Chapter 5 Time Value of Money Time value

Chapter 5 Time Value of Money

Time value • What is the difference between simple interest and compound interest? https: //www. youtube. com/watch? feature=player_embed ded&v=-qgd. MTb. TJl. A

Let’s Look at the worksheet • In the worksheet, is there something special that needs to be done for a present value amount?

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?

• 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?

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?

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

Building Wealth http: //www. youtube. com/watch? feature=player_d etailpage&v=23 zghp. S 9034

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%?

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?

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?

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?

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?

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?

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? 1 2 3 4 5 6 7 80, 000 70, 000 50, 000 60, 000 75, 000 • If the company could reinvest the above cash flow stream at 12%, what would they have at the end of the 7 th year?

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?

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

What is a loan amortization table? • How much interest is paid out of the first month’s payment? • When the couple pays their 180 th 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)

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? 0 6 12 18 24 30 36 42 48 3% 6% 12% 2000 4000 8000 16000 32000 16000 64000 128000 4000 256000 8000 32000 512000

Time • http: //www. youtube. com/watch ? feature=player_detailpage&v=_z p. GZf. Fb. W 4 M

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 = 50 K 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 = ?

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 = 50 K 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 = ?

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 = 50 K 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 = ?

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 = 50 K 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 = ?

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? • If you wanted your retirement income to keep up with an expected inflation rate of 3. 1%, how much would you need? • 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?