Chapter 5 Time Value of Money

Time value

• What is the difference between simple interest and compound interest?

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Let’s Look at the worksheet• In the worksheet, is there something special that needs to

be done for a present value amount?Future Value (FV) $75.00 Solve for PV Present Value (PV) -$50.00Annual Interest Rate (I/Y) Solve for FV Time in Years (N) 5.00 FV (Continuous Compounding) $50.00

Solve for Interest Rate 8.45%Compounding Freq. (m) (P/Y) 1

Solve for Time Is this an Ordinary Annuity (y/n) yPayment (PMT) (A) Effective Interest Rate 8.45%Growth of an Annuity Growth of a Perpetuity PVA

PMT for PVA (5.00)$ Interest for PVA (per period) 0.08$ FVA PMT for FVA #DIV/0!Interest for FVA 0.08$ PV of Perpetuity #DIV/0!PV of Growing Annuity PV of Growing Perpetuity #DIV/0!

FV Example

• If you were to invest $3,000 today, what would it be worth in 1 year if you can earn 10% on your investments on average? 2 Years? 5 years?

Future Value (FV) Solve for PV Present Value (PV) -$3,000.00Annual Interest Rate (I/Y) 10.00% Solve for FV $3,300.00Time in Years (N) 1.00 FV (Continuous Compounding)$3,315.51

Solve for Interest Rate Compounding Freq. (m) (P/Y) 1





•What does the word value or worth mean to you?

PV Example

• When you were 10 years old your grandfather tells you that upon college graduation (age 22) he will give you $30,000. Inflation is expected to be 3.5%. What is this amount worth as a 10 year old?

Future Value (FV) $30,000.00 Solve for PV -$19,853.50Present Value (PV)Annual Interest Rate (I/Y) 3.50% Solve for FV Time in Years (N) 12.00 FV (Continuous Compounding) $0.00


PV example

• When you retire at age 65, your retirement fund promises to pay you $150,000 the first year of your retirement. You are now 25. If inflation is 4%, what is this worth to you in today’s money?• If the company can earn 12% on its

retirement investments, how much must they put away today to get the above payment?





Complete this for your age.

Annuities

• What are some examples of cash flows that are annuity cash flow streams?• What is the difference between

an annuity due and an ordinary annuity?

Annuity Example

• If you started at age 19 to save 2,000 per year at the end of the year and could average 11% per year in earnings, how much would you have at retirement at age 65?

Future Value (FV) Solve for PV $0.00Present Value (PV)Annual Interest Rate (I/Y) 11.00% Solve for FV $0.00Time in Years (N) 46.00 FV (Continuous Compounding) $0.00


Solve for Time Is this an Ordinary Annuity (y/n) yPayment (PMT) (A) -$2,000.00 Effective Interest Rate 11.00%Growth of an Annuity Growth of a Perpetuity PVA

PMT for PVA Interest for PVA (per period)#NUM!FVA 2,192,337.60$

• Would it make a difference if you started at the beginning of the year instead of the end? How much?



Solve for Time Is this an Ordinary Annuity (y/n) nPayment (PMT) (A) -$2,000.00 Effective Interest Rate 11.00%Growth of an Annuity Growth of a Perpetuity PVA

PMT for PVA Interest for PVA (per period)#NUM!FVA 2,433,494.74$

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Building Wealth




Annuity Example

• If you started saving $1,500 per year on a monthly basis for 18 years toward your child’s college education, how much would you have if you invested and earned 8%? 12%?



Solve for Time Is this an Ordinary Annuity (y/n) yPayment (PMT) (A) -$125.00 Effective Interest Rate 8.30%Growth of an Annuity Growth of a Perpetuity PVA

PMT for PVA Interest for PVA (per period)#NUM!FVA 60,010.77$



Solve for Time Is this an Ordinary Annuity (y/n) yPayment (PMT) (A) -$125.00 Effective Interest Rate 12.68%Growth of an Annuity Growth of a Perpetuity PVA

PMT for PVA Interest for PVA (per period)#NUM!FVA 94,732.58$

Annuity Example

• You have analyzed your retirement plan and have concluded that you need 3,850,000 at age 62. You are currently 25. If you can invest at 12% on average, how much must you invest monthly to achieve the financial goal?

Future Value (FV) $3,850,000.00 Solve for PV -$46,427.02Present Value (PV)Annual Interest Rate (I/Y) 12.00% Solve for FV Time in Years (N) 37.00 FV (Continuous Compounding) $0.00



PMT for PVA (469.94)$ Interest for PVA (per period)#NUM!FVA PMT for FVA (469.94)$

Use your age.

Annuity example

• Let’s assume that at age 62 you have saved the amount in the above slide. You think you will live to be 88 years old. During retirement, you plan to earn 8% on your investments. How much can you withdraw every month for the remainder of your life?

