Time Value of Money (2) and Inflation

Personal Finance:Personal Finance:Another PerspectiveAnother Perspective

Objectives

A. Understand the impact of inflation on A. Understand the impact of inflation on investinginvesting

B. Know how to solve problems relating to B. Know how to solve problems relating to Annuities, Future Value of an annuity, and Annuities, Future Value of an annuity, and Present Value of an annuityPresent Value of an annuity

C. Know how to solve problems relating to C. Know how to solve problems relating to amortized loansamortized loans

A. Understand the Impact of Inflation on Investing

What is inflation?• Inflation is the increase in the volume of money

and credit relative to available goods and services resulting in a continuing rise in the general price level

• In other words, your money can buy less goods and services than it could before.

• To compensate, you must pay more money (for the same amount of goods)

Inflation (continued)

What is the impact of inflation on investing?• Inflation has a negative impact on your investments

• You have the same amount of money but your money can buy less

• Inflation forces us to save more, because our dollars will be worth less in the future.

• What is your “real return” after inflation?

• Your real return is the return after the impact of inflation. There is a very specific way to calculate this return.

Investment Problem #1:The Future Value of a Wedding

I have six wonderful daughters (and one great son). This year, the average wedding cost is estimated to be $20,000.

Assuming 4% inflation, what will it cost in 15 years for all six weddings for my daughters (and I hope this doesn’t happen—at least all in one year)?

Average wedding cost: $20,000, 4% inflation, cost per wedding in 15 years? Cost for all 6 daughters wedding?

Answer #1: Future Costs of Weddings and Inflation

• Clear registers, set to end of period, 1 payment per year

• 20,000 = PV, 15 = N, 4 = I and solve for FV ?

• FV = $36,019 per wedding• Total Cost = $ 36,019 x 6 = ?

• Total costs = $216,114• I need to save now• Inflation will raise my costs by

($36,019/20,000) over 80%!!!!

Investment Problem #2:Adjusting for Inflation

Assuming you have an investment making a 10% return, and inflation of 6%, what is your real return on this investment?

Assuming a 10% return and 6% inflation, what is your real return on this investment?

Answer #2Inflation

The traditional (and incorrect) method for calculating real returns is: Nominal return – inflation = real return. This would give:

10% - 6% = 4% The correct method is: (1 + nominal return)/(1 +

inflation) – 1 = real return(1.10/1.06)-1 = 3.77%

The traditional method overstates return in this example by 6% (4%/3.77% -1)

Be very careful of inflation, especially high inflation!!

Answer #2 (continued)

While some have argued that it is OK to subtract inflation (π) from your nominal return (rnom), this overstates your real return (rreal).

The linking formula is: (1+rreal) * (1+π) = (1 + rnom)

Multiplied out and simplified: rreal+ π + rreal π = rnom

Assuming the cross term rreal π is small, the formula condenses to:

rreal+ π = rnom or the Fisher Equation

The correct method is to divide both sides by (1+π) and subtract 1 to give: rreal = [(1 + rnom)/ (1+π)] - 1

B. Know How to Solve Problems Relating to Annuities

What is an Annuity?• A series of equal dollar payments coming at the

end of each time period for a specified number of time periods, generally months or years.

What is a Compound Annuity?• An investment that involved depositing an equal

sum of money at the end of each year for a certain number of year and allowing it to grow

Can you find the Present and Future Value of each of these types?

• Yes!

Solving Problems Relating to Annuities

Problem:• You want to determine the value of a series of

equal dollar payments either currently or at some point in the future

Problem Statement:• What will be the future (present) value of a series

of annual (monthly) payments x years in the future if my interest rate is y%?

Key Information Needed:• Amounts, years in the future and the interest rate

Investment Problem #3:Annuities

When you retire at age 60, you plan to have $750,000 saved and you get paid at the end of each year. Assuming an interest rate of 7% and that you will need payments for 30 years (you expect to die at age 90), how much could you receive each year for your $750,000 that you have saved? Will it be different if you receive payments at the beginning of each year?

Retire at age 60 with $750,000 saved, 7% interest rate, 30 years. How much will you receive at the end of each year? What about

if you get paid at the beginning of each year?

Answer #3:Annuities

Assuming you need payments for 30 years and interest rates are 7%, you can receive at the end of each year:

• -750,000= PV, End mode, 30 = N, 7 = I%, Solve for Payment?

• PVA = $60,439.80 or $60,440 Assuming payments at the beginning of each year:

• -750,000= PV, Begin mode, 30 = N, 7 = I%, Solve for Payment?

• PVA = $56,486.79 or $56,486

Start saving for retirement the month you graduate. It will make a big difference on what you will be able to retire with!

Investment Problem #4: Compound Annuities

You are looking to buy a new Polaris 700 quad (four wheeler) to clean the snow from your driveway (ha!). Instead of borrowing the $7,000 for the quad, you want to save for it each month. How much will you need to save each month, assuming you can get 7% on your investments and you want to buy the quad in 50 months? How much if you can get 7% and want it in 24 months?

