are exactly as expected, move is usually minimal because the information is thought to be already priced in.
- The Employment Situation Summary (the “big” report) comes out on the first Friday of each month and is produced by the Bureau of Labor Statistics (BLS).
- It surveys around 60,000 households to estimate labor-market activity.
- By the time it’s released, there is already some information from the Job Openings report (JOLTP or similar) helping form expectations.
- A correction/clarification from the lecturer: the report released today was a Job Openings report (labor-market report). The ADP report would come out tomorrow (first Wednesday normally, delayed to Thursday due to a holiday).
- Summary points: three major labor-market indicators discussed for the week—Job Openings (today’s report), ADP (tomorrow), and the Employment Situation Summary (Friday). The class will study the Employment Situation in detail next.
Present Value and the Time Value of Money
Core idea: money today is more valuable than the same amount in the future because you can invest it to earn returns.
Question: would you prefer $100 today or $100 a year from now? Most would take $100 today.
Present value (PV) concept: PV of a future amount is its value today, discounted by the opportunity cost of capital.
Discounting principle: to find the present value of a future amount, divide by
where is the periodic discount rate and is the number of periods until receipt.Simple example with 10% return:
- If you can earn 10% per year, receiving one year from now is equivalent to receiving today:
- If you can earn 10% per year, receiving one year from now is equivalent to receiving today:
General present-value formula:
- Present value of a future value:
- The term is called discounting; you’re converting future dollars into today’s dollars.
- Present value of a future value:
Example: contest with a $50,000 payment today plus $50,000 per year for four more years, at a 10% discount rate.
- Payments: $50,000 today, then $50,000 at years 1, 2, 3, 4.
- Present value:
PV = 50{,}000 + rac{50{,}000}{1.10} + rac{50{,}000}{1.10^2} + rac{50{,}000}{1.10^3} + rac{50{,}000}{1.10^4} \
= 50{,}000 imes igl(1 + 0.9091 + 0.8264 + 0.7513 + 0.6830igr) \
\
\,\approx\ 208{,}500.
- Interpretation: the lump-sum equivalent today is about $208,500$; paying $50,000 today plus four future payments is worth about that today under a 10% discount rate.
Relationship to investments: if you must choose between a lump sum today and a stream of future payments, you convert future payments to present value and compare on a like-for-like basis.
Key intuition: the discount rate r reflects the opportunity cost of capital (the next-best alternative investment, e.g., bank account, money market, stock, etc.). As r rises, PV falls; as r falls, PV rises.
Worked note on alternative investments: the choice between a stream of future payments and a lump sum is affected by taxes, inflation, and personal preferences; these factors can complicate direct comparisons but do not change the basic PV framework.
Bond Valuation: Present Value of a Bond
Core idea: the price of a bond is the present value of all future cash flows (coupons and principal) discounted at the relevant discount rate.
Bond price formula (general):
PV =\sum_{t=1}^{T} \frac{C}{(1 + r)^t} + \frac{F}{(1 + r)^T}
where:- is the coupon payment per period,
- is the face value (par) of the bond,
- is the discount rate per period,
- is the number of periods until maturity.
Example 1 (two-year bond): face value , annual coupon rate 3% ⇒ , maturity in 2 years, discount rate .
- Present value:
PV = \frac{30}{(1 + 0.06)^1} + \frac{30}{(1 + 0.06)^2} + \frac{1000}{(1 + 0.06)^2} \approx 946.\n - Note: the final year includes both the coupon and the face value, typically shown as or as , both yield the same result.
- Present value:
Price movement with discount rate: if goes up, bond price falls; if goes down, bond price rises. This inverse relationship is intuitive because higher alternative returns make the fixed bond less attractive.
Example 2 (Toyota bond with quarterly coupons):
- Face value , quarterly coupon ⇒ annual coupon cash flows = , so annual coupon rate is .
- If the bond is sold in the primary market for , the coupon rate (4%) is what matters for the issuer and initial buyer.
- If sold in the secondary market for , the yield to the buyer is higher than the coupon rate because the price is below par; the yield approximates the coupon rate adjusted for price, i.e., the buyer’s return is higher than 4% due to paying less than par.
Yield vs coupon rate in primary vs secondary markets:
- Primary market: coupon rate is the key metric for the issuer and initial investor since the price is typically par.
- Secondary market: yield is the key metric, and it equals (roughly) the coupon rate when price ≈ par; otherwise, yield moves with price.
Quick takeaway: the price of a bond is the present value of its cash flows, and the price moves inversely with the discount rate (interest rates).
Stock Valuation and the Perpetuity Growth Model
- Stocks as streams of dividends: similar PV logic applies, but with an important caveat: dividends can grow over time and the time horizon is uncertain (stocks can be held indefinitely).
- Fixed-dividend perpetuity (no growth): if a stock pays a dividend D every year forever and the discount rate is r, then
- Growing perpetuity (dividends grow at rate g): if dividends grow at rate , the Gordon Growth Model gives
- If the dividend just paid is D0 and dividends grow at rate g, the next year's dividend is , and the value is
- Some instructors use the form with D1 directly as the numerator: .
