1. PowerPoint® presentation by
Fundamental Financial Accounting Concepts Third Edition by Edmonds, McNair, Milam, Olds
PowerPoint® presentation by
J. Lawrence Bergin

2. Present and Future Values used in Accounting for Debt Transactions
Chapter 10 - Appendix
Present and Future Values used in Accounting for Debt Transactions
LOANS & BONDS 1

3. Chapter 10 - Appendix Topics:
Introduction to Present Value and Future Value - Basic Principles
- Using P.V. to calculate loan payments
- Using F.V. to calculate Bond Sinking Fund payments
- Using P.V. to calculate a Bond’s selling price
The Effective Interest Method of Premium and Discount Amortization
Bonds sold with Accrued Interest.

4. Present Value - Key Concept
The longer you have to wait to receive your money, the less it is worth in terms of today’s money This is called the Time Value of Money.
Why?
If you had the money today you could be investing it and earning a return on it.
Today
Future

5. The Time Value of Money and Investment Strategy
Business (and many personal) investments span several years. Therefore, the time value of money is an important consideration.
Other things being equal, investments that promise returns faster are usually preferable to investments that promise returns later.

6. Future Value of a single deposit
If you invested $10,000 today in an investment that promises a 10% annual return over the next three years, how much would the investment be worth at the end of the three years?
Deposit $10,000
+ Year 1 interest
Bal. end yr. 1/beg. Yr. 2
+ Year 2 interest
Bal. end yr. 2/beg. Yr. 3
+ Year 3 interest
Balance at end of Yr. 3
1,000 (10,000 x .10)

7. Future Value of a single deposit
If you invested $10,000 today in an investment that promises a 10% annual return over the next three years, how much would the investment be worth at the end of the three years?
This is called COMPOUND Interest. We are earning interest on BOTH the original deposit AND all previously earned interest that was left in the investment.
Deposit $10,000
+ Year 1 interest
Bal. end yr. 1/beg. Yr. 2
+ Year 2 interest
Bal. end yr. 2/beg. Yr. 3
+ Year 3 interest
Balance at end of Yr. 3
1,000 (10,000 x .10)
11,000
1,100 (11,000 x .10)

8. Future Value of a single deposit
If you invested $10,000 today in an investment that promises a 10% annual return over the next three years, how much would the investment be worth at the end of the three years?
Deposit $10,000
+ Year 1 interest
Bal. end yr. 1/beg. Yr. 2
+ Year 2 interest
Bal. end yr. 2/beg. Yr. 3
+ Year 3 interest
Balance at end of Yr. 3
1,000 (10,000 x .10)
11,000
1,100 (11,000 x .10)
12,100
1,210 (12,100 x .10)

9. Future Value of a single deposit
If you invested $10,000 today in an investment that promises a 10% annual return over the next three years, how much would the investment be worth at the end of the three years?
Deposit $10,000
+ Year 1 interest
Bal. end yr. 1/beg. Yr. 2
+ Year 2 interest
Bal. end yr. 2/beg. Yr. 3
+ Year 3 interest
Balance at end of Yr. 3
1,000 (10,000 x .10)
11,000
1,100 (11,000 x .10)
12,100
1,210 (12,100 x .10)
$13,310

10. Future Value of a single deposit
If you invested $10,000 today in an investment that promises a 10% annual return over the next three years, how much would the investment be worth at the end of the three years? A: $13,310
The same answer can be calculated easier by using the Future Value tables on the next slide.
Future Value tables show the future value factor for various rates of return (interest %) and various lengths (periods) of the investment.
The factor is the amount that $1 would accumulate to in the future.

11. Future Value Tables The 10%, three year FV factor is 1.33100.
What does this mean?
If $1 is deposited today (the present) in an account that earns 10% annual interest for three years, then the account will have a balance of $1.33 (rounded) at the end of the third year (in the future).
But, we invested $10,000. How much is in our account?
$10,000 one-time deposit X FV factor = $13,310

12. Future Value of an Ordinary Annuity
If you invested $1,000 at the END of EACH of the next 3 years in an investment that promises a 10% annual return, how much would the investment be worth at the end of the three years?
A: $3,310
Beg. Balance $
+ Year 1 interest
+ Deposit at end of Yr ,000
Bal. end Yr. 1/beg. Yr $ 1,000
+ Year 2 interest
+ Deposit at end of Yr. 2
Bal. end Yr. 2/beg. Yr. 3
+ Year 3 interest
+ Deposit at end of Yr. 3
Balance at end of Yr. 3
100 (1,000 x .10)
1,000
$2,100
210 (2,100 x .10)
1,000
$3,310

13. Future Value of an Ordinary Annuity
What is an Ordinary Annuity?
Annuity
An equal amount of receipt or payment each period for several periods.
Ordinary
Payments/Receipts occur at the END of each period.
Annuity Due or Annuity in Advance
Payments/Receipts occur at the BEGINNING of each period.
There are only Ordinary Annuity Tables in your text, so all ANNUITY examples assume end of period payments/receipts.

