CERTIFIED FINANCIAL PLANNER CERTIFICATION PROFESSIONAL EDUCATION PROGRAMFinancial Planning Process & Insurance Session 4 Present Value Annuity Due Serial Payment Future Sum Amortization
PV of a Serial Payment When Kim retires in 15 years, she wants to receive the equivalent of a retirement income of $50,000 at the beginning of each year. She also wants the income to adjust annually for inflation. Kim believes that inflation will average 4% and that she can earn 7% on her investments. Assuming she wants to plan for 25 yearsof retirement, and she just received a sizable settlement from an auto accident she was in, how much will Kim need to invest today in order to provide the desired income?
Three Steps of Present Value Serial Payment Process PVAD Serial PMT Calculation Inflation-Adjusted Rate (BEG) • Inflate One Payment Rate of Inflation Today Future Discount Step 2 ResultDiscount (Investment) Rate
Step 1: PV of a Serial Payment HP10BII/10BII+ PV +/– 50,000 4 I/YR N 15 FV = Answer 1: $90,047 (Becomes the PMT in Step 2)
Step 2: PV of a Serial Payment HP10BII/10BII+ Set to [BEGIN] mode – 1.07 1 1.04 100 I/YR = +/– PMT 90,047 N 25 PV = 2.8846 Answer 2: $1,634,171 (Becomes the FV in Step 3)
Shortcut to Calculate Inflation-Adjusted Interest Rate The following steps relate a shortcut method for arriving at the inflation-adjusted interest rate. To do this calculation on the calculator (assuming a 4% inflation rate and a 7% investment return) use the following keystrokes: • Enter 1 plus the inflation rate (e.g. 1.04) • Press the INPUT key • Then enter 1 plus the interest rate (e.g. 1.07) • Press the [orange SHIFT] key • Then press the percent change key • Your answer should be on the calculator screen as 2.8846
Step 3: PV of a Serial Payment HP10BII/10BII+ FV 1,634,171 +/– I/YR 7 15 PV N = Final Answer: $592,300
Three Steps of Present Value Serial Payment Process PVAD Serial PMT Calculation Inflation-Adjusted Rate (BEG) • Inflate One Payment Rate of InflationPV=$50,000I/YR= 4N = 15FV = $90,047 (becomes PMT) PMT=$90,047 PMT = $90,047 PMT = $90,047 Today Future N = 25 I/YR = ([1.07/1.04] 1)×100 IAIR = 2.8846PMT= 90,047 I/YR = 2.8846 N = 25 PV = $1,634,171 (Begin Mode) Discount Step 2 ResultDiscount (Investment) RateFV = $1,634,171N = 15I/YR = 7PV = $592,300
Serial Payment For A Future Sum Today 1st Serial Payment Future Delay of 1 Period To begin saving… Inflation Adjustment
Example of Serial Payment of a Future Sum Mark Blevins, your client wants to retire in 5 years: • In today’s dollars, he’ll need $100,000 at that time. • Inflation will average 4% over the long run. • Annual after-tax return on investments is 7%. You need to determine a series of inflating payment amounts that will add up to $121,665 in five years: • Future value of $100,000 inflated 4% annually for 5 years is $121,665.29 (payment amounts are not known). • Enter desired lump sum of $100,000 (i.e., stated in today’s dollars) as Future Value. These steps on a financial calculator are identical to those for payment for an ordinary annuity, except that here the inflation- adjusted interest rate is used to calculate initial payment.
Calculation of Serial Payment of a Future Sum 1 2 3 4 5 0 FV $ 25,736.31 $19,634.11 ×1.04 = 25,014.74 $20,419.48 ×1.04 = 24,313.39 $21,236.26 ×1.04 = $22,085.71 ×1.04 = 23,631.71 22,969.14 $ 121,665.29 HP10BII/10BII+ This calculation determines: • Serial payment to be made each year • Based on the effect of inflation • Amount payments will grow • Total amount will be attained 100 1.07 1.04 – 1 Each sum is invested at 7% = I/YR 2.8846 equaling 100,000 FV 5 N PMT = $18,879 1.04 PMT = Answer: $19,634 Serial payment at the end of the first year.
Amortization • Amortization is the process of liquidating a debt by making installment payments. • Amortization calculations are done to divide a series of payments, into amounts that applies to interest and principal. • The amortization process involves two sets of calculations: • the first step calculates the periodic payment; • the second step identifies the interest and principal amounts.
Amortization Calculation In the process of assisting Barney and Betty to calculate what they still owe on their home, you are provided with the following information: They purchased their home 8 years ago for $239,500. They made a 20% down payment, and financed the balance using a 30-year mortgage with a 5.15% interest rate. Taxes and insurance increase the payment by $300 per month. In the process of calculation you tell them that they have an outstanding principal balance of what amount? • $129,524 • $164,365 • $165,071 • $206,338
Amortization Solution (1) • Set the calculator for 12 p/yr. • End Mode. • 20% down payment is $47,900 • Balance financed of $191,600 as the PV • Calculate the regular monthly payment: • N = 360 (or 30 years times 12 months per year). • I/YR = 5.15 • Calculate the payment or PMT = $1,046.19
Amortization Solution (2) • In calculating 8 years of payments, we are examining the results of 96 payment periods or 8 times 12 = 96; • To accomplish this we must press the following keys: • 1 [INPUT]; • 96 [SHIFT], • [AMORT] look under the FV key for AMORT. • Once this has all been done the following should be on your screen 1 – 96. • Then push the [=] key and the principal paid thus far in 8 years will show up; press the [=] key again and interest paid to date shows up. • Press [=] key one more time and the remaining principal balance will be displayed.
CERTIFIED FINANCIAL PLANNER CERTIFICATION PROFESSIONAL EDUCATION PROGRAMFinancial Planning Process & Insurance Session 4End of Slides