Chapter 5 Time Value of Money

Transcription

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
Simple interest pays only on principal
Compound is the way the world works
b. In the worksheet, is there something special that needs to be done for a present
value amount?
Negative cash flows represent outflows ; investments
We 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)
Present Value (PV)
Annual Interest Rate (I/Y)
Time in Years (N)
Compounding Freq. (m) (P/Y)
Future Value (FV)
Present Value (PV)
Time in Years (N)
Solve for PV
-$3,000.00
10.00%
2.00
Solve for FV
$3,630.00
FV (Continuous Compounding) $3,664.21
Solve for Interest Rate
1
Solve for PV
-$3,000.00
10.00%
5.00
Solve for FV
$4,831.53
1
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 pay
What 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)
Present Value (PV)
Time in Years (N)
$30,000.00
Solve for PV
3.50%
12.00
-$19,853.50
Solve for FV
FV (Continuous Compounding)
$0.00
1
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 =
Future Value (FV)
Present Value (PV)
Time in Years (N)
$150,000.00
Solve for PV
4.00%
40.00
-$31,243.36
Solve for FV
$0.00
1
a. If the company can earn 12% on its retirement investments, how much must they
put away today to get the above payment?
Future Value (FV)
Present Value (PV)
Time in Years (N)
$150,000.00
12.00%
40.00
Solve for PV
-$1,612.02
Solve for FV
1
6. What are some examples of cash flows that are annuity cash flow streams?
Loans
Retirement plan contributions
$0.00
Systematic savings plans
7. What is the difference between an annuity due and an ordinary annuity?
Annuity due starts today / investment problems
Ordinary annuity starts end of the period / corporate cash flows & loans
Draw 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?
Future Value (FV)
Present Value (PV)
Time in Years (N)
11.00%
46.00
Solve for PV
$0.00
Solve for FV
$0.00
$0.00
1
Solve for Time
Is this an Ordinary Annuity (y/n)
Payment (PMT) (A)
Growth of an Annuity
Growth of a Perpetuity
y
-$2,000.00
Effective Interest Rate
11.000%
PVA
PMT for PVA
Interest for PVA (per period) #NUM!
FVA
$
2,192,337.60
9. Would it make a difference if you started at the beginning of the year instead of the end?
How much?
Future Value (FV)
Present Value (PV)
Time in Years (N)
11.00%
46.00
Solve for PV
$0.00
Solve for FV
$0.00
$0.00
1
Solve for Time
Payment (PMT) (A)
n
-$2,000.00
11.000%
PVA
PMT for PVA
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%?
Future Value (FV)
Present Value (PV)
Time in Years (N)
8.00%
18.00
Solve for PV
$0.00
Solve for FV
$0.00
$0.00
12
Solve for Time
Payment (PMT) (A)
y
-$125.00
8.300%
PVA
PMT for PVA
FVA
$
60,010.77
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
Future Value (FV)
Present Value (PV)
Time in Years (N)
$3,850,000.00
12.00%
37.00
Solve for PV
Solve for FV
-$46,427.02
$0.00
12
Solve for Time
Payment (PMT) (A)
y
12.683%
PVA
PMT for PVA
$
(469.94)
FVA
PMT for FVA
$
(469.94)
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)
Present Value (PV)
Time in Years (N)
Solve for PV
-$3,850,000.00
8.00%
26.00
Solve for FV
$30,605,216.75
$30,817,205.32
12
Solve for Time
Payment (PMT) (A)
y
PVA
PMT for PVA
8.300%
$
29,360.03
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?
Future Value (FV)
Present Value (PV)
Time in Years (N)
7.00%
30.00
Solve for PV
$0.00
Solve for FV
$0.00
$0.00
1
Solve for Time
Payment (PMT) (A)
y
$50,000.00
PVA
7.000%
$
(620,452.06)
b. If you could invest at 9%, how much could you withdraw for the 30 years, if you
invest the lump sum?
Future Value (FV)
Present Value (PV)
Time in Years (N)
Solve for PV
-$620,452.00
9.00%
30.00
Solve for FV
$8,231,957.64
$9,232,159.31
1
Solve for Time
Payment (PMT) (A)
y
PVA
PMT for PVA
9.000%
$
60,392.53
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?
Future Value (FV)
Present Value (PV)
Time in Years (N)
13.00%
25.00
Solve for PV
$0.00
Solve for FV
$0.00
$0.00
1
Solve for Time
Payment (PMT) (A)
y
$60,000.00
3.75%
13.000%
PVA
$
(439,799.10)
PMT for PVA
