2 FEDERAL RESERVE & MARKET ACTIVITY (BS38) Definition 4.1 Discount Rate The discount rate is the periodic percentage return subtracted from the future cash flow for computing present value. The Fed also influences another rate, the Federal Funds Rate. This is the interest rate charged by banks when banks borrow overnight from each other (Not from Federal Reserve) The Federal Reserve Board of Directors uses several tools to influence market activity. These include: Discount Window Lending: The Federal Reserve Board votes whether to raise or lower the official government discount rate; this is the interest rate charged by federal district banks to member public and private banks. Reserve Requirements: The Fed sets the reserve requirement on member bank accounts; this regulates the amount of loans that banks may lend to business and individual borrowers Open Market Operations: The Fed buys and sells marketable currencies and government securities in the global financial marketplace; this affects supply and demand conditions.
3 FORMULA 4.1 & EXAM 2 QUESTION: ROR1
4 GEOMETRIC MEAN / ARITHMETIC MEAN OR RETURNS
5 ROR A ROR G (TR33) So, to get the average annual rate of return we simply take the average of the returns for the 3 years (Formula 4.3):
6 BASIS POINT (FF6) 100 Basis Points (bp) = 1% 5% is 5*100 = 500 bp, 0.50% is 0.50*100 = 50 basis points Ex: You targeted 12.3% return but missed by 240 basis points bp 240 bp= 990 basis points990 basis points = 9.9%
7 TIME VALUE OF MONEY FV = Future value PV = Present value N = Number of Periods r = Discount Rate Annuities Amortization
8 TIME LINES r% CF 0 CF 1 CF 2 CF 3 Show the timing of cash flows. Tick marks occur at the end of periods, so Time 0 is today; Time 1 is the end of the first period (year, month, etc.) or the beginning of the second period.
9 LS4A:FIND FV OF A DEPOSIT LONG AGO GIVEN ANNUAL COMPOUNDING: A deposit exactly 17 years ago of $2,500 earns 11.6% annual interest compounded annually. There have been no other deposits or withdrawals. How much is in the account right now? % 2500 FV =? OR How much interest does the account earn?
10 RULE OF 72 (TR1) The approximate number of periods in which a sum of money doubles equals 72 divided by the periodic rate of return. So, if for example, you make 12% a year, the approximate doubling period at 12% a year is:
11 SENSITIVITY TO COMPOUNDING FREQUENCY Note: The period is one year in all the cases. The only difference is how often the compounding is done within a year. The more often the compounding is done, the more interest on interest is earned.
12 EFFECTIVE RATE Effective rate is closely related to compounding frequency The effective annual rate is the amount of interest that accrues on one dollar in one year Effective Rate = (1+ APR/m) m 1 APR = Annual Percentage Rate m = The frequency of compounding per year Effective Rate is higher than APR when m>1 You are more likely to be quoted APR for debt such as loans or credit You are more likely to be quoted Effective rate for deposits or investments
13 EXERCISE 4.3A, #2 In Calculator: FV = $15,000 N = 20 (= 10*2) I/Y = (=6.25/2) Find: PV =? Or by Hand: FV = PV*(1+r) N 15,000 = PV*( /2) 20 15,000 = PV* PV = $8,106
14 REAL AND NOMINAL (QUOTED) RATE LS24. For example, if the Bureau of Census reports that wages went up last year 6% and inflation was 4%, then they will say that represents approximately a 2% growth in real earnings. If you make 6% more but prices are up 4%, your purchasing power or wealth is up 2%. Again, this is an approximation.
15 DOUBLING (TR2) Holding everything else constant When the interest rate doubles then the total interest more than doubles. When the term doubles then the total interest more than doubles. When the beginning wealth doubles then the total interest exactly doubles.
16 WHICH IS BETTER? TR3, TR4, TR5 These investments return a total of $1000 over the same duration and there is a positive interest rate. Biggest Present Value A: An investment generating most of the cash flows at the beginning of its life. Smallest Present Value B: An investment generating most of the cash flows at the end of its life. Year Project A Project B Total 1,000 1,000
17 TIME VALUE RELATION FOR MIXED CASH FLOWS
19 INTEREST FACTORS (TR15) FOR ANNUITY Ordinary Annuity r% PMT PMT PMT a. the Future value interest factor for an annuity, FVIFA(r,N), equals the total accumulation in an account earning the periodic rate r that results from a series of N one-dollar deposits b. the Present value interest factor for an annuity, PVIFA(r,N), equals the initial deposit into an account earning the periodic rate r that perfectly finances a series of N one dollar withdrawals N is the number of cash flows (not the number of periods).