                                     

                                                             

Save for a $7,000 quad, assuming 7% interest rates and 50 months? 24 months?

Answer #4:Compound Annuities

• 50 Months:• Clear memories, set payments to 12 (monthly), set

to end mode

• -7,000 = FV, 50 = N, 7 = I%, PMT = ?

• You will need to save $120.98 each month to have it in 50 months

• 24 months:• -7,000 = FV, 24 = N, 7 = I%, PMT = ?

• You will need to save $272.57 each month to have it in 24 months

Investment Problem #5:Present Value of an Annuity

Two people wish to buy your house. The first offers you $200,000 today, while the second offers you 25 annual payments of $14,200 at the end of each year for 25 years.

• What is the present value of each offer, assuming a 5% discount rate?

• Who should you sell it to?

Offer 1: $200,000 today. Offer 2: 25 annual payments of $14,200 each year. Assuming 5% interest rates, what is the

Present Value of each offer? Which should you take?

Answer #5: Present Value of Annuities

A. What is the Present Value of each offer:

Offer 1: Present value = $200,000

Offer 2: Clear memories, set 1 payment year and end of period

• -14,200 = PMT, 25 = N, 5 = I%, Solve for PV?

• Present Value of Offer 2 = $200,134

B. Which is the better offer?

Offer 1 and Offer 2 are roughly the same

• Take either one (however, Offer 1 is more certain)

Know how to evaluate different cash flows!

Investment Problem #6:FV of an Annuity

Brittany, 22, started working full time and plans to deposit $2,000 annually into a Roth IRA earning 6%. How much will she have in:

• 20 years?

• 30 Years?

• 40 Years? If she increased his investment return to 10%, how

much would he have after each of the three time periods?

Comment on the differences over time.

Brittany deposits $2,000 each year earning 6%. How much will she have in 20, 30 or 40 years? How much if she increased the

return to 10%?

Answer #6:Present Value of an Annuity

6% interest, $2,000 PMT• 20 Years = $73,571

• 30 Years = $158,114

• 40 Years = $309,524

10% Interest• 20 Years = $114,550 (Difference = $40,979)

• 30 Years = $328,988 ($170,874)

• 40 Years = $885,185 ($575,661)

Your rate of return and time make a big difference!

C. Know how to solve problems relating to Amortized Loans

• What is an Amortized Loan?• A loan paid off in equal installments, both

principle and interest

• With an amortized loan the interest payment declines as your outstanding principal declines; therefore, with each payment you will be paying an increasing amount towards the principal of the loan.

• Examples -- car loans or home mortgages

Solving Amortized Loan Problems

Problem:• You want to determine either the payment, time or

interest rate necessary for a loan

Problem Statement:• If I want to borrow z amount for x years at y%

interest, what will be my p or payment?

Key Information Needed:• Borrowed amount, years, interest rates, and

payments

Investment Problem #7:Buying a Car (With Four “Easy” Payments)

What are the monthly payments to repay $40,000 at 15% interest for a new Suburban SUV with for 48 months (4 years)? How much interest will you have paid for the SUV?

$40,000 at 15% interest for 48 months. How much interest will you pay? Interest paid is payments * months – amount

borrowed.

Answer #7: Buying that SUV

A. Clear memories, set payments to monthly and to end mode

• PV = -40,000, N = 48, I = 15 PMT = ?

• PMT = $1,113.23

B. Interest Paid = $1,113.23 * 48 = $53,435 – 40,000 = $13,435

(that is the cost of another small car!)

Buy the car, but not on credit. Save for it!

Investment Problem #8:Becoming a Millionaire

Your buddy thinks that to become a millionaire is totally beyond his earning abilities. You, the financial wizard that you are, plan to show her otherwise. Assuming your friend is 25 years old, and will retire at age 65, and assuming an 8% interest rate:

• How much will she have to save each month to reach her goal of becoming a millionaire when she retires at age 65?

• How much each month if she earns 10% on her investments?

Goal: to retire with a million saved in 40 years. How much will she need to save each month assuming 8% interest rate? 10%?

Answer #8:the Millionaire

At 8% interest:• Clear your memory and set payments to monthly.

FV = 1,000,000 N = (40*12) I = 8%, Solve for Payment (PMT)

• PMT = $286.45 At 10% interest:

• Clear your memory and set payments to monthly. FV = 1,000,000 N = (40*12) I = 10%, Solve for Payment

• PMT = $158.13 Its not that hard to become a millionaire if you will

save your money and invest a specific amount every month!

Questions

Are you comfortable with solving amortized loan problems?

Review of Objectives

A. Do you understand the impact of inflation on A. Do you understand the impact of inflation on investing?investing?

B. Can you solve problems relating to Annuities, B. Can you solve problems relating to Annuities, Future Value of an annuity, and Present Future Value of an annuity, and Present Value of an annuity?Value of an annuity?

C. Do you know how to solve problems relating C. Do you know how to solve problems relating to amortized loans?to amortized loans?