Value Present of a Single Sum PVSS
Problem FV =$1,000 I/YR = 4% N=5 PV = ? Keystrokes 1000,FV 4, I/YR 5, N PV -821.93
PVSS Solving for N
Problem FV = $1,000 I/YR = 6% PV = -$800 N= ? Keystrokes 1000, FV 6, I/YR 800, +/-, PV N 3.83
PVSS Solving for I/YR
Problem FV = $1,000 PV = -$800 N=5 I/YR = ? Keystrokes 1000, FV 800, +/-, PV 5, N I/YR 4.56
Future Value of a Single Sum FVSS
Problem PV = $1,000 I/YR = 7% N = 20 FV = ? Keystrokes 1000,+/-,PV 7, I/YR 20, N FV 3,869.68
FVSS Solving for N
Problem PV = -$10,000 I/YR = 5% FV = $20,000 N=? Keystrokes 10000, +/-, PV 5, I/YR 20000, FV N 14.21
FVSS Solving for I/YR
Problem PV = -$10,000 FV = $20,000 N = 10 I/YR = ? Keystrokes 10000, +/-, PV 20000, FV 10, N I/YR 7.18
Present Value of an Annuity PVA
Annuity is an periodic cash flow stream
Dollar amount is constant over time Set number of periods (not in perpetuity)
Ordinary annuity has cash flows at the end of each period Annuity due has cash flows at the beginning of each period A 4 or 5 variable problem with 1 unknown.
PVA
Problem PMT = $1,000 N = 20 I/YR = 5% PV = (?) Keystrokes 1000, PMT 20, N 5, I/YR PV -12,462.21
Present Value of an Annuity Due PVAD
Problem PMT = $1,000 N = 20 I/YR = 5% PV = (?) Keystrokes
Set calculator to BEGIN by (orange), (BEG/END)
1000, PMT 20, N 5, I/YR PV -13,085.32
Future Value of an Annuity FVA
Problem PMT = -3,000 I/YR = 6% N = 30 FV = ? Keystrokes 3,000,+/-,PMT 6, I/YR 30,N FV 237,174.56
FV Annuity Due FVAD
Problem PMT = -3,000 I/YR = 6% N = 30 FVAD = ? Keystrokes
[orange],[BEG/END] sets the calculator to BEGIN
3,000,+/-,PMT 6, I/YR 30,N FV 251,405.03
Amortization Schedule
Loan payments on self amortizing loans can be broken down in to principal and interest components. In the early years of a loan more of the payment goes towards interest than principal, in later years the opposite is true Your financial calculator can provide you with the breakdown for any loan payment.
Amortization Breakdown AMORT
Problem
12,000, PV 5, N 6, I/YR PMT -2,848.76
Find the interest/principal breakdown of the third loan payment and the resulting loan balance
Keystrokes (after calc. pmt) 3,[INPUT],[orange], [AMORT]
= -2,391.87 principal = -456.89 interest = 5,222.88 balance
TAKING IT UP A NOTCH
Now that youve got the basics covered youre ready to handle more complex problems like
Unequal Cash Flows More frequent compounding/discounting
Effective Interest Rates APRs and APYs
Complex Annuities
Unequal Cash Flows
Equal annual payments isnt always a realistic situation. IRA contributions, for example, have been ratcheting higher over the past few years and future contribution limits will be indexed to inflation. By inputting the individual cash flows into the financial calculator we can calculate the present value of a cash flow stream.
PV Unequal CF Stream #1
Problem CF0 = -$2,000 CF1 = $500 CF2 = $750 CF3 = $1,000 I/YR = 5% Keystrokes 2000,+/-, CFj 500, CFj 750, CFj 1000, CFj 5, I/YR [orange] NPV 20.30
PV Unequal CF Stream #2
Problem CF0 = -$2,000 CF1 = $500 CF2 = $500 CF3 = $750 CF4 = $750 I/YR = 5% Keystrokes 2000,+/-, CFj 500, CFj , 2,[orange], Nj 750, CFj, 2, [orange], Nj 5, I/YR [orange] NPV 194.61
PV Unequal CF Stream #3
Problem CF0 = -$3,000 CF1-10 = $500 CF11 = $800 CF12 = -$1000 I/YR = 6% Keystrokes 3000,+/-, CFj 500, CFj , 10,[orange], Nj 800, CFj 1000, +/-, CFj 6, I/YR [orange] NPV 604.50
Solving for the Internal Rate of Return - IRR%
The internal rate of return is the interest rate that makes the net present value equal to zero. When a cash flow stream has a positive NPV the IRR>i% When a cash flow stream has a negative NPV the IRR<i% When a cash flow stream has an NPV of zero the IRR=i%
IRR Cash Flow Stream # 3
Problem CF0 = -$3,000 CF1-10 = $500 CF11 = $800 CF12 = -$1000 NPV = $604.50 IRR = ? Keystrokes 3000,+/-, CFj 500, CFj , 10,[orange], Nj 800, CFj 1000, +/-, CFj [orange] IRR/YR 10.27
FV of Unequal CF Stream
This is one of the more difficult financial calculator because problems its a two step process.