20 PERPETUITY (FOR EVER)
21 PERPETUITY EXAMPLE So an account with a starting balance of $1,590,909 will forever earn yearly interest of $140,000 which will be enough to pay the professor s salary.
22 APPLICATION OF TIME VALUE OF MONEY Capital Budgeting Decisions Should we build this plant?
23 CAPITAL BUDGETING TECHNIQUE: PAYBACK PERIOD The payback period is the length of time required to recover an investment s cost. The shorter the payback period, the better. The longer the payback period, the worse it is. Advantage: It s easy to compute! Disadvantages: No definite Accept or Reject Decision. it ignores all the cash flows past the end of the payback period. this ignores Time Value For you: You spend 300,000 in college and after graduation you make 50,000 per year. What is your payback period for college investment?
24 CF 0 = 21, months will cover = 12*1,200 = 14,400 After 13 th, 14 th, 15 th and 16 th month, it will cover = 14, ,400*4 = 20,000. Almost there. 17 th Month will bring in 1400 more but we only need 1000 more for 21,000 total. Time to make 1,000 = 1000/1400 = 0.71 months So, PBP = = Months
25 CAPITAL BUDGETING TECHNIQUE: NET PRESENT VALUE The NPV for a project is the amount of capitalized economic profit that a project creates. NPV Decision Rule: Accept the project if NPV>0 because it creates more than it costs Reject the project if NPV<0 because it consumes more than it returns
26 QUIZ 15 QUESTION: CB20
27 WHAT IS THE PROJECT S NPV? ACCEPT OR REJECT? Year CF t = = CC 1 (1+r) 1+ CC 2 (1+r) 2 CC 3 (1+r) 3 -CC (1+.10) 1+ (1+10) 2 = $18.79 (1+10) CF0-100 ENTER CF1 10 ENTER CF2 = 60 ENTER CF3 = 80 ENTER NPV I = 10 ENTER CPT
28 CAPITAL BUDGETING TECHNIQUE: INTERNAL RATE OF RETURN The IRR for a project is the financing rate at which the project s NPV is zero. (Cost = Benefit)
29 FIND IRR: TQ9 In the Calculator: CF0=-2,000, CF1=610, F1=1, CF2=1640, F2=1, CF3= , F3=1; Scroll back through to make sure you did everything right. Then hit IRR then CPT to find IRR=34.3% And so now you compare this IRR to whatever the market s financing rate. If IRR is bigger than the financing rate, then Great! If IRR is less than the financing rate, then you want to pass on the project.
30 DRAWING TIME LINES: $100 LUMP SUM DUE IN 2 YEARS; 3-YEAR $100 ORDINARY ANNUITY $100 lump sum due in 2 years r% 3 year $100 ordinary annuity r%
32 WHAT IS THE FUTURE VALUE (FV) OF AN INITIAL $100 AFTER 3 YEARS, IF I/Y = 10%? Finding the FV of a cash flow or series of cash flows when compound interest is applied is called compounding. FV can be solved by using the arithmetic, financial calculator, and spreadsheet methods % 100 FV =?
