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NAME: ____________________________ PERCENT ________POINTS _______ 5 problems on FUTURE VALUE and PRESENT VALUE (2 points each) (show work for possible partial credit) 1. PRESENT VALUE of $10,000, at 2.3%, 2 years 2. FUTURE VALUE of $10,000, at 1.25%, 1 year 3. FUTURE VALUE of $1,000, at 3.5%, 4 years 4. PRESENT VALUE of $1,000,000, at 0.5%, 6 months 5. FUTURE VALUE of $750, at 0.75%, 9 months 6. This graph shows an initial equilibrium in the Market for Loanable Funds. a. Show the changes in the graph if the fiscal authorities (i.e. Congress and President) increase government spending substantially. (6 points) the b. In this case the equilibrium interest rate (choose one) . . . i. increases ii. decreases c. In this case the equilibrium quantity of loans (choose one) . . . i. increases ii. decreases 7. If the Market for Loanable Funds shows a nominal interest rate of 7%, use the Fisher Equation -- inominal = E(INF) + rreal -- to find the real rate of interest if expected inflation is 3%. (2 points) 8. For each of the following, indicate whether it takes place in the primary market or the secondary market for securities. (circle the correct answers) (2 points) a. the first b. exchange A successful startup corporation decides to issue shares to the public for time. (primary/secondary) You buy 100 shares of Apple Inc., which is listed on the NASDAQ (primary/secondary) Unit II: Markets Interest Rates; Securities Unit II: Markets Basic principles of interest rates & fixed-income markets: ▪time preference ▪ time-value of money ▪ future value (compounding) ▪ present value (discounting) Unit II: Markets You will use compounding (future value) and discounting (present value) in all financial applications FOREVER. Unit II: Markets “. . . the European philosophical tradition . . . consists of a series of footnotes to Plato” -- Alfred North Whitehead “All finance is a series of footnotes to compounding and discounted present value”. --Lawrence Morgan Unit II: Markets People prefer consumption now to consumption later. So, if they are to defer consumption – that is, if they are to save – they require getting something additional in the future. That is the rate of interest. e.g. to forego $1.00 now you require $1.10 one year from now. That is a 10% (= 0.10) rate of interest. And $1.10 is the future value of $1.00. Future Value of $1 for 1 year = $1.10 𝐹𝑉 $1,1 𝑦𝑒𝑎𝑟, 𝑖 = $1 × 1 + 𝑖 1 𝐹𝑉 $𝑥, 1 𝑦𝑒𝑎𝑟, 𝑖 = $𝑥 × 1 + 𝑖 1 𝐹𝑉 $100,1 𝑦𝑒𝑎𝑟, 10% = $100 × 1 + 𝑖 1 = $110 Unit II: Markets The same principle works for periods longer or shorter than 1 year: 𝐹𝑉 $𝑥, 𝑇𝑦𝑒𝑎𝑟𝑠, 𝑖 = $𝑥 × (1 + 𝑖)𝑇 e.g. for $100 for 2 years at 5% FV($100, 2 years, 5%) = e.g. for $100 for 6 months (= 0.5 year), at 5% FV($100, 0.5 years, 5%) = Unit II: Markets Present value If you turn future value around, you get present value 𝐹𝑢𝑡𝑢𝑟𝑒 𝑣𝑎𝑙𝑢𝑒 = $1.10 = 1.10 × $1 divide both sides of the equation by 1.10 𝐹𝑢𝑡𝑢𝑟𝑒 𝑣𝑎𝑙𝑢𝑒 1.10 = $1.10 1.10 = 1.10 × 1.10 $1 = $1 = 𝑃𝑟𝑒𝑠𝑒𝑛𝑡 𝑣𝑎𝑙𝑢𝑒 In general 𝐹𝑢𝑡𝑢𝑟𝑒 𝑣𝑎𝑙𝑢𝑒 = 𝑃𝑟𝑒𝑠𝑒𝑛𝑡 𝑣𝑎𝑙𝑢𝑒 × (1 + 𝑖)𝑇 𝑃𝑟𝑒𝑠𝑒𝑛𝑡 𝑣𝑎𝑙𝑢𝑒 = 𝐹𝑢𝑡𝑢𝑟𝑒 𝑣𝑎𝑙𝑢𝑒 1+𝑖 𝑇 Unit II: Markets Present value So Present Value of $x to be paid in T years discounted at r is ... 