Unformatted text preview: Time Value of Money—2
Compounding and Discounting
Cash Flow Streams 0 1 2 3 4 Angkor Wat, Cambodia Comments on Horizon Case In Testing Center Th/Fr (closes 11:30 am Friday)
What to bring—up to 3 pages (one side = one page) of notes, spreadsheets
What is/are the problem(s) to solve? (you decide)
How do you solve it (them)? (you decide)
What do the following mean? “Surplus”, “Earned Surplus” = Retained Earnings
“Extraordinary” = Onetime Event
“2/10, net 30”
“Due from Stockholders” = Loans to Owners Tuneup Problem Your company has received a $50,000 loan from an industrial finance company. The annual payments are $6,202.70. If the company is paying 9% interest per year, how many loan payments must the company make? 12 13 15 19 None of the above Tuneup Problem Your company has received a $50,000 loan from an industrial finance company. The annual payments are $6,202.70. If the company is paying 9% interest per year, how many loan payments must the company make? 12
13
15 (setup; 50000 PV, 6202.70 PMT, 9 I/Y, N)
19
None of the above Tuneup Problem2 Your grandmother invested one lump sum 17 years ago at 4.25 percent annual interest. Today, she gave you the proceeds of that investment which totaled $5,539.92. How much did your grandmother originally invest?
a.
$2,700.00
b.
$2,730.30
c.
$2,750.00
d.
$2,768.40
e.
None of the above Tuneup Problem2 Your grandmother invested one lump sum 17 years ago at 4.25 percent interest. Today, she gave you the proceeds of that investment which totaled $5,539.92. How much did your grandmother originally invest?
a.
$2,700.00
b.
$2,730.30 (5539.92 FV, 4.25 I/Y, 17 N PV)
c.
$2,750.00
d.
$2,768.40
e.
None of the above Other Cash Flow Patterns 0 1 2 3 Perpetuity
Suppose you will receive a fixed payment every period (month, year, etc.) forever. This is an example of a perpetuity. You can think of a perpetuity as an annuity that goes on forever. Present Value of a Perpetuity
Present Value of a Perpetuity When we find the PV of an annuity, we think of the following relationship: PV = PMT (PVIFA i, n ) Mathematically (PVIFA i, n ) = 0 1 1
n
(1 + i) i 1
= We said that a perpetuity is an annuity where n = infinity. What happens to this formula when n gets very, very large? i Result: PV of Perpetuity Simply: PV = PMT x (1/i), or PMT
PV =
i Example
What should you be willing to pay in order to receive $10,000 annually forever, if you require 8% per year on the investment?
PV = $10,000/.08 = $125,000 Annuity: Ordinary vs. “Annuity Due” $1000 $1000 $1000 0 1 2 $0 3 This is where we use the “Begin Mode” on your calculator. Example 1 What is the present value of three annual payments of $1,000 starting today if the discount rate is 6%?
Set up calculator (remember “Begin” mode)
N = 3, PMT = 1000, I/YR = 6
PV = 2,833.39 $1000 $1000 $1000 0 1 2 $0 3 Example 2 What is the future value of three annual payments of $1,000 starting today if the discount rate is 6%?
Set up calculator (remember “Begin” mode)
N = 3, PMT = 1000, I/YR = 6
FV = 3,374.62 $1000 $1000 $1000 0 1 2 $0 3 Multiple Step Problem What would you pay today for the cash flow below if the discount rate is 6%?
Can you think of at least five ways to solve this problem? Pick one and do it. 0 1000
1000 1000 4 5 6 1000 7 0 8 Multiple Step Problem—Step 1 What would you pay today for the cash flow below if the discount rate is 6%? What pattern is this?
0 1000
1000 1000 4 5 6 1000 7 0 8 End mode, N=3, PMT=1000, I=6; PV4=2673.01 Multiple Step Problem—Step 2 What would you pay today for the cash flow below if the discount rate is 6%? 0 0 0 0 2673.01
2673.01 0 1 2 3 4 N=4, FV=2673.01, I=6; PV0 = 2117.28 Another Way
Multiple Step Problem—Step 1 What would you pay today for the cash flow below if the discount rate is 6%? What pattern is this?