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%?
Future Value (FV)
Present Value (PV)
Time in Years (N)
12.00%
Solve for PV
$0.00
Solve for FV
$0.00
$0.00
1
Solve for Time
Payment (PMT) (A)
y
$10,000.00
#DIV/0!
12.000%
PVA
$
PMT for PVA
FVA
PMT for FVA
Interest for FVA
#VALUE!
PV of Perpetuity
$
(83,333.33)
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?
Pds
1
80,000
2
70,000
3
70,000
4
50,000
5
50,000
6
60,000
7
75,000
Cash Flow
0
1
2
3
4
5
6
7
8
9
10
11
$80,000
$70,000
$70,000
$50,000
$50,000
$60,000
$75,000
Discount Rate
14.00%
Number of Periods
PV of Future Cash Flows
Net Present Value
IRR
FV of Cash Flows
7
$284,166.61
$284,167
#NUM!
$711,061.24
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
19. What is the Effective interest rate for a 12%, monthly compounded investment?
Quarterly?
Future Value (FV)
Present Value (PV)
Time in Years (N)
12.00%
Solve for PV
$0.00
Solve for FV
$0.00
$0.00
12
Solve for Time
Payment (PMT) (A)
y
$10,000.00
#DIV/0!
12.683%
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?
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%
b. When the couple pays their 180th payment, what is the balance?
Period
0
1
2
178
179
180
181
182
PMT
Interest PMT
$1,388.02
$1,388.02
$1,388.02
$1,388.02
$1,388.02
$1,388.02
$1,388.02
$962.81
$961.41
$627.31
$624.81
$622.30
$619.78
$617.25
Principal
Reduction
$425.21
$426.61
$760.71
$763.21
$765.72
$768.24
$770.77
Remaining
Balance
$292,500.00
$292,074.79
$291,648.18
$189,815.70
$189,052.49
$188,286.76
$187,518.52
$186,747.75
c. If they paid an extra 50 per month, how much interest would they save?
Loan Amount
$292,500.00
Pmt per Period
$1,388.02
Loan Maturity (yrs)
30
Total AMT Paid
$499,687.71
12
$207,187.71
Impact of Accelerated PMTS
Years of Loan
Total AMT Paid
Interest Saved
28.08
$484,525.24
$15,162.47
Extra Periodic PMT
Biweekly impact
=PMT/12
3.95%
$50.00
d. If they paid biweekly payments, how much would they save? (divide monthly
payments by 12)
Loan Amount
$292,500.00
Pmt per Period
$1,388.02
Loan Maturity (yrs)
30
Total AMT Paid
$499,687.71
12
$207,187.71
Years of Loan
Total AMT Paid
Interest Saved
25.93
$467,856.90
$31,830.81
Extra Periodic PMT
Biweekly impact
=PMT/12
3.95%
$115.67
21. What is a loan amortization table?
Segments annuity payment s into principal and interest components
Why 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?
Future Value (FV)
Present Value (PV)
Time in Years (N)
$75.00
-$25.00
25.00
Solve for PV
Solve for FV
$25.00
4.49%
1
Solve for Time
Payment (PMT) (A)
y
4.492%
23. What did I earn at age 65 when the stock was worth $250?
Future Value (FV)
Present Value (PV)
Time in Years (N)
$250.00
-$25.00
65.00
Solve for PV
Solve for FV
$25.00
3.61%
1
Solve for Time
Payment (PMT) (A)
y
3.606%
24. Describe the rule of 72.
Setup the following table:
0
6
12
18
24
30
36
42
48
3%
2,000
6%
2,000
4,000
4,000
8,000
16,000
8,000
32,000
Do one column at a time
12%
2,000
4,000
8,000
16,000
32,000
64,000
128,000
256,000
512,000
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
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
Future Value (FV)
Present Value (PV)
Time in Years (N)
Solve for PV
-$50,000.00
3.00%
35.00
Solve for FV
$140,693.12
FV (Continuous Compounding)$142,882.56
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
PMT
8
30
1
140693
Time in Years (N)
8.00%
30.00
Solve for FV
$0.00
$0.00
1
Solve for Time
Payment (PMT) (A)
y
$140,693.00
PVA
8.000%
$
(1,583,891.31)
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
G
8
30
1
140,693
3
Time in Years (N)
8.00%
30.00
Solve for FV
$0.00
$0.00
1
Solve for Time
Payment (PMT) (A)
y
$140,693.00
3.00%
PVA
$
PMT for PVA
PV of Growing Annuity $
8.000%
(1,583,891.31)
(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
PMT
2,135,115 -15,000
12
35
12
Future Value (FV)
Present Value (PV)
Time in Years (N)
$2,135,115.00
-$15,000.00
12.00%
35.00
Solve for PV
Solve for FV
$1,000,294.97
12
Solve for Time
Payment (PMT) (A)
y
PVA
PMT for PVA
12.683%
$
(179.67)