14. Future Value Tables The 10%, three year FV annuity factor is 3.31000.
What does this mean?
If $1 is deposited at the end of each of the next 3 years in an account that earns 10% annual interest, then the account will have a balance of $3.31 at the end of the third year (in the future).
But, we invested $1,000. How much is in our account?
$1,000 per yr. X FV ord. annuity factor = $3,310

15. Present Value of Single Amount Table
APPLICATION:
The Future amount is known. We want to know the present amount. There is only one payment or receipt involved.
EXAMPLE:
How much must you deposit today (the “present”) in order to have $13,310 in your account at the end of three years (the “future”)? Your account pays 10% interest compounded annually.
SOLUTION:
There is only ONE deposit, so this is NOT an annuity. It is a single amount. The rate is 10% per period.
Look up the Present Value of $1 factor for 10%, 3 years.

16. Present Value Tables
Desired balance in 3 yrs. X 10%, 3 period PV factor.
$13, X =
$9,999.94
Recall the FV of $1 example done earlier. We deposited $10,000 on day 1 and showed that the account would accumulate to $13,310 in three years.
The Present Value application goes in the opposite direction. The difference between $10,000 and 9, is due to the rounding in the table factors.

17. Present Value of Ordinary Annuity Table
APPLICATION:
The Future amount is known. We want to know the present amount. A series of equal payments or receipts at the end of each period is involved.
EXAMPLE:
How much would you be willing to pay today (the present) for an investment that would pay you $1,000 at the end of each of the next three years? You have other investment opportunities that can earn you 10% compounded annually.
SOLUTION:
There are three $1,000 receipts, so this is an annuity. The rate is 10% per period (the best alternative use).
Look up the PV Ordinary Annuity factor for 10%, 3 years.

18. Present Value Tables Solution:
$1,000 annual recpt. x PV ord. ann. factor, 10%, 3 periods.
$1, x =
$2,486.85
If you pay $2, for the investment you would earn a 10% annual return on the investment.

19. Using Present Value to calculate Loan Payments
Early in Chapter 10 we calculated a loan amortization schedule for this ABC Co. loan.
ABC Co. signed a $100,000, 3 yr. Promissory Note which carried an 8% annual interest rate. Payments are to be made annually on December 31 of each year for $38,
Note
Question: How was the $38, payment calculated? 50

20. Using Present Value to Calculate Loan Payments
$ amount borrowed today (“the present”)
Payment =
PV Ordinary Annuity Factor*
*END of year payments
$ 100,000
Annual Payment =
PV Ordinary Annuity Factor*

21. Present Value Tables Solution: $100,000 borrowed today Payment =
PV Ordinary Annuity, 8%, 3 periods
$100,000
Payment = = $38, (rounded)

22. Using Present Value to calculate Home Mortgage Payments
You just purchased a home for $150,000.
You make a $15,000 down payment and take out a 30 year, % mortgage for the $135,000 balance due.
MONTHLY payments are required. Each payment includes principal and interest.
Question: How much are the monthly payments? 50

23. Using Present Value to calculate Home Mortgage Payments
Question: How much are the monthly payments on the $135,000, 12%, 30 year mortgage?
The PV and FV tables are based on ANNUAL compounding; one payment/receipt per year. So, if there is more than one payment or receipt in a year, we have to make an adjustment to the periods and rate used in the Tables.
ADJUSTMENT:
Divide the annual rate by the number of Payments/Receipts in a year.
12% divided by 12 monthly payments = 1% per month
Multiply the # of years by the # of Payments/Receipts in a year.
30 years X 12 payments per year = 360 payments in loan 50