Future Value (FV) Solve for PV Present Value (PV) -$3,850,000.00Annual Interest Rate (I/Y) 8.00% Solve for FV $30,605,216.75Time in Years (N) 26.00 FV (Continuous Compounding)$30,817,205.32



PMT for PVA 29,360.03$

With respect to money what do the following people worry about?

• College student 19 years old.• Young married person 31 years old with

a child age 5.• A stable working married adult age 50,

children are out of the house and college.

• A senior citizen age 64 recently retired.

Annuity Example• You win a prestigious sweepstake award. The

company offers you $50,000 per year for the next 30 years or a lump sum. Answer the following questions.

• If the company can invest at 7%, how much would they need to invest to pay the promised cash flow stream? This is the amount of the lump sum offer?

• If you could invest at 9%, how much could you withdraw for the 30 years, if you invest the lump sum?



Solve for Time Is this an Ordinary Annuity (y/n) yPayment (PMT) (A) $50,000.00 Effective Interest Rate 7.00%Growth of an Annuity Growth of a Perpetuity PVA (620,452.06)$

PMT for PVA Interest for PVA (per period)#NUM!FVA

Future Value (FV) Solve for PV Present Value (PV) -$620,452.00Annual Interest Rate (I/Y) 9.00% Solve for FV $8,231,957.64Time in Years (N) 30.00 FV (Continuous Compounding)$9,232,159.31



PMT for PVA 60,392.53$

Annuity Example

• At retirement you want to receive $60,000 per year for 25 years and can earn 13%. How much must you invest to achieve this goal?

• If you are concerned about the 3.75% inflation rate, how much must you invest?



Solve for Time Is this an Ordinary Annuity (y/n) yPayment (PMT) (A) $60,000.00 Effective Interest Rate 13.00%Growth of an Annuity Growth of a Perpetuity PVA (439,799.10)$



Solve for Time Is this an Ordinary Annuity (y/n) yPayment (PMT) (A) $60,000.00 Effective Interest Rate 13.00%Growth of an Annuity 3.75%Growth of a Perpetuity PVA (439,799.10)$

PMT for PVA Interest for PVA (per period)#NUM!FVA PMT for FVA Interest for FVA PV of Perpetuity (461,538.46)$ PV of Growing Annuity (571,956.47)$

Annuity

• If you wanted to receive $10,000 per year for ever, how much would you need to invest at 12%?• What kind of cash flow stream is

this?

Future Value (FV) Solve for PV $0.00Present Value (PV)Annual Interest Rate (I/Y) 12.00% Solve for FV $0.00Time in Years (N) FV (Continuous Compounding) $0.00


Solve for Time #DIV/0!Is this an Ordinary Annuity (y/n) yPayment (PMT) (A) $10,000.00 Effective Interest Rate 12.00%Growth of an Annuity Growth of a Perpetuity PVA -$

PMT for PVA Interest for PVA (per period)#NUM!FVA PMT for FVA Interest for FVA PV of Perpetuity (83,333.33)$

Change the interest rate to 10%. How much must you invest? How does the perpetuity work?

Mixed Cash Flows

• A company is planning a project that will provide the following cash flow stream. If they can earn 14% on average, what is the value of this project?

• If the company could reinvest the above cash flow stream at 12%, what would they have at the end of the 7th year?

1 80,0002 70,0003 70,0004 50,0005 50,0006 60,0007 75,000

Pds Cash Flow01 $80,000 Discount Rate 14.00%2 $70,0003 $70,000 Number of Periods 74 $50,0005 $50,000 PV of Future Cash Flows $284,166.616 $60,0007 $75,000 Net Present Value $284,16789 IRR #NUM!

1011 FV of Cash Flows $711,061.24

Pds Cash Flow01 $80,000 Discount Rate 12.00%2 $70,0003 $70,000 Number of Periods 74 $50,0005 $50,000 PV of Future Cash Flows $301,528.076 $60,0007 $75,000 Net Present Value $301,52889 IRR #NUM!

1011 FV of Cash Flows $666,582.49

Compounding frequency

• How do you change the compounding frequency in a time value problem?• What is the Effective interest rate

for a 12%, monthly compounded investment? Quarterly?



Solve for Time Is this an Ordinary Annuity (y/n) yPayment (PMT) (A) Effective Interest Rate 12.00%







Example • A newly married couple is considering buying a new

home. The house of their dreams costs $325,000. They have 10% to put down on the home and can borrow at 3.95%.

