Appendix C PowerPoint

8/10/2019 Appendix C PowerPoint

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Appendix C BACK OF TEXTBOOK

Hint: Not in back of Chapter 10!

Time Value of Money$$$$


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Its about Interest ! And time and money

And No, you

dont haveto beEinstein toget this!


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Time Value of Money.

The SAME amount of Money is worth moreTODAY, then in the FUTURE.

Why? Because you could take that money and invest

it and earn interest on it.

How is interest calculated?


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Time Value of Money. . . .

What is Simple Interest?You borrow $5,000

For 2 yearsAt 12%

How much interest is earned the first year?How much interest is earned the second year?


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Simple Interest

You borrow $5,000For 2 years

At 12%$5,000 * 12% = 600$5,000 * 12% = 600

$1,200Ending Balance (with interest) = $6,200


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Simple Interest

You borrow $1,000For 3 yearsAt 9%$1,000 * 9% = 90$1,000 * 9% = 90$1,000 * 9% = 90

$180Ending Balance (with interest) = $1,180


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Time Value of Money. . . . youpractice

What is Compound Interest?You borrow $1,000, For 3 years, At 9%

How much interest is earned the first year?

But the next year, since you havent been paid,

you will earn interest on the principal plus theunpaid interest And the next year(s)you earn interest on

interest

$90


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Time Value of Money. . . . youpractice

What is Compound Interest?You borrow $1,000

For 3 yearsAt 9%How much interest is earned the first year?

How much interest is earned the second year?How much interest is earned the third year?

First try this on YOUR OWN (use thenotes section of the Course Pack)

and then go to next slide to checkyour work.


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Time Value of Money. . . . What is Compound Interest?You borrow $1,000For 3 yearsAt 9%$1,000 * 9% = 90.00 (then you ADD the interest to

the principal for the second year)$1,090 * 9% = 98.10

$1,188.10 *9%= 106.93$295.03

Ending Balance (with interest) = $1,295.03

Question: Why doyou add the interest

to the second andthird years?


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Why do you add the interest to thesecond and third years?

Because it wont be paid off until the end ofthe third year.

So, during the second and third years, youhave earned interest, but you havent been paid for it yet .

Thus, you earn interest on interest .


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Lets do the SAME exampleusing theTables

If I put $1,000 in an account, what will it be worthin 3 years?

We know Present Value: $1,000 Interest Rate: 9% N = 3 Table ____ Factor: ____ Future Value? _____


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Table 1 Example Future Value of aSingle Amount

If I put $1,000 in an account, what will it be worthin 3 years?

We know Present Value: $1,000 Interest Rate: 9% N = 3 Table 1 Factor: 1.29503 Future Value? $1,000 * 1.29503 = $1,295.03


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You Practice FV of a single amount

---------------------------------------------------- Today 18 years later

PV = $20,000 FV= ???I = 6%

Your grandma gave your parents $20,000 when you were born,for College 18 years later. What is the future value of

$20,000??

Use Table 1 to get the factor.First, try this on YOUR OWN andthen See Page C5


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You Practice FV of a single amount

---------------------------------------------------- Today 18 years later

PV = $20,000 FV= ???

I = 6%Your grandma gave your parents $20,000 when you were born,

for College 18 years later. What is the future value of$20,000??

Using Table 1 factor = 2.85434 * $20,000 =$57,086.80


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What about Annuities?

Question: What are annuities?


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FV of an Annuity A series of equal dollar amounts are paid or received.

Examples: you own a CD of $1,000 paying 6% interest per year = $60/year.

The $60 is an annuity. You are buying a car and your payments are $350 each month. You are saving money for a trip to France and put $1,000 into an

interest bearing bank account each December 31 for 3 years.

Note: A CD is a certificate of deposit, a type of savingsaccount earning interest.


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Practice FV of an Annuity -------|-------------|-----------|-----------|--- Today 25,000 25,000 25,000 25,000

PV =n/a FV= ???I = 6%Payments = $25,000A company is saving $25,000 per year for the purpose of

replacing a printing press.In four years, what will be the balance in this account?