33 SOLVING FOR FV: THE ARITHMETIC METHOD After 1 year: FV 1 = PV ( 1 + r ) = $100 (1.10) = $ After 2 years: FV 2 = PV ( 1 + r ) 2 = $100 (1.10) 2 =$ After 3 years: FV 3 = PV ( 1 + r ) 3 = $100 (1.10) 3 =$ After n years (general case): FV n = PV ( 1 + r ) n
34 SOLVING FOR FV: THE CALCULATOR METHOD Solves the general FV equation. Requires 4 inputs into calculator, and will solve for the fifth. (Set to P/Y = 1 and END mode.) INPUTS N I/Y PV PMT FV OUTPUT
35 WHAT IS THE PRESENT VALUE (PV) OF $100 DUE IN 3 YEARS, IF I/Y = 10%? Finding the PV of a cash flow or series of cash flows when compound interest is applied is called discounting (the reverse of compounding). The PV shows the value of cash flows in terms of today s purchasing power % PV =? 100
36 SOLVING FOR PV: THE ARITHMETIC METHOD Solve the general FV equation for PV: PV = FV n / ( 1 + r ) n PV = FV 3 / ( 1 + r ) 3 = $100 / ( 1.10 ) 3 = $75.13
37 SOLVING FOR PV: THE CALCULATOR METHOD Solves the general FV equation for PV. Exactly like solving for FV, except we have different input information and are solving for a different variable. INPUTS OUTPUT N I/Y PV PMT FV
38 SOLVING FOR N: IF SALES GROW AT 20% PER YEAR, HOW LONG BEFORE SALES DOUBLE? Solves the general FV equation for N. Same as previous problems, but now solving for N. INPUTS OUTPUT N I/Y PV PMT FV
39 WHAT IS THE DIFFERENCE BETWEEN AN ORDINARY ANNUITY AND AN ANNUITY DUE? Ordinary Annuity r% Annuity Due PMT PMT PMT r% PMT PMT PMT
40 SOLVING FOR FV: 3-YEAR ORDINARY ANNUITY OF $100 AT 10% $100 payments occur at the end of each period, but there is no PV. INPUTS OUTPUT N I/Y PV PMT FV 331
41 SOLVING FOR PV: 3-YEAR ORDINARY ANNUITY OF $100 AT 10% $100 payments still occur at the end of each period, but now there is no FV. INPUTS OUTPUT N I/Y PV PMT FV
42 SOLVING FOR FV: 3-YEAR ANNUITY DUE OF $100 AT 10% Now, $100 payments occur at the beginning of each period. Set calculator to BGN mode. INPUTS OUTPUT N I/Y PV PMT FV
43 SOLVING FOR PV: 3 YEAR ANNUITY DUE OF $100 AT 10% Again, $100 payments occur at the beginning of each period. Set calculator to BGN mode. INPUTS OUTPUT N I/Y PV PMT FV
44 A company pays $7,000 for a new machine, plans a 20% annual return on the investment, and expects these annual cash flows over the next six years:
45 UNEVEN CASH FLOW
46 EDITING CASH FLOW DATA
47 COMPUTING NPV Use an interest rate per period (I) of 20%.
48 NPV PROFILES AND CROSSOVER RATES To create an NPV profile, plot NPV on the Y axis and the discount rate on the X axis. Since the discount rate should be sensitive to changes in project risk, the NPV profile will show how sensitive the projected NPV is to the appropriate discount rate.
49 NPV PROFILES: EXAMPLE NPV of S and L 1,200 1, Crossover Rate 8.1% % 5% 10% 15% 20% 25% -400 Discount Rates Project S Project L
50 FINDING THE CROSSOVER RATE (CB2A - 35) Use the NPV profiles The crossover rate is the rate at which both projects have the same NPV. Take the difference in the projects' cash flows each period and calculate the IRR. Period Project A Project B Difference IRR The crossover rate is 11.8%. At this rate, NPV A = NPV B = $50.71 Project A is better if discounting rate < 11.8% Project B is better if discounting rate > 11.8%
51 PENSION PLANS
52 TWO PRIMARY TYPES OF PENSION PLANS
53 SUMMARY OF 401(K) DEFINED CONTRIBUTION PLANS s/trs%20member%20handbook.pdf
54 PENSION PLAN ATTRIBUTES (BS24) Which statement most accurately describes pension plans in the USA? a. The 401k plan is a defined benefit plan that is the most common pension plan in the USA today b. In a 401k plan employer contributions increase the employee's current taxable income c. Companies used to offer employees defined benefit plans but, as time goes on, defined contribution plans are becoming more common d. Two choices, A and C, are correct e. The three A-B-C choices are all correct ANSWER: C
1 Simple interest 2 5. Time value of money With simple interest, the amount earned each period is always the same: i = rp o We will review some tools for discounting cash flows. where i = interest earned
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