𝑃𝑉 $𝑥, 𝑇 𝑦𝑒𝑎𝑟𝑠, 𝑖 = examples: 𝑃𝑉 $1, 2 𝑦𝑒𝑎𝑟𝑠, 10% = 𝑃𝑉 $1, 0.5 𝑦𝑒𝑎𝑟𝑠, 10% = $𝑥 (1+𝑖)𝑇 Unit II: Markets Present value Note: as r rises, PV falls; as i falls, PV rises Bond prices: the price of a bond is the Present value of the payments it will make For short-term instruments (e.g. Treasury bills) there is only one payment; for long-term bonds there are many payments (interest payments, and eventually the “face value” of the bond). The price or PV of the bond is the sum of the PVs of all those payments. Unit II: Markets Present value Note: as i rises, PV falls; as i falls, PV rises. Compare PV of $100 to be received in 2 years at (a) 10% and (b) at 5%: 𝑃𝑉 $100,2 𝑦𝑒𝑎𝑟𝑠, 10% = 𝑃𝑉 $100,2 𝑦𝑒𝑎𝑟𝑠, 5% = Unit II: Markets The Rate of Interest (continued) Where does “the interest rate” come from? (actually many interest rates) LOANABLE FUNDS THEORY Unit II: Markets The Rate of Interest (continued) LOANABLE FUNDS THEORY is basic supply and demand theory DEMAND FOR LOANABLE FUNDS (demand for credit) from . . . a) Households (for car, house, appliances, . . . ) b) Businesses (for investment, trade finance, inventory finance, . . . ) c) Government (for infrastructure, uneven tax receipts, general spending) d) Foreign sources (all of the above) Unit II: Markets The Rate of Interest (continued) Interest Rate r LOANABLE FUNDS THEORY is basic supply and demand theory Demand for loanable funds Quantity of Loans Unit II: Markets The Rate of Interest (continued) LOANABLE FUNDS THEORY is basic supply and demand theory SUPPLY OF LOANABLE FUNDS (supply of credit) from . . . a) b) c) d) Households from savings (directly or indirectly) Business (retained earnings) Government (budget surplus, tax receipts) Foreign supply (all of the above). Unit II: Markets The Rate of Interest (continued) Interest Rate r LOANABLE FUNDS THEORY is basic supply and demand theory Supply of loanable funds Quantity of Loans Unit II: Markets The Rate of Interest (continued) LOANABLE FUNDS THEORY is basic supply and demand theory Equilibrium determination of interest rate Interest Rate r S D Quantity of Loans Unit II: Markets The Rate of Interest (continued) This is supply and demand for credit. It determines an interest rate (the price of credit). Once you know the interest rate, you can calculate the price of a bond or loan (more about this later). Unit II: Markets Factors that affect interest rates (or the price of bonds) a) Economic growth generally, strong growth will shift the demand for credit -- and probably the supply of credit – to the right. This tends to push interest rates higher. Unit II: Markets Factors that affect interest rates (or the price of bonds) Interest Rate r S S´ r2 r1 D Quantity of Loans D´ Unit II: Markets Factors that affect interest rates (or the price of bonds) b) Inflation Distinguish nominal interest rates and real interest rates. 1. the nominal rate is that actual rate that borrowers pay and lenders receive. 2. if there is inflation, the dollars that a borrower pays back and a lender receives are worth less than when the loan was made, so the real rate of interest is lower. Unit II: Markets Factors that affect interest rates (or the price of bonds) b) Inflation (continued) The difference between nominal and real rates is the rate of inflation. If the borrower receives 5% interest but inflation has been 4%, the real rate is 1%. (actually expected inflation) i = E(INF) + rR or rR = i – E(INF) (called the “Fisher effect”) Unit II: Markets Factors that affect interest rates (or the price of bonds) b) Inflation (continued) Unit II: Markets Figure 4.5 Expected Inflation and Interest Rates (ThreeMonth Treasury Bills), 1953–2013 Unit II: Markets Factors that affect interest rates (or the price of bonds) c) Monetary policy basically, if the central bank increases the rate of growth of the money supply, that will