Use Table 2 to get the factor. First, try this on YOUR OWN andthen See Page C7


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Practice FV of an Annuity -------|-------------|-----------|-----------|--- Today 25,000 25,000 25,000 25,000

PV =n/a FV= ???

I = 6%Payments = $25,000

A company is saving $25,000 per year for the purpose ofreplacing a printing press.

In four years, what will be the balance in this accounts?Using Table 2 factor = 4.37462 * $25,000 =$109,365.50


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Present Value: whats it worth now?

Single Amount Example: What do I have to put into thebank NOW, to have $1,000 in 1 year? assume 10%interest rate

We know: Present Value: ???? (what we are solving for) Interest Rate: 10% N = 1 Table 3 Factor: 0.90909 Future Value? $1,000 PV = $1,000 * 0.90909 = $909.09


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Winning the lottery.

You win the lottery and have to choosebetween receiving $10,000 in three years orreceiving the discounted amount today?

Solve for present value Given I = 8% N = 3

PV = ?????

First, try this on YOUR OWN andthen See Page C10


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Winning the lottery. You win the lottery and have to choose

between receiving $10,000 in three years orreceiving the discounted amount today?

Solve for present value Given I = 8% N = 3


First, try this on YOUR OWN andthen See Page C10


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What about Present Value of anannuity?

For example, instead of making payments, Ill just pay Cash NOW.


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Present Value: whats it worth now?

Annuity Example: "I'm making payments of $1,000for the next 3 years. If I chose NOT to pay on time,but pay in CASH, what would they charge me?

We know Present Value: _____ Interest Rate: 10% N = 3 Table ____ Factor: ____ Payments: $1,000

Note: This isa good onefor knowingwhen you buya car. If youhave themoneyNOW


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Present Value- Annuity

$1,000 * 2.48686 = $2.486.86

The present value is Lower The $1,000 + 1,000 + 1,000 = 3,000 worth of

payments is discounted to $2,487 (rounded).

So.you get a discount of $ 513 if you pay NOW,because you dont have to pay the interest of 10%


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Present Value- Annuity -practice ---------|-----------|-----------|-----------|-----------| Today 6,000 6,000 6,000 6,000 6,000

PV =?? FV= ???

I = 12%Payments = $6,000 Kildare Co. signs a lease (lease to own) requiring annual

payments of $6,000. If you pay the lease off upfront, howmuch would you pay?

Solve for present value The ($6,000 * 5 years ) = $30,000 worth of payments is

discounted to ____________ First, try this on YOUR OWN andthen See Page C12


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Present Value- Annuity -practice -------|-------------|-----------|-----------|---------| Today 6,000 6,000 6,000 6,000 6,000

PV =?? FV= ???I = 12%Kildare Co. signs a lease (lease to own) requiring 5 annual

payments of $6,000. If you pay the lease off upfront, howmuch would you pay?



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Appendix C applications -Bonds In Chapter 10, you studied Bonds. Bonds are issued

at Face Value, or Discount or Premium We know

The Bond Selling Price varies depending on Market InterestRate:

Face Value (Market interest rate = Bond contract rate) Discounted from Face Value (Market interest rate > Bond contract

rate)

Premium higher than Face Value (Market interest rate < Bondcontract rate)

Question: How is the selling price of a bondcalculated?


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Appendix C applications -Bonds

NEED TO KNOW: Bond Interest Rate (the contract rate) Face Value of Bond Issuance ($1,000 x number of bonds

sold) Bond Interest Payments (Face Value of Bond Issuance x

semi annual bond interest (contract) rate Market Interest Rate


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The Cash Flow of Bonds

Lets say you have 1,000 bonds.

Review: What is the face value of a single bond?

Stop and Answer before checking thenext slide


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Lets say you have 1,000 bonds. that you sell atFace Value.

Review: What is the face value of a single bond?

$1,000

Review: What is the face value of the entirebond issuance of 1,000 bonds?


