EXAM 2 // FIN. 3100 // CH 5, 7, 8, 9
Finding Number of Periods (n) Excel
=NPER(rate,pmt,pv,fv,type) O.A.(end of year) = Type = 0 A.D. (beginning of year) = Type = 1
Finding PMT (PMT Excel Function)
=PMT(rate, nper, pv, fv, type) O.A.(end of year) = Type = 0 A.D. (beginning of year) = Type = 1
number of periods
(number of years)*(periods per year) = NM
Time Value of money Variables
-The number of periods/ term (N) the length of the investment (in months/years) if payments are involved, the number of payments -The interest rate (i) / Rate of Return (r) the interest rate paid (or interest rate earned) -Present Value (PV) the value today (at beginning of investment) -Payment amount (PMT) monthly, yearly, etc. payment -Future Value (FV) the value in the future (at the beginning of investment)
An asset's risk can be analyzed in two ways:
1) on a stand-alone basis, where the asset is considered by itself (2) on a portfolio basis, where the asset is held as one of a number of assets in a portfolio.
Once Solved - Annuity Due (beginning of year)
2nd Payment - it will display end then 2nd ENTER then display BGN CPT - FV (With an Annuity Due) to change back, 2nd, payment, then 2nd enter and it will change it back to end.
Effective Annual Rate
= (1 + (periodic rate/compounding periods)) ^ (compounding periods) - 1 the interest rate expressed as if it were compounded once per year
Excel - N (number of years/months) function
=NPER(rate,pmt,pv, fv, type)
Excel - Rate (interest rate) function Interest Formula (written)
=RATE(nper,pmt,pv,FV,Type,Guess) Pv is the present value that the future payment is worth now. Pv must be entered as a negative amount. Price = Face Value / (1+i)^n FV = PV (1+i)^n nper - The total number of payment periods. pmt - The payment made each period. pv - The present value, or total value of all loan payments now. fv - [optional] The future value, or desired cash balance after last payment. Default is 0. type - [optional] When payments are due. 0 = end of period. 1 = beginning of period. Default is 0. guess - [optional] Your guess on the rate. Default is 10%.
Effective Annual Rate Excel Formula
=effect(nominal_rate, npery) =(1+APR/n)^n - 1 npery is the number of payments per year nominal rate =nominal(function)
Amortized Loan
A loan in which the principal as well as the interest is payable in monthly or other periodic installments over the term of the loan. A loan that is repaid in equal payments over its life.
Sinking Fund Provision
A provision in a bond contract that requires the issuer to retire a portion of the bond issue each year. a protective provision that requires the firm periodically to set aside an amount of money for the retirement of its preferred stock. This money is then used to purchase the preferred stock in the open market or through the use of the call provision, whichever method is cheaper
annuity
A series of equal payments at fixed intervals for a specified number of periods.
Original Issue Document (OID) Bond
Any bond originally offered below it's par value
Foreign Bonds
Bonds issued by foreign governments or by foreign corporations
Municipal Bonds
Bonds issued by state and local governments
Treasury Bonds
Bonds issued by the federal government, sometimes referred to as government bonds.
PV of Perpetuity
Cash Flow / Interest Rate
bond securities
Collateralized Bond; Debenture; General Obligation (no collateral)
The Process of Going to FV from PV is called
Compounding
Types of Bonds
Corporate Bonds Government Bonds - Federal Govt. - Treasuries; Bills (less than 1 yr, sold at discount) - Notes (2-10 yrs) Bonds (10+ yrs) - Municipal Bonds - Issued by States or local governments - Tax Benefit - Interest is not subject to Federal income taxes Zero Coupon Bonds - No interest rate. Payments equal zero. Sold at a discount Floating Rate Bonds - Variable interest rate - Usually tied to LIBOR
Opportunity Cost
Cost of the next best alternative use of money, time, or resources when one choice is made rather than another The rate of return you could earn on an alternative investment of similar risk what is the best alternative cost of those resources?
