Chapter 5 Time Value of Money - tmcbusinessfaculty.weebly.com · Web viewChapter 5 Time Value of Money. What is the difference between simple interest and compound interest? Compounding

Chapter 5 Time Value of Money

1. What is the difference between simple interest and compound interest?a. Compounding Interest

https://www.youtube.com/watch?feature=player_embedded&v=-qgdMTbTJlA

b. In the worksheet, is there something special that needs to be done for a present value amount?

Negative cash flows represent outflows ; investmentsWe must “tell” the computer which way the cash is flowing

2. 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?

3000 * 1.10 = $3,300

Future Value (FV) Solve for PV Present Value (PV) -$3,000.00Annual Interest Rate (I/Y) 10.00% Solve for FV $3,630.00Time in Years (N) 2.00 FV (Continuous Compounding) $3,664.21

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



Simple interest pays only on principalCompound is the way the world works

https://www.youtube.com/watch?feature=player_embedded&v=-qgdMTbTJlA

What is the difference between 1 year and 2 years above? Can you explain the difference?

Interest earns interest

3. What does the word value or worth mean to you?What would you payWhat should the price be?If you could hold it in your hands, how much would you have?

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

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


5. When you retire at age 65, your retirement fund promises to pay you $150,000 the first year of your retirement. If inflation is 4%, what is this worth to you in today’s money? How old are you? N =

a. If the company can earn 12% on its retirement investments, how much must they put away today to get the above payment?





6. What are some examples of cash flows that are annuity cash flow streams?LoansRetirement plan contributionsSystematic savings plans

7. What is the difference between an annuity due and an ordinary annuity?Annuity due starts today / investment problemsOrdinary annuity starts end of the period / corporate cash flows & loansDraw time line

8. 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?

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

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 11.000%Growth of an Annuity Growth of a Perpetuity PVA

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



Solve for Time Is this an Ordinary Annuity (y/n) nPayment (PMT) (A) -$2,000.00 Effective Interest Rate 11.000%Growth of an Annuity Growth of a Perpetuity PVA

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

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

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

12. Lets assume that at age 62 you have saved the amount in problem 13. 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) $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


Solve for Time Is this an Ordinary Annuity (y/n) yPayment (PMT) (A) Effective Interest Rate 12.683%Growth of an Annuity Growth of a Perpetuity PVA

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

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$



Solve for Time Is this an Ordinary Annuity (y/n) yPayment (PMT) (A) -$125.00 Effective Interest Rate 8.300%Growth of an Annuity Growth of a Perpetuity PVA

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

13. 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.

a. 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?

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

14. 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?

a. 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) $50,000.00 Effective Interest Rate 7.000%Growth of an Annuity Growth of a Perpetuity PVA (620,452.06)$

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$



Solve for Time Is this an Ordinary Annuity (y/n) yPayment (PMT) (A) $60,000.00 Effective Interest Rate 13.000%Growth of an Annuity 3.75%Growth of a Perpetuity PVA (439,799.10)$

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)$ PV of Growing Perpetuity (461,538.46)$

15. If you wanted to receive $10,000 per year forever, how much would you need to invest at 12%?

a. What kind of cash flow stream is this?perpetuity

16. 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?

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) $10,000.00 Effective Interest Rate 12.000%Growth of an Annuity Growth of a Perpetuity PVA -$

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

1 80,000

2 70,000

3 70,000

4 50,000

5 50,000

6 60,000

7 75,000

17. If the company could reinvest the above cash flow stream at 14%, what would they have at the end of the 7th year?

18. How do you change the compounding frequency in a time value problem?M = P/Y periods per year

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

19. What is the Effective interest rate for a 12%, monthly compounded investment? Quarterly?

20. 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%. What are the monthly payments on a 30 year mortgage?

a. How much interest is paid out of the first month’s payment?

b. When the couple pays their 180th payment, what is the balance?

c. If they paid an extra 50 per month, how much interest would they save?

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 12.683%

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%

0 $292,500.001 $1,388.02 $962.81 $425.21 $292,074.792 $1,388.02 $961.41 $426.61 $291,648.18

178 $1,388.02 $627.31 $760.71 $189,815.70179 $1,388.02 $624.81 $763.21 $189,052.49180 $1,388.02 $622.30 $765.72 $188,286.76181 $1,388.02 $619.78 $768.24 $187,518.52182 $1,388.02 $617.25 $770.77 $186,747.75

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

d. If they paid biweekly payments, how much would they save? (divide monthly payments by 12)

21. What is a loan amortization table?Segments annuity payment s into principal and interest componentsWhy is this important

22. 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?

