Chapter 5 Time Value of Money. Time value What is the difference between simple interest and...

Chapter 5 Time Value of Money

Time value

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

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gdMTbTJlA

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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?

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

• http://www.youtube.com/watch?feature=player_detailpage&v=_zpGZfFbW4M

http://www.youtube.com/watch?feature=player_detailpage&v=_zpGZfFbW4M



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


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








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


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








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


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






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. Time value What is the difference between simple interest and...

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