Zero Coupon Bond Formula
EXCEL = PV CALC = solve for PV
Current Bond Price Formula
EXCEL =PV CALC = Put in N, I/Y, PMT, FV, END MODE
With a Financial Calculator - if you have PV, i, N, and PMT, you can solve for:
FV
Present Value Formula
FV / (1+i)^n
Excel (TVM) - FV function
FV function = FV(rate,nper,pmt,pv,type) type refers to: whether payment comes at the end of the year (type = 0) or at the beginning of the year (type = 1). Pv is the present value that the future payment is worth now. Pv must be entered as a negative amount.
FV of Annuity Due Fromula
FVA(ordinary)*(1+i) With a Calculator, input variables just as an ordinary annuity, but now set to begin mode
A dollar today is worth less than a dollar tomorrow.
False
The "cost" referred to in the concept of opportunity cost is always monetary.
False
Uneven Cash Flow
First, you enter all of the cash flows and the interest rate; then the calculator or computer discounts each cash flow to find its present value and sums these PVs to produce the PV of the stream. You must enter each cash flow in the calculator's "cash flow register," enter the interest rate, and then press the NPV key to find the PV of the stream. NPV stands for "net present value."
PV of Ordinary Annuity Formula
Formula Approach = PMT * [ (1-1/(1+i)^n / i ] Calc Approach = N, I/YR, PV, -PMT, FV, end mode Excel = PV(rate,nper,pmt,pv,type) Type = 1
FV Ordinary Annuity Formula
Formula Approach= PMT * ((1+i)^n - 1)/i) Calc Approach- N, I/YR, PV, PMT = FV Excel = FV(rate,nper,pmt,pv,type) Type = 0
Uneven Cash Flow in Excel
In Excel: AMT / ((1+r)^n) AMT = amount of cash going in for the year r = interest rate (so 1.03 if at 3%) n = number of year you're solving for do this for each line in the year! then SUM up the answers (per year)
Risk: Inflation Risk
Inflation will eat up the purchasing power of the interest the bond pays.
Simple Interest
Interest earned only on the original principal amount invested
Risk: Interest Rate Risk
Interest rates change which will cause the value of the bond to either increase or decrease.
Risk: Call Risk (Refinance)
Interest rates fall and the company calls the bond.
Probability Distributions
Listings of all possible outcomes or events with a probability (chance of occurrence) assigned to each outcome.
Time Value of Money -> Calculator Buttons
N = Number of Periods I / Y = Interest Rate per Year PV = Present Value PMT = Payment FV = Future Value CPT = Compute
Ordinary Annuity vs. Annuity Due
Ordinary annuity - no of interest periods is equal to number of payments Annuity due - no of interest periods is one less than no of payments /
With a Financial Calculator - if you have FV, i, N, and PMT, you can solve for:
PV
Excel (TVM) - PV Function
PV Function = PV(rate,nper,pmt,fv,type) type refers to: whether payment comes at the end of the year (type = 0) or at the beginning of the year (type = 1). Pv is the present value that the future payment is worth now. Pv must be entered as a negative amount.
Perpetuity Formula
PV of a Perpetuity = PMT/1 Price = Annual Payment / Rate of Return
FV formula
PV(1+i)^n
Changing Semiannual to Annual
Periodic Rate (Iper) = stated annual rate / number of payments per year
TVM in Calculator - Tips and Tricks
Remember, if you put in a PV and FV, one has to be negative, or you'll get an error (recommend PV negative)
The Risk Return Relationship
Risk and return are directly related - Historical Returns - Statistical Analysis - Risk Premium
Risk: Default Risk
Risk the company will miss an interest or principal payment or the payment will be late.
Diversification
Spreading out investments to reduce risk - minimizing unsystematic risk - correlation - the expected return and standard deviation Diversification reduces unsystematic risk but not systematic risk Investing in multiple investments. - Spreading the risk among several investments. - Different investments should have low levels of correlation.
Company Risk
Standalone Risk (single investment, company specific, unsystematic) Portfolio Risk (2+ investments, market risk, systematic risk) • Recession or high unemployment • High inflation • Interest rate increases • Changes taxes or regulations • And so forth
Under an amortized loan, the periodic payments are all equal. However, the fraction of the payment that represents interest declines over time. True or false?
