Copyright © 2007 Prentice-Hall. All rights reserved 1 The Time Value of Money: Present Value of a...

Copyright © 2007 Prentice-Hall. All rights reserved 1

The Time Value of Money: The Time Value of Money: Present Value of a Bond and Present Value of a Bond and Effective Interest AmortizationEffective Interest Amortization

The Time Value of Money: The Time Value of Money: Present Value of a Bond and Present Value of a Bond and Effective Interest AmortizationEffective Interest Amortization

Appendix to Chapter 15


Time Value of MoneyTime Value of MoneyTime Value of MoneyTime Value of Money

• Interest – cost of using money

• Borrower – interest expense

• Lender – interest revenue


Present ValuePresent ValuePresent ValuePresent Value

1 2 3 4 5 6

$100,000????



Depends on three factors:

1. Dollar amounts to be paid in the future

2. Length of time between investment and future payment

3. Interest rate

Computing present value is called discounting


Future ValueFuture ValueFuture ValueFuture Value

1 yr

?????$1,000

10%

Interest = $1,000 x .10 = $100Principal = 1,000Future value $1,100

OrFuture value = 1,000 x 1.10 = $1,100

PresentValue

FutureValue

If you invest $1,000 today and earn 10% interest, you will have $1,100 at the end of one year



1 yr

????? $1,100

10%

Present value x 1.10 = $1,100Present value = $1,100/1.10Present value = $1,000

PresentValue

FutureValue

Present value is just taking the interest out. If you can earn 10% interest and want to receive $1,100 in one year, you will have to invest $1,000 today



1 yr

????? $1,100

10%

Present value x 1.10 = $1,100Present value = $1,100/1.10Present value = $1,000

PresentValue

FutureValue

2 yrs

Present value x 1.10 = $1,000Present value = $1,000/1.10Present value = $909

What if you would like to receive $1,100 in TWO years instead. How much would you have to invest today?

1,000


Present Value of $1 TablePresent Value of $1 TablePresent Value of $1 TablePresent Value of $1 Table

1 yr

????? $1,100

10%PresentValue

FutureValue

2 yrs

Present Value = Future Value x Table Factor = $1,100 x 0.826 = $909

Look on the Present Value of $1 table. Find the table factor where the percentage rate and the number of periods intersect


Present Value of an AnnuityPresent Value of an AnnuityPresent Value of an AnnuityPresent Value of an Annuity

1 yr

????? $1,100

10%PresentValue

FutureValue

2 yrs

Present Value of $1,100 in one year:$1,100 x 0.909 = $1,000

$1,100

Present Value of $1,100 in two years:$1,100 x 0.826 = $909

$1,000 + $909 = $1,909

Now, what if you would like to receive $1,100 at the end of EACH year for 2 years? How much would you have to invest today?

If you invest $1,909 today and earn 10% interest compounded annually, you can withdraw $1,100 at the end of each year for two yearsThis type of cash flow is called an annuity – equal cash flows over equal periods of time at a constant rate of interest


Present Value of an Annuity TablePresent Value of an Annuity TablePresent Value of an Annuity TablePresent Value of an Annuity Table

1 yr

????? $1,100

10%PresentValue

FutureValue

2 yrs

$1,100

Present Value of an Annuity = Payments x Table Factor = $1,100 x 1.736 = $1,909.60


Present Value of a BondPresent Value of a BondPresent Value of a BondPresent Value of a Bond

1 2 3 4 5 6

$100,000

One type of cash flow is the principal that will be received when the bond matures. (Present value of $1)


Present Value of a BondPresent Value of a BondPresent Value of a BondPresent Value of a Bond

1 2 3 4 5 6

$4,500$4,500$4,500 $4,500 $4,500 $4,500

Another type of cash flow is the interest payments that will be received every six months. (Present value of an annuity)


Present Value of a BondPresent Value of a BondP15A-2aP15A-2a

Present Value of a BondPresent Value of a BondP15A-2aP15A-2a

• What are the future cash flows?– $88,000 lump sum (present value of $1)– $5,280 interest payments based on stated rate

(present value of annuity)

• What is the market rate?– 6% (12%/2)

• How many times is interest compounded?– 20 (10 years x 2)


Present Value of a BondPresent Value of a BondP15A-2a.P15A-2a.