• How much must they borrow?• What are the monthly payments on a 30 year

mortgage?• What is the total cost of the loan for the 360 months?• Loan Analysis worksheet

Loan Amount $292,500.00 Pmt per Period $1,388.02

Loan Maturity (yrs) 30 Total AMT Paid $499,687.71

PMT per Year (P/Y) m 12 Total Financing Costs $207,187.71

Annual Interest Rate 3.95%

What is a loan amortization table?• How much interest is paid out of the first month’s

payment?• When the couple pays their 180th payment, what is the

balance?• If they paid an extra 50 payment per month, how much

interest would they save?• If they paid biweekly payments, how much would they

save? (divide monthly payments by 12)

0 $292,500.001 $1,388.02 $962.81 $425.21 $292,074.792 $1,388.02 $961.41 $426.61 $291,648.183 $1,388.02 $960.01 $428.01 $291,220.17

180 $1,388.02 $622.30 $765.72 $188,286.76181 $1,388.02 $619.78 $768.24 $187,518.52360 $1,388.02 $4.55 $1,383.47

Period PMT Interest PMTPrincipal Reduction

Remaining Balance





Impact of Accelerated PMTSExtra Periodic PMT $50.00 Years of Loan 28.08Biweekly impact =PMT/12 Total AMT Paid $484,525.24

Interest Saved $15,162.47





Impact of Accelerated PMTSExtra Periodic PMT $115.67 Years of Loan 25.93Biweekly impact =PMT/12 Total AMT Paid $467,856.90

Interest Saved $31,830.81

Example of returns

• When I was born my Grandfather purchased a stock for $25. When I was 25 the stock was worth $75. What did I earn on the investment?

• What would I earn at age 65 if the stock was then worth $250?

Future Value (FV) $75.00 Solve for PV Present Value (PV) -$25.00Annual Interest Rate (I/Y) Solve for FV Time in Years (N) 25.00 FV (Continuous Compounding) $25.00


Future Value (FV) $250.00 Solve for PV Present Value (PV) -$25.00Annual Interest Rate (I/Y) Solve for FV Time in Years (N) 65.00 FV (Continuous Compounding) $25.00


The Rule of 72.What is this rule?

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3%

2000

4000

8000

6%

2000

4000

8000

16000

32000

12%

2000

40008000

1600032000

64000128000

256000

512000

Time

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Retirement example• You currently earn 50,000 per year and have been able to save $15,000 in a retirement

account. You will retire in 35 years at age 60 and inflation is 4%. What will your income need to be in year 1 of retirement to maintain your current lifestyle?

PV = 50K FV = ? N=35 I/Y=4% m=1 PMT = 0

• If you live to 90, how much do you need in your pension fund at age 60 with 8% return. PVA = ? FV = 0 N=30 I/Y=8% m=1 PMT = 197304

• If you wanted your retirement income to keep up with an expected inflation rate of 4.5%, how much would you need?

PVA = ? FV = 0 N=30 I/Y=8% m=1 PMT = 197304 Growth of annuity = 4.5%

• How much must you invest each month in your retirement plans to get your desired

growing retirement income if you can earn a 12% return?

PV = -15000 FV = 3539071 N=35 I/Y=12% m=12 PMT for FVA = ?



PV = 50K FV = ? N=35 I/Y=4% m=1 PMT = 0









Solve for Time Is this an Ordinary Annuity (y/n) yPayment (PMT) (A) $197,304.00 Effective Interest Rate 8.00%Growth of an Annuity Growth of a Perpetuity PVA (2,221,205.68)$



PV = 50K FV = ? N=35 I/Y=4% m=1 PMT = 0









Solve for Time Is this an Ordinary Annuity (y/n) yPayment (PMT) (A) $197,304.00 Effective Interest Rate 8.00%Growth of an Annuity 4.50%Growth of a Perpetuity PVA (2,221,205.68)$

PMT for PVA Interest for PVA (per period)#NUM!FVA PMT for FVA Interest for FVA PV of Perpetuity (2,466,300.00)$ PV of Growing Annuity (3,539,071.58)$



PV = 50K FV = ? N=35 I/Y=4% m=1 PMT = 0







Future Value (FV) $3,629,071.00 Solve for PV Present Value (PV) -$15,000.00Annual Interest Rate (I/Y) 12.00% Solve for FV Time in Years (N) 35.00 FV (Continuous Compounding)$1,000,294.97



PMT for PVA (411.98)$ Interest for PVA (per period) 0.01$ FVA PMT for FVA (411.98)$

Retirement example• You currently earn $XXXX per year and have been able to save $XXX in a

retirement account. You will retire in X years at age 65 and inflation is 3.1%. What will your income need to be in year 1 of retirement to maintain your current lifestyle?

• If you live to 90, how much do you need in your pension fund at age 60 with 8% return?


• How much must you invest each month in your retirement plans to get your desired growing retirement income, if you can earn a 12% return?

Chapter 5 Time Value of Money

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Transcript of Chapter 5 Time Value of Money