First compute the NPV Then find the FVSS of that NPV Next slide uses CF Stream #2 in calculating FV
FV Unequal CF Stream #2
Problem CF0 = -$2,000 CF1 = $500 CF2 = $500 CF3 = $750 CF4 = $750 I/YR = 5% NPV = 194.61 FV = ? Keystrokes 2000,+/-, CFj 500, CFj , 2,[orange], Nj 750, CFj, 2, [orange], Nj 5, I/YR [orange] NPV 194.61, +/-, PV 4, N FV 236.55
More Frequent Cash Flows
Annual cash flows in personal finance is typically the exception and not the norm
Monthly mortgage payments Semi-annual coupon interest payments Automatic Investment Programs
We need to know how to use the financial calculator when cash flows or interest calculations take place at different time intervals
Bond Valuation
Problem Bond with a 6% coupon pays interest semiannually. If investors require an 8% return, what is the price of a $1,000 face value bond with 4 years to maturity? Keystrokes 2, [orange], P/YR 30, PMT, 1000, FV 8, I/YR 4, [orange], xP/YR PV -932.67
Finding YTM on a Bond
Problem A bond with a face value of $1,000 is priced at $1,100. It pays semiannual interest at a coupon rate of 5 percent and has 7 years until it matures. What is its yield to maturity? Keystrokes 2,[orange], P/YR 1000, FV 1100, +/-, PV 25, PMT 7.5, [orange], x P/YR I/YR 3.47
Effective Rates
Nominal rates dont consider the effect of more frequent compounding on interest payments. Effective rates adjust for more frequent compounding. EAR = (1 + nominal rate/# periods)^#per-1 for a 5% nominal interest paid semiannually the EAR = (1+.05/2)^2 1=.0506 = 5.06%
Effective Rates (1)
Problem 6 % interest is paid quarterly, what is the effective rate? Keystrokes 4, [orange], P/YR 6, I/YR [orange] EFF% 6.1364 by formula it is: (1+.06/4)^4-1=.061364
Effective Rates (2)
Problem What is the APR of a 5% loan if interest compounds: weekly? daily ? Keystrokes
52, [orange], P/YR 5, I/YR [orange], EFF% 5.1246 365, [orange], P/YR 5, I/YR [orange], EFF% 5.1267
APRs and APYs
APRs are truth-in-lending-act based calculations that allow borrowers to compare rates across lenders. APYs are truth-in-savings act based calculations that allow investors to compare rates across financial institutions. Keep them straight by remembering that your borrow at a rate but earn a yield.
APRs
Takes the periodic rate and multiplies it by the number of periods in a year to arrive at the APR. If your credit card charges a monthly rate of 1.25% then the APR for the credit card is: APR = 1.25% x 12= 15% The EAR is (1.0125)^12-1= .1608 = 16.08% EAR is not equal to APR but APY is equivalent to the EAR
More frequent compounding
When interest is compounded more frequently then it is paid you have to adjust the interest rate to reflect the disparity. Compounded daily/paid monthly for example on a CD. In this situation you need to use the effective rate as your interest rate, rather than the nominal rate.
More Frequent Compounding
Problem
You invest $500 in a two year CD that compounds interest monthly but credits it to your account annually. The CD pays a 4% nominal rate. What is the maturity value?
Keystrokes
12, [orange], P/YR 5, I/YR [orange] EFF% 5.1162 I/YR 1,[orange], P/YR 500, +/-,PV 2, N FV 552.47
Payments Growing by a Constant Percentage
Where the annuity payment is growing at a constant rate.
Inflation indexed IRA contribution limits are an example of a model that uses that approach.
The financial calculator solution is to adjust the expected investment return by the expected growth rate, and then calculate the time value of money.
Payments growing by a constant percentage
Cathy Client plans on maximizing her contributions to an IRA account until she retires thirty years from now. Assume a contribution today of $3,000, growth in contribution limits of 3%/yr. and average annual returns of 6%.
[orange] BEG/END {set to Begin} 1.06,,1.03,-,1, x,100,= I/YR {sets I/YR to 2.9126} 3000,+/-, PMT 30, N PV 61,203.24 +/-,PV, 0, PMT 6, I/YR, 30,N FV 351,520.24