24. Present Value - Ordinary Annuity Table
Monthly Mortgage Payments:
$135,000 borrowed
Payment =
PV factor
= $1,388.63

25. Using Present Value to calculate Home Mortgage Payments
Question: How much of the first month’s payment is interest on the mortgage? How much of the first 2 months’ payments is a reduction in the loan balance?
Mort. Monthly Interest Principal Mort. Balance
Beg. of Mo. Payment Portion Repayment at End of Month
135, , , $134,961.37
134, , , ,922.35
.01 x $135,000 loan balance = $1, interest for month 1.
$1, payment - $1, interest portion = $38.63 debt paym’t
$135,000 - $38.63 = $134, Mort. Balance at end of month 1.
.01 x $134, loan bal. = $1, Interest for month 2. 50

26. Using Present Value to calculate Home Mortgage Payments
Question 1: How much will you pay for this $150,000 house over the 30 years?
Q 2: How much INTEREST will you pay?
Answer #1:
360 payments x $1, = $499,906.80
+ Downpayment = ,000.00
Total paid $514,906.80
Answer #2:
$499, payments - $135,000 Mortgage = $364,906.80
Total Interest 50

27. Using Future Values to calculate Bond Sinking Fund Payments
On the maturity date, this fund must have a balance equal to $100,000 which is the face amount of the bonds that must be repaid to the bondholders on that date. The sinking fund Trustee predicts that the investments in the fund will earn 8% annually over the three years.
How much does the Blimp Corp. have to deposit in a Bond Sinking Fund at the end of each of the three years of the bond term?
$100,000 (desired FUTURE amount)
Required fund deposit =
FV Ord. Annuity, 8%, 3 years

28. Future Value Tables Solution: $100,000 (future amount needed)
Annual deposit =
(FV Ord. Annuity, 8%, 3 periods)
= $30,803.35

29. Calculating Payments or Receipts:
When do we use FV vs. PV?
Why did we use PV to calculate the Mortgage payments, but FV to calculate the Bond Sinking Fund payments?
Mortgage: We know the amount borrowed TODAY (ie, the “present”). Use PV.
Sinking Fund: The known amount is a FUTURE amount (ie, the amount we want to ACCUMULATE by a date three years in the FUTURE). Use FV.

30. Calculating Payments or Receipts: When do we use FV vs. PV?
Never mix PV amounts with FV factors or FV amounts with PV factors.
If the numerator is a Present $ amount divide by a PV factor.
If the numerator is a Future $ amount divide by a FV factor.

31. Calculating the Bond Selling Price
Recall that the Blimp Corp. bonds were issued at % of the $100,000 face amount.
These bonds have a 10% annual stated rate, but other similar risk investments were only yielding an 8% annual return. So, investors want our bond, which pushes up its price. How far? Just enough so that the investors’ return will only be 8% even though the bonds pay 10% cash interest.

32. Calculating the Bond Selling Price
The Bond Selling Price is the Present Value (because the investor must buy the bonds today, the “present”) of everything the investor will receive from this investment over the life of the bonds. The market interest rate demanded by investors is used for the PV calculations.

33. Calculating the Bond Selling Price What does the investor get back?
Cash interest each six months for 3 years, and repayment of the face amount at the end of the third year.
Remember, the interest is paid semi-annually, so we have to adjust the ANNUAL rates.
Stated rate 10% annually = 5% for 6 months
Market rate 8% annually = 4% for 6 months
3 years = six, 6-month interest periods

34. Present Value Tables Bond Selling Price:
PV of Principal (once, at end of yr. 3)
$100, X = $ 79,032
+PV of Cash Interest
$ X =
ISSUE PRICE to yield 8% annually = $

35. Present Value Tables Cash Interest = Bond Selling Price:
5% stated x Face
Bond Selling Price:
PV of Principal (once, at end of yr. 3)
$100, X = $ 79,032
+PV of Cash Interest ($5,000 each 6 months)
$ 5, X = ,211
ISSUE PRICE to yield 8% annually = $105,243
$105,243/$100,000 = = %

36. GAAP requires the use of the Effective Interest Method.
Effective Interest Method of Bond Premium/Discount Amortization
GAAP requires the use of the Effective Interest Method.
Basic concept: Effective Interest is a constant % of a changing carrying value.
Let’s look at the amortization schedule for the Blimp Corp. bonds.

37. Effective Interest Method of Bond Premium Amortization
.04 x $105,243 = $4,210 Effective Interest Exp. for the first interest period.
.04 x $104,453 = $4,178 effective Interest Exp. For the second interest period.