- If the dividend just paid is D0 and dividends grow at rate g, the next year's dividend is , and the value is
- In-class example from the lecture (growing perpetuity approximation):
- Dividend yield D = 5 per year, growth g = 2% (0.02), discount rate r = 6% (0.06).
- Using the simplified form (as presented):
- Note: if you instead interpret D as the next-year dividend D1 instead of the current D0, then use with D1 = D0(1+g).
- Special note on inflation: growth in dividends is often tied to inflation, and some formulations use an effective discount rate (r − g) to reflect real-valued returns.
- Another widely used form: for stocks with indefinite horizon and constant growth, the Gordon Growth Model applies; for non-growing dividends, use a plain perpetuity with P0 = D / r.
- Summary intuition: higher expected growth (g) or lower required return (r) increases stock value; higher discount rates (r) decrease it.
Primary vs Secondary Markets: Coupon Rate, Yield, and Pricing
- Primary market (new issue):
- The issuer sells to investors at a price (often par) and pays a fixed coupon rate based on the face value.
- The coupon rate is the annual coupon divided by the face value, and it largely determines the promised income to the investor.
- Secondary market (trading existing bonds):
- The buyer’s yield depends on the purchase price. If the bond trades above par, yield falls below the coupon; if it trades below par, yield rises above the coupon.
- Example: a bond with a $1,000 face value and a $40 annual coupon trades at $900 in the secondary market; the coupon rate is still 4% (40/1000), but the yield to the buyer is higher because they paid less than par.
- Takeaway: coupon rate is a property of the instrument; yield is the return to the buyer given the market price.
GDP and National Income Accounting: What GDP Measures and How
- Core definition: GDP is the market value of expenditures on final goods and services produced within a country during a specific period.
- Market value reflects the price at which goods and services are sold; prices reveal value because they show what people are willing to pay.
- Final goods and services: only the last sale to the final user is counted to avoid double-counting intermediate goods.
- The three routes to GDP (in-class focus):
- Expenditure method (the primary method): sum of expenditures on final goods and services.
- Value-added method: sum of value added at each stage of production across all firms.
- Income method: sum of incomes earned in the production of goods and services (wages, profits, rents, etc.).
- Expenditure method intuition: count only the value of final goods and services purchased by end users.
- Example toy economy (illustrative): suppose an economy produces 100 oranges, 50 bicycles, and 20 rock concerts.
- If oranges sell for $1 each, bicycles for $100 each, and rock concerts for $200 each, then GDP would be:
- Note on the transcript’s numbers: the exact arithmetic shown had some inconsistencies (e.g., a mis-typed total for rock concerts). The key point is that GDP is the weighted sum of final goods by their market prices, not a simple count of items.
- Final vs intermediate goods: we only count the final sale. In the car example:
- Stages: iron ore -> steel -> wholesale car -> retailer -> consumer.
- Value added at each stage (illustrative):
- Iron mine sells iron to steel mill for $1,000 (value added by iron mine = $1,000).
- Steel mill adds $2,000 value (turning $1,000 input into $3,000 of steel value).
- Auto manufacturer adds $7,000 value (turning $3,000 into $10,000 wholesale car value).
- Retailer adds $5,000 value (turning $10,000 into a $15,000 car for the consumer).
- The total value added across all stages equals the final price to the consumer: $15,000 (which matches the final sale price). This demonstrates why the value-added method yields the same GDP figure as the expenditure method.
- Why expenditure method is used: it is often the least costly to measure (one transaction) rather than tracing value added across all stages.
- GDP is geographically bound (GDP is domestic): if a Toyota plant in Kentucky builds a car for sale in the US, that counts toward US GDP even though Toyota is a Japanese company. If Ford builds cars in Japan, those counts toward Japan’s GDP. This is what is meant by GDP being geographically balanced; gross national product (GNP) is the alternative concept discussed for later.
- “Water in the tub” analogy: GDP measures the flow of new production entering the economy during the period, not the stock of assets already in place. Old desks, chairs, and buildings counted in earlier periods are not recounted when measuring GDP for the current period.
- Quick takeaway: GDP = market value of expenditures on final goods and services produced within a country; it can be decomposed into the expenditure components and is equivalent, under the value-added method, to the sum of value created at each stage of production.
- GNP vs GDP: GDP is geographically bound to production within the territory; GNP would count production by residents regardless of location, which will be discussed in a future lecture.
Key Concepts and Practical Implications
- The present value framework ties directly to asset pricing: higher expected inflation or higher discount rates reduce asset values (PV of future cash flows falls as r rises).
- The discount rate reflects opportunity costs across competing investments (bank accounts, stocks, real estate), not just a single risk-free rate.
- Inflation and growth expectations affect stock valuations through dividends (D) and the growth rate (g) in the Gordon Growth Model.
- Interest-rate expectations (e.g., Fed policy) influence asset prices: if rate cuts are anticipated, the present value of future dividends and coupon payments tends to rise, pushing stock prices up in anticipation.
- In macro practice, the three approaches to GDP should align in the sense that they measure the same economic activity from different angles, helping verify the robustness of the data.
- Ethical and practical implications: understanding how asset prices respond to interest rates informs monetary policy implications for households, pension funds, and governments; the distributional effects of inflation and interest-rate changes can be broad across sectors.