lower short-term interest rates -- unless the money supply grows so rapidly that expected inflation increases. Unit II: Markets Factors that affect interest rates (or the price of bonds) c) Monetary policy Interest Rate r S S´ r1 r2 D Quantity of Loans Unit II: Markets Factors that affect interest rates (or the price of bonds) d) Fiscal policy a budget deficit represents additional demand for credit, so this raises interest rates; a budget surplus reduces interest rates. although this is demand from the government (particularly the national government) all the rates are connected so this will have an impact on corporate, municipal, and other interest rates. Unit II: Markets Factors that affect interest rates (or the price of bonds) d) Fiscal policy S Interest Rate r r2 r1 D Quantity of Loans D´ Unit II: Markets Factors that affect interest rates (or the price of bonds) e) Foreign demand for credit Foreign entities can borrow or lend in our market. However, even activity in foreign markets affects our domestic market since the markets are all connected. (This will also affect the foreign exchange markets.) Unit II: Markets Recent history of U.S. short-term interest rate Unit II: Markets Securities These are the basic items which are bought and sold in financial markets: principally stocks and bonds. They allow savings to move to investors more-or-less anonymously and therefore allow investors to mobilize large amounts of resources. Unit II: Markets Securities ❖Primary Market: securities are originally issued or sold in the primary market (new stock is issued, new bonds are sold) – this is typically used to raise capital for an enterprise. Unit II: Markets Securities ❖Secondary Market: after the securities are issued in the primary market, they can be bought and sold in the secondary market; the prices of the securities varies – an investor will be more willing to buy securities in the primary market if it is possible to liquidate the investment at will; otherwise the investor would have to hold shares forever or hold bonds until maturity. Unit II: Markets Securities Valuation (overview) 1. Information (and even misinformation) is key to valuations. 2. Securities regulation tries to see to it all relevant information is public. 3. Cash flows are the central to valuation – you will work with these in detail shortly. 4. Efficient Markets Hypothesis – the hypothesis that the market price reflects all the information about an asset so that no one can reliably earn returns higher than that of the overall market – HIGHLY CONTROVERSIAL UNIT II: MARKETS CLASS OUTLINE I. Interest rates These are the basis of all financial markets All finance is a series of footnotes to compounding and discounted present value”. A. Basic principles of interest rates & fixed-income markets: 1. Time preference 2. Time value of money 3. Future value (compounding) 4. Present value (discounting) B. Time preference and the time value of money People prefer consumption now to consumption later. if they defer consumption – if they SAVE – they require something additional in future THAT IS THE RATE OF INTEREST REMEMBER THAT 10% MEANS 0.10 – that's what we use in calculations. C. Future value (compounding) If you invest $1 for one year at a rate of r percent, the "future value" of that $1 is what you get back – the $1 plus interest – after one year. 𝐹𝑉($1,1 𝑦𝑒𝑎𝑟, 𝑖) = $1 × (1 + 𝑖)1 Same thing for $x: 𝐹𝑉($𝑥, 1 𝑦𝑒𝑎𝑟, 𝑖) = $𝑥 × (1 + 𝑖)1 e.g. 