0 1000
1000 1000 4 5 6 1000 7 0 8 Begin mode, N=3, PMT=1000, I=6; PV5=2833.39 Another Way
Multiple Step Problem—Step 2 What would you pay today for the cash flow below if the discount rate is 6%? 0 0 0 0 0 2833.39
2833.39 0 1 2 3 4 N=5, FV=2833.39, I=6; PV0 = 2117.28 5 Try This Problem Retirement Example After graduation, you plan to invest $400 per month in the stock market. If you earn 6% per year on your stocks, how much will you have accumulated when you retire after working 30 years?
N=360, I=0.5, PMT=400; FV = $402,000 What if you can earn 12% per year?
N=360, I=1, PMT=400; FV = $1,398,000
Lesson learned? Team Assignment
Upon retirement, your goal is to spend 5 years traveling around the world. To travel in style will require $250,000 per year at the beginning of each year. If you plan to retire in 30 years, what are the equal monthly (endofmonth) payments necessary to achieve this goal? The funds in your retirement account will compound at 10% annually. Approach to the Problem How much do we need to have by the end of year 30 to finance the trip?
250 250 250 250 250 27 28 29 30 31 32 33 34 35 Approach to the Problem
Using your calculator,
Mode = BEGIN PMT = $250,000
N = 5
I%YR = 10
P/YR = 1
PV = $1,042,466 Approach to the Problem Now, assuming 10% annual compounding, what monthly payments will be required for you to have $1,042,466 at time 30? Approach to the Problem
• Using your calculator,
Mode = END
P/YR = 1 N = 360
I%YR = 0.8333
FV = $1,042,466
PMT = $461.17 So, you would have to place $461.17 in your retirement account, which earns 10% annually, at the end of each of the next 360 months to finance the 5year world tour. HOW DOES IT APPLY TO YOU? Suppose you are 22 years old. If you plan to retire at 65, how much do you need to save every month to have $2,000,000. Assume you can earn 12%.
N=516, I/Yr = 1, FV = 2,000,000, then…
Solve for PMT = $118.51 HOW DOES IT APPLY TO YOU? But, suppose you wait until you are 35. How much must you save to reach the same goal?
With N = 360, PMT = $572.25
What if you wait until you are 45 or 55?
PMT (age 45) = $2,021.72
PMT (age 55) = $8,694.19
MORAL? Start saving early! What is a Bond? Longterm (multiyear) loan to a corporation or governmental entity
Considered a legal obligation of the borrower
Defined by loan covenants
Coupon rate is fixed for the duration of the bond
Bonds may trade at any price after they are issued Bond Computation Bonds pay interest (called the “coupon rate”) usually semiannually
Let’s assume 8% coupon paid at end of each year on the par value of a $10,000 bond.
Maturity is 10 years
At this time, the $10,000 is paid back.
If your required rate of return on the bond is 9%, what would you pay for this bond? Bond Computation
0 1 2 P? 800 800 3 4 5 6 7 8 9 10 800 800
800 800
800 800
800 800
의의 의의 의의의의의 의의의의
10,000
8% coupon means you receive $10,000 x .08 = $800 at end of each year
N = 10 years
I = 9 (NOT the 8% coupon rate!)
PV of coupon payments = $5,134 (8000 의 의의의의 )
You also receive the $10,000 in 10 years
N=10, I=9, FV=10,000
PV of principle paid in 10 years = $4,224 < 의의의 1 의의의의 의의 4224 의 의
의)
Total PV = $5134 + $4224 = $9,358
Note: many calculators do this in one step, not two, so you can enter N=10, i=9, FV=10,000, PMT=800; PV = $9,358 Job Search Minute:
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Develop a list of thoughtful questions. Prepare for openended introductory questions! Reconfirm interview details: time, location, etc. Check your appearance carefully. Allow plenty of time to get to the interview. Ending Thought
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 Fall '11
 JimBrau
 Compounding, December 25, Multiple Step Problem—Step

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