Present Value of a BondPresent Value of a BondP15A-2a.P15A-2a.

Present value of $88,000 to be receivedin 20 interest payment periods at 6% interest $88,000 x 0.312 $27,456

Present value of annuity of $5,280 to be received 20 times at 6% interest$5,280 x 11.470 60,562

Total present value $88,018

Use the present value of annuity table. Find the factor where the number of interest

payment periods = 20 (twice a year for 10 years) and the interest rate = 6% (12%/2

times a year)

This is the amount an investor would be willing to pay in order to receive both

the principal and interest payments in the future

Use the present value of 1 table. Find the factor where the number of interest payment periods = 20 (twice a year for 10 years) and the interest rate = 6% (12%/2 times a year)

Note: the present value should be $88,000.

The difference of $18 is due to rounding to

three decimal places in the present value tables


Present Value of a BondPresent Value of a BondP15A-2bP15A-2b













Present Value of a BondPresent Value of a BondP15A-2cP15A-2c













Effective-Interest AmortizationEffective-Interest AmortizationEffective-Interest AmortizationEffective-Interest Amortization

• Preferred method over straight-line • When amounts are materially different, GAAP

requires effective-interest method • Allocates bond interest expense over life of

bonds in a way that yields constant rate of interest


Effective-Interest MethodEffective-Interest MethodEffective-Interest MethodEffective-Interest Method

• Interest expense = Carrying value x market rate of interest

• Cash = Face x stated rate of interest• Difference is amount of premium or discount to

amortize


Amortization TableAmortization TableAmortization TableAmortization Table

Amortization Table

Semiannual Interest Period

(a) Interest

Payment

(b) Interest Expense

(b-a) Discount

Amortization

Discount Account Balance

Bond Carrying Amount


P15A-5P15A-5P15A-5P15A-5

1. $200,000 x 1.10 = $220,000

2. Interest payments = $200,000 x 4% = $8,000


P15A-5P15A-5P15A-5P15A-5 Amortization Table


(a) Interest

Payment


(a-b) Premium

Amortization

Premium Account Balance


$220,0005/31/08 $20,000

$8,000 $6,60011/30/08

5/31/09

$1,400 18,600 218,600

8,000 6,558 1,442 17,158 217,158

Face x Stated Rate

Carrying Value x Market Rate


P15A-5P15A-5P15A-5P15A-5

GENERAL JOURNAL

DATE DESCRIPTION REF DEBIT CREDIT

May 31 Cash 220,000Premium on Bonds Payable 20,000

Bonds Payable 200,000

Nov 30 Interest Expense 6,600Premium on Bonds Payable 1,400

Cash 8,000


P15A-5P15A-5P15A-5P15A-5

GENERAL JOURNAL


2009

May 31 Interest Expense 6,558Premium on Bonds Payable 1,442

Cash 8,000


P15A-8P15A-8P15A-8P15A-8





P15A-8P15A-8P15A-8P15A-8 Amortization Table


(a) Interest

Payment


(b-a) Discount

Amortization

Discount Account Balance


$379,45512/31/01 $20,545

$14,500 $15,1786/30/02

12/31/02

$678 19,867 380,133

14,500 15,205 705 19,162 380,838


P15A-8P15A-8P15A-8P15A-8

GENERAL JOURNAL


Dec 31 Cash 379,455Discount on Bonds Payable 20,545

Bonds Payable 400,0002002

Jun 30 Interest Expense 15,178Discount on Bonds Payable 678Cash 14,500


P15A-8P15A-8P15A-8P15A-8

GENERAL JOURNAL


2002

Dec 31 Interest Expense 15,205Discount on Bonds Payable 705Cash 14,500


End of Chapter 15 AppendixEnd of Chapter 15 AppendixEnd of Chapter 15 AppendixEnd of Chapter 15 Appendix

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