𝐹𝑉($100,1 𝑦𝑒𝑎𝑟, 10%) = $100 × (1 + 𝑖)1 = $110 For longer or shorter periods: 𝐹𝑉($𝑥, 𝑇𝑦𝑒𝑎𝑟𝑠, 𝑟) = $𝑥 × (1 + 𝑖)𝑇 e.g. FV($100,2 years,5%) = FV($100,6 months = 0.5 year,5%) = D. Present value (discounting) This is the INVERSE of future value: If you know you will receive $1.10 one year from now, and the interest rate is 10%, what is that expected amount worth now? Page 1 of 6 That is "present value" 𝐹𝑢𝑡𝑢𝑟𝑒 𝑣𝑎𝑙𝑢𝑒 1.10 = $1.10 1.10 1.10 = 1.10 × $1 = $1 = 𝑃𝑟𝑒𝑠𝑒𝑛𝑡 𝑣𝑎𝑙𝑢𝑒 In general: 𝑭𝒖𝒕𝒖𝒓𝒆 𝒗𝒂𝒍𝒖𝒆 = 𝑷𝒓𝒆𝒔𝒆𝒏𝒕 𝒗𝒂𝒍𝒖𝒆 × (𝟏 + 𝒊)𝑻 𝑷𝒓𝒆𝒔𝒆𝒏𝒕 𝒗𝒂𝒍𝒖𝒆 = 𝑭𝒖𝒕𝒖𝒓𝒆 𝒗𝒂𝒍𝒖𝒆 (𝟏+𝒊)𝑻 So, the present value of $x to be received afterT years discounted r%: 𝑃𝑉($𝑥, 𝑇 𝑦𝑒𝑎𝑟𝑠, 𝑟 ) = $𝑥 (1+𝑖)𝑇 e.g. 𝑃𝑉($1,2 𝑦𝑒𝑎𝑟𝑠, 10%) = 𝑃𝑉($1,6 𝑚𝑜𝑛𝑡ℎ𝑠 = 0.5 𝑦𝑒𝑎𝑟𝑠, 10%) = Present Value is used to compute the price of all bonds, short-term and long-term. For short-term markets there is only one payment; for long-term markets there are many payments of both interest and principal. NOTE: PV and interest rate move inversely: as i rises, PV declines; as i declines, PV rises. compare PV of $100 to be received in 2 years, discounted (a) 10% (b) 5% 𝑃𝑉($100,2 𝑦𝑒𝑎𝑟𝑠, 10%) = 𝑃𝑉($100,2 𝑦𝑒𝑎𝑟𝑠, 5%) = E. Where do interest rates come from? LOANABLE FUNDS THEORY Basic supply and demand: 1. Demand comes from . . . Page 2 of 6 Interest Rate r Quantity of Loans Supply comes from . . . Interest Rate r 2. Quantity of Loans 3. Equilibrium determination of interest rate Interest Rate r S D Quantity of Loans NOTE: this is the supply and demand for credit; its price is the interest rate. Once that is known, you can calculate the present value of a bond, etc. F. Factors that affect interest rates a. Economic Growth: Page 3 of 6 Interest Rate r S S´ r2 r1 D D´ Quantity of Loans b. Inflation: if prices are rising (1) credit demanders (deficit units) (2) credit suppliers (surplus units -- together these increase the interest rate S´ S Interest Rate r r2 E(INF) r1 D´ D Quantity of Loans terms: nominal interest rate : the actual rate in a transaction real interest rate : the interest rate adjusted for inflation if the borrower pays 5% per annum but expected inflation is 4%, the "real" interest rate is 5% - 4% = 1% this is the "Fisher Effect": 𝒓𝒏𝒐𝒎𝒊𝒏𝒂𝒍 = 𝒓𝒓𝒆𝒂𝒍 + 𝑬(𝑰𝑵𝑭) or 𝒓𝒓𝒆𝒂𝒍 = 𝒓𝒏𝒐𝒎𝒊𝒏𝒂𝒍 = 𝑬(𝑰𝑵𝑭) Here, the real interest rate is the difference between the blue and red lines: Page 4 of 6 c. Monetary policy: Interest Rate r S S´ r1 r2 D Quantity of Loans d. Fiscal policy: S Interest Rate r r2 r1 D D´ Quantity of Loans e. Foreign demand and supply: the same things but from foreign sources. Recent history of U.S. short-term interest rates Page 5 of 6 II. Securities A. Financial markets primarily buy and sell securities B. Primary market C. Secondary market After a security is issued in the primary market it can be sold to someone else. (This is most of what you see in the daily trading of stocks and bonds.) D. Valuation of securities 1. Information is the key. 2. Securities regulation tries to be sure all relevant information is public. 3. Cash flows are crucial to valuation. 4. "Efficient markets hypothesis" – that the market price reflects all relevant information so no one can reliably earn higher-than-market returns. HIGHLY CONTROVERSIAL Page 6 of 6
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NAME: ____________________________
PERCENT

________POINTS _______

5 problems on FUTURE VALUE and PRESENT VALUE (2 points each) (show work
for possible partial credit)
1.

PRESENT VALUE of $10,000, at 2.3%, 2 years
PV= FUTURE VALUE
(1+i)T
= 10,000
(1+0.023)2
= $1...


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