session 4 present value annuity due serial payment future sum amortization
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©2015, College for Financial Planning, all rights reserved.
Session 4Present Value Annuity DueSerial Payment Future SumAmortization
CERTIFIED FINANCIAL PLANNER CERTIFICATION PROFESSIONAL EDUCATION PROGRAMFinancial Planning Process & Insurance
Session Details
Module 3
Chapter(s)
3
LOs 3-7 Calculate the inflation-adjusted payment for a future sum.
4-2
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 years of 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?
4-3
Three Steps of Present Value Serial Payment Process
Today
1. Inflate One Payment Rate of Inflation
3. Discount Step 2 ResultDiscount (Investment) Rate
Future
2. PVAD Serial PMT Calculation Inflation-Adjusted Rate (BEG)
4-4
Step 1: PV of a Serial Payment
HP10BII/10BII+
=
50,000 PV
4 I/YR
15 N
FV
+/–
Answer 1: $90,047(Becomes the PMT in Step 2)
4-5
Step 2: PV of a Serial Payment
Answer 2: $1,634,171(Becomes the FV in Step 3)
1.07 –
HP10BII/10BII+
Set to [BEGIN] mode
100
90,047 PMT
N
= I/YR
1
25
PV
=
1.04
+/–
2.8846
4-6
Formula for Inflation-Adjusted Interest Rate (IAIR)
100 1 rate inflation 1
rate interest 1
4-7
Shortcut to Calculate Inflation-Adjusted Interest Rate
The following steps relate a shortcut method for arriving at theinflation-adjusted interest rate.To do this calculation on the calculator (assuming a 4%
inflation rateand a 7% investment return) use the following keystrokes:
1. Enter 1 plus the inflation rate (e.g. 1.04)
2. Press the INPUT key
3. Then enter 1 plus the interest rate (e.g. 1.07)
4. Press the orange SHIFT key
5. Then press the PERCENT CHANGE key
6. Your answer should be on the calculator screen as 2.88464-8
Step 3: PV of a Serial Payment
Final Answer: $592,300
HP10BII/10BII+
1,634,171 FV
7 I/YR
15
PV
+/–
N
=
4-9
Three Steps of Present Value Serial Payment Process
Today
3. Discount Step 2 ResultDiscount (Investment) RateFV = $1,634,171N = 15I/YR = 7PV = $592,300
2. PVAD Serial PMT Calculation Inflation-Adjusted Rate (BEG)
Future
PMT
= $9
0,04
7PM
T =
$90,
047
PMT=
$90,
047
N = 25
I/YR = ([1.07/1.04] 1)×100IAIR = 2.8846 PMT= 90,047I/YR = 2.8846N = 25PV = $1,634,171(Begin Mode)
1. Inflate One Payment Rate of InflationPV=$50,000I/YR= 4N = 15FV = $90,047 (becomes PMT)
4-10
Session Details
Module 3
Chapter(s)
3
LOs 3-8 Calculate the present value for an inflation-adjusted payment.
4-11
Serial Payment For A Future Sum
Today
Delay of 1 Period
To begin saving…
Inflation
Adjustment
Future
1st Serial
Payment
4-12
Example of Serial Payment of a Future Sum
Mark Blevins, your client, wants to retire in five 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 five 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 the inflation-adjusted interest rate is used to calculate initial payment.
4-13
Calculation of Serial Payment of a Future Sum
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
2.8846
Answer: $19,634
Serial payment at the end of the first year.
1.07 –
HP10BII/10BII+
100
100,000 FV
N
1.04
= I/YR
1
5
PMT =
1.04
PMT = $18,879
FV21 3 4
$25,736.31
25,014.74
24,313.39
$121,665.29
$20,419.48×1.04
=
$19,634.11×1.04
=
23,631.71
22,969.14
0 5
$22,085.71×1.04
=
$21,236.26×1.04
=
Each sum is
invested at 7%
equaling
4-14
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 apply to interest and principal.
• The amortization process involves two sets of calculations: o the first step calculates the
periodic payment; o the second step identifies
the interest and principal amounts.
4-15
Amortization Question
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 eight 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?
a. $129,524b. $164,365c. $165,071d. $206,338
4-16
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:
o N = 360 (or 30 years times 12 months per year)
o I/YR = 5.15 o Calculate the payment or PMT =
$1,046.19
4-17
Amortization Solution (2)
• In calculating eight years of payments, we are examining the results of 96 payment periods or 8 x 12 = 96;
• To accomplish this we must press the following keys: o 1 [INPUT]; o 96 [SHIFT], o [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 eight 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.
4-18
Question 1
Anne Marie wants to accumulate a sum of money that will provide her with an additional $5,000 of income per year. How much will she need to have in the fund to provide that amount of money each year, assuming the funds earn 8% annually? (LO 3-1)a. $33,550b. $36,234c. $62,500d. $78,433
4-19
Question 2
Wayne Johnson wants to accumulate enough funds to send his son, Mark, to college. Mark is 4 years old, and it is expected that he will begin a four-year college program at age 18. The annual tuition today is $12,500. Wayne estimates that the annual inflation for college tuition will be 6% and he can get an 8% return on his money. How much does Wayne need to put aside today in order to meet this goal?a. $36,738b. $37,432c. $38,487d. $109,432
4-20
Question 3
An individual has $2,500 to invest and wants to accumulate $4,000 at the end of five years. What annual rate of return is required to meet this goal if earnings on the investment are compounded monthly?(LO 3-5)a. 9.4%b. 9.6%c. 9.7%d. 9.8%
4-21
©2015, College for Financial Planning, all rights reserved.
Session 4End of Slides
CERTIFIED FINANCIAL PLANNER CERTIFICATION PROFESSIONAL EDUCATION PROGRAMFinancial Planning Process & Insurance
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