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Lets say you have 1,000 bonds that you sell atFace Value.

Review: What is the face value of a bond?

$1,000

Review: What is the face value of the entirebond issuance of 1,000 bonds?

$1,000 * 1,000 bonds =$100,000


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The Cash Flow of Bonds Bond Interest Rate (the contract rate) = 10%

Face Value of Bond Issuance ($1,000 * number of bondssold) = $100,000

Bond Interest Payments (Face Value of Bond Issuance *semi annual bond interest (contract) rate =

($100,000 * 10%)/2 = $10,000/2 = $5,000 Years

=5


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The Cash Flow of Bonds - cont Bond Interest Rate (the contract rate) = 10%

Face Value of Bond Issuance ($1,000 * number of bonds sold) = $100,000

Bond Interest Payments (Face Value of Bond Issuance * semi annual bond interest (contract) rate =($100,000 * 10%)/2 = $10,000/2 = $5,000

Years = 5

There are TWO CASH OUTFLOWS with Bonds Interest Payment every six months = $5,000 Payment of principal at the end of the bond = $100,000

You have to calculate the Present Value of eachcash flow to get the total Market Price of the Bondat the Market Interest Rate


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Cash Flow of the Principal After 5 years. The company must pay back the

bond, at FACE VALUE. I (interest), FV (future value), N (periods)

10%, $100,000, 5 years => 10 periods----|----|----|----|----|----|----|----|----|----|---

$100,000

$100,000 is the principal of the loan.The $100,000 is a single amount. We pay back the Bond, in the

future, at FACE Value, regardless of what what the SellingPrice of the Bond was.

Fill in the table on your Course pack,then See Page C13


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Cash Flow of Interest Paid Im LOCKED IN WITH:

I (interest), FV (future value), N (periods)10%, $100,000, 5 years => 10 periods

----|----|----|----|----|----|----|----|----|----|--- $5,000 $5,000 $5,000 $5,000 $5,000 $5,000 $5,000 $5,000 $5,000 $5,000

$5,000 will be paid out in interest, every six months for 10 periods,over the life of the bond, for a total of $50,000.

The $5,000 is an annuity. We use the Bond contract rate to calculatethe $5,000. It doesnt change, regardless of the Selling Price ofthe Bond.


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Present Value of Bonds -Face Value If contract rate is 10% and market is 10%. . . . You can

sell the Bond at face value . Proof:---------------------------------------------

---------------------------------------------

$5,000 $5,000 $5,000 $5,000 $5,000$5,000 $5,000 $5,000 $5,000 $5,000

Total = $100,000

I market = 5%, table 4, factor = 7.72173 x $5,000 = $38,609

I market

= 5%, table 3, factor =.61391 x $100,000 = $61,391

$61,391 + 38,609 = $100,000 would be Issue Price or100


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Present Value of Bonds -Discount If contract rate is 10% and market is 12%. . . . You can

sell the Bond at discount . Proof:---------------------------------------------

---------------------------------------------

$5,000 $5,000 $5,000 $5,000 $5,000

$5,000 $5,000 $5,000 $5,000 $5,000

Total = $92,639

I market = 6% , table 4, factor = 7.36009 x $5,000 = $36,800

I market = 6% , table 3, factor =.55839 x $100,000 = $55,839

$ 55,839 + 36,800 = $92,639 would be Issue Price or92.639


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Present Value of Bonds -Premium If contract rate is 10% and market is 8%. . . . You can

sell the Bond at premium . Proof:---------------------------------------------

---------------------------------------------

$5,000 $5,000 $5,000 $5,000 $5,000

$5,000 $5,000 $5,000 $5,000 $5,000

Total = $108,111

I market = 4% , table 4, factor = 8.11090 x $5,000 = $40,555

I market = 4% , table 3, factor =.67556 x $100,000 = $67,556

$ 67,556 + 40,555 = $108.111 would be Issue Priceor 108.111


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Appendix C You are responsible for pages C1-C14


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End of Appendix C Good Bye and Good Luck!


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Documents

Appendix C PowerPoint