38. Effective Interest Method of Bond Premium Amortization
Note that when there is a premium the Bond Carrying Value starts at the Isuue Price and gradually decreases to the face value at the end.

39. Effective Interest Method of Bond Premium Amortization
Question: What is the Total Bond Liability to be reported on the 12/31/05 balance sheet?
Answer: $101,887 = the Carrying Value on that date.

40. Effective Interest Method of Bond Premium/Discount Amortization
Journal Entries:
Issue Date:
Cash ,243
Premium on Bonds ,243
Bonds Payable-face 100,000
First Interest date, 6/30/04:
Bond Interest Expense ,210
Premium on Bonds
Cash ,000
Effective Interest Method of Bond Premium/Discount Amortization

41. Effective Interest Amortization of a Discount
On Jan. 2, 2004, CeeDees Corp. sells $100,000 in bonds having a stated rate of 7% annually. The bonds mature in 3 years, and interest is paid semi-annually. The market rate is 10% annually.
Present Value analysis shows that these bonds would be issued for $92,386. 17

42. Effective Interest Method of Bond Discount Amortization
.05 x $92,386 = $4,619 Effective Interest Exp. for the first interest period.
.05 x $93,505 = $4,675 effective Interest Exp. for the second interest period.

43. Effective Interest Method of Bond Discount Amortization
Note that when there is a discount the Bond Carrying Value starts at the Issue Price and gradually INCREASES to the face amount at maturity.

44. Effective Interest Method of Bond Discount Amortization
Journal Entries:
Issue Date:
Cash ,386
Discount on Bonds ,614
Bonds Payable-face 100,000
First Interest date, 6/30/04:
Bond Interest Expense
Discount on Bonds Cash
Effective Interest Method of Bond Discount Amortization

45. Effective Interest Method of Bond Discount Amortization
Journal Entries:
Issue Date:
Cash ,386
Discount on Bonds ,614
Bonds Payable-face 100,000
First Interest date, 6/30/04:
Bond Interest Expense ,619
Discount on Bonds ,119 Cash ,500
Effective Interest Method of Bond Discount Amortization

46. Amortization of Premiums and Discounts
Straight-line amortization:
Interest Expense is the same for each period.
Effective Interest amortization:
Interest Expense is different each period because it is a % of the Carrying Value which is changing each period. 17

47. Accrued Interest
How come we both got checks from ABC Co. for the SAME amount of interest. I’ve owned my bonds for 6 months. You only bought yours 2 months ago?
That’s because I had to pay 4 months of accrued interest when I bought my bonds.

48. Accrued Interest
When bonds are sold between interest payment dates the purchaser must pay the company the interest that has accrued on the bonds since the last interest date.
On the next interest date the bondholder gets a check for the full six months of interest. Part of this cash is for the period of time the investor has held the bonds. The rest is a “refund” of the accrued interest paid when the bonds were purchased.

49. Accrued Interest Example:
ABC Co. was authorized to issue $100,000 of 12% bonds on July 1, Interest is payable on June 30th and December 31st of each year.
Kristin purchased a $1,000 face amount bond on November 1, 2004 at 100 plus accrued interest. How much did she pay?
$1,000 x 100% = $1,000
+ Accrued interest: (July-Oct.) = ($1,000 x .12 x 4/12)
Total paid $1,040

50. Accrued Interest $1,000 x 100% = $1,000
+ Accrued int: (July-Oct.) = ($1,000 x .12 x 4/12)
Total paid $1,040
ABC Co. journal entry on Nov. 1st:
Cash $1,040
Bond Payable-face $1,000
Interest Payable
The Accrued Interest is a LIABILITY for ABC because they will have to refund this amount to the bondholder on the next interest payment date.
ABC Co. journal entry when Kristin is paid on Dec. 31st:
Bond Interest Exp. (for 2 mo.) $
Interest Payable
Cash $

51. Accrued Interest - Horizontal Model
ABC Co. journal entry on Nov. 1st:
Cash $1,040
Bond Payable-face $1,000
Interest Payable
ABC Co. journal entry when Kristin is paid on Dec. 31st:
Bond Interest Exp. (for 2 mo.) $
Interest Payable
Cash $
Nov , , ,040FA
Dec (60) (40) (20) (20) (60)OA
Jun (60) (60) (60) (60)OA

52. Chapter 10
The End