23. What did I earn at age 65 when the stock was 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

Solve for Interest Rate 4.49%Compounding Freq. (m) (P/Y) 1

Solve for Time Is this an Ordinary Annuity (y/n) yPayment (PMT) (A) Effective Interest Rate 4.492%

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


Solve for Time Is this an Ordinary Annuity (y/n) yPayment (PMT) (A) Effective Interest Rate 3.606%

24. Describe the rule of 72.

Setup the following table:

3% 6% 12%0 2,000 2,000 2,0006 4,00012 4,000 8,00018 16,00024 4,000 8,000 32,00030 64,00036 16,000 128,00042 256,00048 8,000 32,000 512,000

Do one column at a time

Discuss how doubling Interest rate does not double the amount

How long will it take for your money to double in a savings account?

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

Retirement example

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

You currently earn $50,000 and have been able to save $15,000 in a retirement account. You expect to retire in 35 years at age 60. Inflation is expected to be at 3% for the foreseeable future. (age 30)

1) What will you need to receive as income in year one of retirement to maintain your current lifestyle?

FV PV I/Y N M PMT-50000 3 25 1

2) If you live to be 90, how much do you need to accumulate to pay the cashflow in question 1, if you can earn 8% during retirement?

FV PV I/Y N M PMT8 30 1 140693

3) If you want your retirement income to keep up with inflation, how much do you need to accumulate?

FV PV I/Y N M PMT G8 30 1 140,693 3

Future Value (FV) Solve for PV Present Value (PV) -$50,000.00Annual Interest Rate (I/Y) 3.00% Solve for FV $140,693.12Time in Years (N) 35.00 FV (Continuous Compounding)$142,882.56


Annual Interest Rate (I/Y) 8.00% Solve for FV $0.00Time in Years (N) 30.00 FV (Continuous Compounding) $0.00


Solve for Time Is this an Ordinary Annuity (y/n) yPayment (PMT) (A) $140,693.00 Effective Interest Rate 8.000%Growth of an Annuity Growth of a Perpetuity PVA (1,583,891.31)$

Annual Interest Rate (I/Y) 8.00% Solve for FV $0.00Time in Years (N) 30.00 FV (Continuous Compounding) $0.00


Solve for Time Is this an Ordinary Annuity (y/n) yPayment (PMT) (A) $140,693.00 Effective Interest Rate 8.000%Growth of an Annuity 3.00%Growth of a Perpetuity PVA (1,583,891.31)$

PMT for PVA PV of Growing Annuity (2,135,115.13)$

4) How much must you invest each month in your retirement plan to get the amount needed for retirement, if you can earn 12% on your invested dollars?

FV PV I/Y N M PMT2,135,115

-15,000 12 35 12

5) If you are investing a certain amount today, what return do you need to receive to get the desired amount?

FV PV I/Y N M PMT2,135,115

-15,000 35 12 -150

Future Value (FV) $2,135,115.00 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 (179.67)$

Future Value (FV) $2,135,115.00 Solve for PV Present Value (PV) -$15,000.00Annual Interest Rate (I/Y) Solve for FV Time in Years (N) 35.00 FV (Continuous Compounding) $15,000.00


Solve for Time Is this an Ordinary Annuity (y/n) yPayment (PMT) (A) -$150.00 Effective Interest Rate 15.219%Growth of an Annuity Growth of a Perpetuity PVA

PMT for PVA Interest for PVA (per period) 12.30%

Offline Homework (25 points) ______

BUA321 CH05 Homework 25 points

1) If you invested 12,000 today in a mutual fund that is expected to provide an annually compounded average return of 13% over the next 7 years, how much will you have in your account at the end of the 7th year?

28,231

What if the investment compounded interest monthly?

$29,666

2) Your company wants to buy a piece of equipment that will cost 500,000 in 12 years. If you can invest your company’s money at an average return of 10%, how much do you need to invest in a lump sum today to pay cash for the asset?

159,315

What would the monthly investment requirement be?

