1. ©2015, College for Financial Planning, all rights reserved. Session 4 Present Value Annuity Due Serial Payment Future Sum Amortization CERTIFIED FINANCIAL PLANNER CERTIFICATION PROFESSIONAL EDUCATION PROGRAM Financial Planning Process & Insurance

2. Session Details Module3 Chapter(s)3 LOs3-7 Calculate the inflation-adjusted payment for a future sum. 4-2

3. 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

4. Three Steps of Present Value Serial Payment Process Today 1.Inflate One Payment Rate of Inflation 3.Discount Step 2 Result Discount (Investment) Rate Future 2.PVAD Serial PMT Calculation Inflation- Adjusted Rate (BEG) 4-4

5. 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

6. 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

7. Formula for Inflation-Adjusted Interest Rate (IAIR) 4-7

8. 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: 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 2.8846 4-8

9. 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

10. Three Steps of Present Value Serial Payment Process Today 3.Discount Step 2 Result Discount (Investment) Rate FV = $1,634,171 N = 15 I/YR = 7 PV = $592,300 2.PVAD Serial PMT Calculation Inflation- Adjusted Rate (BEG) Future PMT = $90,047 N = 25 I/YR = ([1.07/1.04]  1)×100 IAIR = 2.8846 PMT= 90,047 I/YR = 2.8846 N = 25 PV = $1,634,171 (Begin Mode) 1.Inflate One Payment Rate of Inflation PV=$50,000 I/YR= 4 N = 15 FV = $90,047 (becomes PMT) 4-10

11. Session Details Module3 Chapter(s)3 LOs3-8 Calculate the present value for an inflation- adjusted payment. 4-11

12. Serial Payment For A Future Sum Today Delay of 1 Period To begin saving… Inflation Adjustment Delay of 1 Period To begin saving… Inflation Adjustment Future 1st Serial Payment 4-12

13. 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

14. 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 FV 2134 $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

15. 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

16. 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.$129,524 b.$164,365 c.$165,071 d.$206,338 4-16

17. 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

18. Amortization Solution (2) In calculating eight 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: 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

19. 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.$33,550 b.$36,234 c.$62,500 d.$78,433 4-19

20. 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 5% 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.$36,738 b.$37,432 c.$38,487 d.$109,432 4-20

21. 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

22. ©2015, College for Financial Planning, all rights reserved. Session 4 End of Slides CERTIFIED FINANCIAL PLANNER CERTIFICATION PROFESSIONAL EDUCATION PROGRAM Financial Planning Process & Insurance