True
Coupon Rate
The interest rate which paid (annually) - usually in semi-annual payments
Is this statement true or false? A rational person should choose to receive cash flows from an annuity due of $1,000 per year rather than from a similar ordinary annuity.
True *AD (annuity due) will always have a higher FV than OA(ordinary annuity)
Coupon Payment (Coupon Amount)
The dollar amount of interest that is paid yearly to bond-holders he dollar amount of the interest payments Face Value * Coupon Rate
APR (Annual Percentage Rate)
The periodic rate times the number of periods per year.
Discounting What is discounting?
The process of finding the present value of a cash flow or a series of cash flows; discounting is the reverse of compounding. Reducing the value of future cash flows
Expected Rate of Return (r-hat)
The rate of return expected to be realized from an investment; the weighted average of the probability distribution of possible results
FV of Ordinary Annuity
The sum to be received at some point in the future of identical periodic investments made from present until future point
Term
The time from issuance to maturity (20 years is most common)
The concept of opportunity cost is described in which of the following statements?
The value of what certain resources could have produced had they been used in the best alternative way The cost of choosing between two alternatives
Time Value of Money Calculator How To
To Put In Data: #, then Button (N, I/Y,PV,PMT) I/Y is always a whole number If no payment, put zero To Solve: - After All Numbers are Entered - Hit CPT - Hit (Button) - i.e. FV, I/Y, Etc. To Clear All Buttons / Data: 2nd FV Button (CLEAR TVM)
A lender should prefer to lend at a rate of 10% with semiannual compounding, but a borrower would prefer a loan with a rate of 10%, annual compounding. True or false?
True
Is this statement true or false? If one set up time lines for an ordinary annuity of $1,000 per year for 3 years and a 3-year, $1,000 annuity due, the primary difference between the two time lines is that the $1,000 payments for the annuity due would begin at t = 0 and end at t = 2, whereas the ordinary annuity's payments would begin at t = 1 and end at t = 3.
True
Indenture
a bond contract that specifies the legal provisions of a bond issue bond contract / agreement
Floating-Rate Bond
a bond whose interest rate fluctuates with shifts in the general level of interest rates
Bond
a debt security that promises to make payments periodically for a specified period of time Sold directly from corporation to investor
Bond Rating
a grade of credit quality as reported by credit rating agencies Standard & Poor's or Moody's - Measures the Risk of Default BBB (Baa) or better is investment grade. BB or lower is High Yield (junk) bond.
Risk is...
a hazard, peril, exposure to loss or injury. refers to the chance that some unfavorable event will occur. The possibility that the outcome will be different than expected - the actual return is less than the expected return
Standard Deviation is....
a measure of risk (volatility) - The wider the bell curve the greater the standard deviation - The wider the bell curve the greater the volatility and risk
Uneven Cash Flow Description
a series of cash flows where the amount varies from one period to the next For example, the dividends on common stocks typically increase over time, and investments in capital equipment almost always generate uneven cash flows. Bonds represent the best example of the first type, while stocks and capital investments illustrate the second type.
Which of the Following Statements is true?
a. A deposit will grow faster if simple interest rather than compound interest is paid. b. Compound interest means that interest in future periods is earned on the interest earned in the past, whereas under simple interest, interest is earned only on the original investment. c. It would be better to both lend and borrow money at a rate of 6%, simple interest, rather than at a rate of 6%, compound interest.
Which of the following statements regarding annuities is NOT CORRECT?
a. An annuity is a recurring payment, at set intervals, for a given amount of time. b. An annuity due is like an ordinary annuity with the exception that payments occur at the beginning of each period, instead of at the end of each period. c. The general assumption in finance is that annuity payments occur at the end of the period, so this type of payment is referred to as an ordinary annuity. d. If the interest rate is greater than zero, then the future value of an ordinary annuity is greater than the future value of an annuity due. This occurs because the last payment of the ordinary annuity earns interest, while the last payment of the annuity due does not.