1,808


Solve for Interest Rate





PMT for PVA (1,808.72)$

3) I have just won the LOTTO. The jackpot was 20 million dollars. The state has offered me one million dollars per year for 20 years (ignore taxes) or a lump sum. The lump sum is the present value of the payments. How much must the state invest today (the lump sum amount) to payout the annuity, if they can invest at the T-Bond rate of 6%? (ignore taxes)

11,469,921

If I can invest at an average of 12%, how much can I withdraw from the lump sum per year over the 20 year window?

1,535,579

Should I take the lump sum or the 1 million dollar annuity? WHY?



Solve for Time Is this an Ordinary Annuity (y/n) yPayment (PMT) (A) $1,000,000.00 Effective Interest Rate 6.000%Growth of an Annuity Growth of a Perpetuity PVA (11,469,921.22)$

Future Value (FV) Solve for PV Present Value (PV) -$11,469,921.00Annual Interest Rate (I/Y) 12.00% Solve for FV $110,642,219.72Time in Years (N) 20.00 FV (Continuous Compounding)$126,434,962.26



PMT for PVA 1,535,579.03$

4) Our company is considering a project that will provide the following after tax cash flows to the firm:

CF1 90,000

CF2 125,000

CF3 175,000

CF4 200,000

CF5 190,000

CF6 – 9 165,000

CF10 145,000

If we have a required return of 14% for this project, what is the value

of the project to the company?

799152

If we had to pay 700,000 for the project today, should we purchase

the project?

yes

Pds Cash Flow01 $90,000 Discount Rate 14.00%2 $125,0003 $175,000 Number of Periods 104 $200,0005 $190,000 PV of Future Cash Flows $799,152.776 $165,0007 $165,000 Net Present Value $799,1538 $165,0009 $165,000 IRR #NUM!

10 $145,00011 FV of Cash Flows $2,962,636.19121314151617181920

5) When you retire you will initially require an annual income of 125,000 per year. You anticipate living for 25 years during retirement with an 8% investment return. How much do you need in your pension plans to cover this need?

1334347

How much will you have to invest monthly over the next 35 years to acquire that amount of money, if you can earn 13% on your investments?

593.81

6) I want to purchase a house in Florida. The current value is $350,000. I would like to put 25% down and make the purchase in 5 years. Houses in the area are appreciating at 6% per year. The forecasted mortgage rate at the time of purchase is 7.5% for 30 years.

Future cost of the house?

468378



Solve for Time Is this an Ordinary Annuity (y/n) yPayment (PMT) (A) $125,000.00 Effective Interest Rate 8.000%Growth of an Annuity Growth of a Perpetuity PVA (1,334,347.02)$

Future Value (FV) $1,334,347.00 Solve for PV -$52,650.48Present Value (PV)Annual Interest Rate (I/Y) 13.00% Solve for FV Time in Years (N) 25.00 FV (Continuous Compounding) $0.00



PMT for PVA (593.81)$ Interest for PVA (per period) #NUM!FVA PMT for FVA (593.81)$

Future Value (FV) Solve for PV Present Value (PV) $350,000.00Annual Interest Rate (I/Y) 6.00% Solve for FV -$468,378.95Time in Years (N) 5.00 FV (Continuous Compounding)-$472,450.58

Solve for Interest Rate

Down payment?

117,094

Mortgage amount?

351,284

Monthly payments to get down payment, if I can invest at 15%?

17366

Monthly payment of the mortgage?

2456

Copy and Paste Special the first 6 months of the amortization table from the worksheet. What is the reduction in principal in month 1? (3)




PMT for PVA (17,366.86)$ Interest for PVA (per period) #NUM!FVA PMT for FVA (17,366.86)$





0 $351,284.001 $2,456.23 $2,195.53 $260.70 $351,023.302 $2,456.23 $2,193.90 $262.33 $350,760.963 $2,456.23 $2,192.26 $263.97 $350,496.994 $2,456.23 $2,190.61 $265.62 $350,231.375 $2,456.23 $2,188.95 $267.28 $349,964.096 $2,456.23 $2,187.28 $268.95 $349,695.13

Period PMT Interest PMTPrincipal Reduction

Remaining Balance

If you made an additional payment per year (1/12 more per month or made biweekly pmts), How much interest would you save?

139614







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Chapter 5 Time Value of Money - tmcbusinessfaculty.weebly.com · Web viewChapter 5 Time Value of Money. What is the difference between simple interest and compound interest? Compounding