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
PMT
2,135,115 -15,000
35
12
-150
Future Value (FV)
Present Value (PV)
Time in Years (N)
$2,135,115.00
-$15,000.00
35.00
Solve for PV
Solve for FV
14.25%
12
Solve for Time
Payment (PMT) (A)
y
-$150.00
PVA
PMT for PVA
Interest for PVA (per period)
15.219%
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
Future Value (FV)
Present Value (PV)
Time in Years (N)
Solve for PV
-$12,000.00
13.00%
7.00
Solve for FV
$28,231.27
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
Future Value (FV)
Present Value (PV)
Time in Years (N)
$500,000.00
10.00%
12.00
Solve for PV
-$159,315.41
Solve for FV
$0.00
What would the monthly investment requirement be?
1,808
Future Value (FV)
Present Value (PV)
Time in Years (N)
$500,000.00
10.00%
12.00
Solve for PV
-$151,347.80
Solve for FV
$0.00
12
Solve for Time
Payment (PMT) (A)
y
PVA
PMT for PVA
10.471%
$
(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
Future Value (FV)
Present Value (PV)
Time in Years (N)
6.00%
20.00
Solve for PV
$0.00
Solve for FV
$0.00
$0.00
1
Solve for Time
Payment (PMT) (A)
y
$1,000,000.00
PVA
6.000%
$
(11,469,921.22)
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
Future Value (FV)
Present Value (PV)
Time in Years (N)
Solve for PV
-$11,469,921.00
12.00%
20.00
Solve for FV
$110,642,219.72
$126,434,962.26
1
Solve for Time
Payment (PMT) (A)
y
PVA
PMT for PVA
Should I take the lump sum or the 1 million dollar annuity?
12.000%
$
1,535,579.03
WHY?
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
Pds
Cash Flow
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
$90,000
$125,000
$175,000
$200,000
$190,000
$165,000
$165,000
$165,000
$165,000
$145,000
Discount Rate
14.00%
Number of Periods
PV of Future Cash Flows
Net Present Value
10
$799,152.77
$799,153
IRR
#NUM!
FV of Cash Flows
$2,962,636.19
If we had to pay 700,000 for the project today, should we purchase
the project?
yes
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
Future Value (FV)
Present Value (PV)
Time in Years (N)
8.00%
25.00
Solve for PV
$0.00
Solve for FV
$0.00
$0.00
1
Solve for Time
Payment (PMT) (A)
y
$125,000.00
PVA
8.000%
$
(1,334,347.02)
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
Future Value (FV)
Present Value (PV)
Time in Years (N)
$1,334,347.00
Solve for PV
13.00%
25.00
Solve for FV
-$52,650.48
$0.00
12
Solve for Time
Payment (PMT) (A)
y
13.803%
PVA
PMT for PVA
$
(593.81)
FVA
PMT for FVA
$
(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
Future Value (FV)
Present Value (PV)
Time in Years (N)
Solve for PV
$350,000.00
6.00%
5.00
Solve for FV
-$468,378.95
FV (Continuous Compounding)-$472,450.58
Down payment?
117,094
Mortgage amount?
351,284
Monthly payments to get down payment, if I can invest at 15%?
17366
Future Value (FV)
Present Value (PV)
Time in Years (N)
$117,094.00
15.00%
5.00
Solve for PV
-$58,216.41
Solve for FV
$0.00
1
Solve for Time
Payment (PMT) (A)
y
15.000%
PVA
PMT for PVA
$
(17,366.86)
FVA
PMT for FVA
$
(17,366.86)
Monthly payment of the mortgage?
2456
Loan Amount
$351,284.00
Pmt per Period
$2,456.23
Loan Maturity (yrs)
30
Total AMT Paid
$884,242.33
12
$532,958.33
7.50%
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)
Period
PMT
0
1
2
3
4
5
6
Interest PMT
$2,456.23
$2,456.23
$2,456.23
$2,456.23
$2,456.23
$2,456.23
$2,195.53
$2,193.90
$2,192.26
$2,190.61
$2,188.95
$2,187.28
Principal
Reduction
$260.70
$262.33
$263.97
$265.62
$267.28
$268.95
Remaining
Balance
$351,284.00
$351,023.30
$350,760.96
$350,496.99
$350,231.37
$349,964.09
$349,695.13
If you made an additional payment per year (1/12 more per month or made
biweekly pmts), How much interest would you save?
139614
Loan Amount
$351,284.00
Pmt per Period
$2,456.23
Loan Maturity (yrs)
30
Total AMT Paid
$884,242.33
12
$532,958.33
Years of Loan
Total AMT Paid
Interest Saved
23.32
$744,627.54
$139,614.79
Extra Periodic PMT
Biweekly impact
=PMT/12
7.50%
$204.69

Chapter 5 Time Value of Money

Transcription

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