Which of the Following is False?
a. Time lines put verbal information into a diagram that is useful for seeing the cash flows that occur, when they occur, and the interest rate used in the analysis. b. The FV as shown on a time line is always the cash flow at Time = 1. c. Time lines typically show dollars below the line and years above the line. d. Cash flows do not have to occur for every period shown on the time line. A lump sum cash flow can be depicted as easily as annuities on a time line. e. Time lines can show cash flows that occur over years, quarters, or any other periods.
The goal of the investor is to
achieve the highest return with the lowest volatility - The highest mean (average return) - With the lowest standard deviation (volatility)
call provision
agreement giving the issuer the option to repurchase a bond at a specific price prior to maturity a provision in a bond contract that gives the issuer the right to redeem the bonds under specified terms prior to the normal maturity date Call premium - premium paid if called. No-Call provision - bond cannot be called for the time period of the provision.
face value (par value)
amount of money that the bond buyer (lender) lent the issuer and that the lender will receive on repayment the amount of the loan (promised amount to pay back) The stated value in the indenture and the amount to be paid at maturity (usually 1000)
Ordinary (Deferred) Annuity
an annuity for which the cash flow occurs at the end of each period An annuity whose payments occur at the end of each period. TYPE = 0 (excel) END / Reg = Calc
Annuity Due
an annuity for which the cash flows occur at the beginning of the period TYPE = 1 (excel) BEG / Beginning = Calc
Perpetuity
an annuity with an extended life A stream of equal payments at fixed intervals expected to continue forever.
(risk-return) a flatter line suggests that...
an investor is more comfortable bearing risk
(risk-return) a steeper line suggests that...
an investor is very averse to taking on risk if a company is investing in riskier projects, it must offer its investors (both bondholders and stockholders) higher expected returns.
Current Yield Formula
annual coupon/price Price/Value = Annual Payment / Rate of Return
Zero Coupon Bonds
bonds that pay no annual interest but are sold at a discount below par, thus compensating investors in the form of capital appreciation
Fixed-Rate Bonds
bonds whose interest rate is fixed for their entire life
Yield to Maturity Formula
current yield + capital gains yield EXCEL: =rate(Nper, pmt, -(PV), FV(face or future value)) this is a yearly payment - so if it's 6 months (*2) CALC: put in N, I/Y, -PV, PMT, FV - N = # of periods - I/Y = Yield, YTM (yeild to maturity), IRR (int. rate of return) - PV = Price - PMT = Period Payment (coupon) - FV (Future Value / Par / Face Value) SOLVE FOR I/YR CALC Steps: Input any 4 of them, and solve for the 5th by hitting CPT
The slope of the risk-return indicates
how much additional return an individual investor requires in order to take on a higher level of risk
With a Financial Calculator - if you have FV, PV, N, and PMT, you can solve for:
i
Compound Interest
interest earned on both the principal amount and any interest already earned Interest paid on interest previously earned; credited daily, monthly, quarterly or semiannually
Relationship between Bond Values and Interest rates
inversely related; when interest rates go up bond values go down. When interest rates go down bond values go up. (remember the teeter totter)
Corporate Bonds
long-term debt issued by private corporations typically paying semiannual coupons and returning the face value of the bond at maturity
if YTM is constant for x amount of years, what will the price be from today?
nper - # of years using same information, solve for PV =PV
Bond's Current Market Price
solving for price, then the PV solve for pmt = coupon rate * par value EXCEL = PV
Future Value (FV)
the amount to which a cash flow or series of cash flows will grow over a given period of time when compounded at a given interest rate
Mean is...
the average Return
The law of financial risk
the higher the risk, the higher the return required
Compounding
the process of accumulating interest on an investment over time to earn more interest The arithmetic process of determining the final value of a cash flow or series of cash flows when compound interest is applied. PV --> FV
standalone risk
the risk an investor would face if he or she held only one asset No investment should be undertaken unless the expected rate of return is high enough to compensate for the perceived risk. • Management change • Leapfrogged by new technology • Labor problems • And so forth
Present Value (PV)
the value today of a future cash flow or series of cash flows
