1. Accounting Fundamentals Dr. Yan Xiong Department of Accountancy CSU Sacramento The lecture notes are primarily based on Reimers (2003). 7/11/03

2. Chapter 8: Financing with Debt Agenda  Long-term Notes Payable and Mortgage  Time Value of Money  Bonds Payable

3. Agenda t Long-term Notes Payable and Mortgages

4. Business Background Capital structure is the mix of debt and equity used to finance a company. DEBT: Loans Loans from banks, insurance companies, or pension funds are often used when borrowing small amounts of capital. Bonds Bonds are debt securities issued when borrowing large amounts of money. Can be issued by either corporations or governmental units.

5. Notes Payable and Mortgages t When a company borrows money from the bank for longer than a year, the obligation is called a long- term note payable. t A mortgage is a special kind of “note” payable--one issued for property. t These obligations are frequently repaid in equal installments, part of which are repayment of principal and part of which are interest.

6. Example: Borrowing To Buy Land By Using A Mortgage t ABC Co. signed a $100,000, 3 yr. mortgage (for a piece of land) which carried an 8% annual interest rate. Payments are to be made annually on December 31 of each year for $38,803.35. t How would the mortgage be recorded? t What is the amount of the liability ( mortgage payable ) after the first payment is made?

7. Recording the Mortgage t How would the mortgage be recorded in the journal? DateTransaction DebitCredit Jan 1 Land 100,000 Mortgage payable 100,000

8. Example continued... Example continued... t For Yr.1, the outstanding amount borrowed is $100,000 (at 8%), so the interest is: u $8,000 t Payment is $38,803.35, so the amount that will reduce the principal is u $30,803.35 t New outstanding principal amount is u $100,000 - 30,803.35 = $69,196.65

9. Recording The First Payment On A Mortgage t How would the payment on the mortgage be recorded in the journal? DateTransaction DebitCredit Dec 31 Mortgage payable 30,803.35 Interest expense 8,000.00 Cash 38,803.35

10. Amortization Schedule Principle Balance PaymentInterest Reduction in Principle 100,000.0038,803.35 38,803.35 38,803.35 8,000.0030,803.35 69,196.65 5,535.73*33,267.62 *69,196.65 x.08 35,929.03 2,874.32** = 2,874.32 35,929.03 **35,929.03 x.08

11. Agenda t Time Value of Money

12. Time Value of Money t The example of the mortgage demonstrates that money has value over time. t When you borrow $100,000 and pay it back over three years, you have to pay back MORE than $100,000.  Your repayment includes interest--the cost of using someone else ’ s money. t A dollar received today is worth more than a dollar received in the future. t The sooner your money can earn interest, the faster the interest can earn interest.

13. Interest and Compound Interest  Interest is the return you receive for investing your money. You are actually “ lending ” your money, so you are paid for letting someone else use your money. t Compound interest -- is the interest that your investment earns on the interest that your investment previously earned.

14. ? Future Value of a Single Amount How much will today’s dollar be worth in the future? TODAYFUTURE

15. If You Deposit $100 In An Account Earning 6%, How Much Would You Have In The Account After 1 Year? n: i% = 6PV = 100 N = 1 FV = 100 * 1.06 N = 1 FV = 100 * 1.06 PV = FV = PV = FV = 100106 0 1

16. If You Deposit $100 In An Account Earning 6%, How Much Would You Have In The Account After 5 Years? Using a future value table i% = 6PV = 100 n = 5 FV = 100 * ( factor from FV of $1 table, where n = 5) n = 5 FV = 100 * ( factor from FV of $1 table, where n = 5) 0 5 0 5 PV = 100 FV = PV = 100 FV =

17. If You Deposit $100 In An Account Earning 6%, How Much Would You Have In The Account After 5 Years? n: i% = 6PV = 100 N = 1 FV = 100 * 1.3382 N = 1 FV = 100 * 1.3382 0 1 0 1 PV = 100 FV = PV = 100 FV =

18. If You Deposit $100 In An Account Earning 6%, How Much Would You Have In The Account After 5 Years? n: i% = 6PV = 100 N = 1 FV = 100 * ( factor from FV of $1 table, where n = 5) N = 1 FV = 100 * ( factor from FV of $1 table, where n = 5) 0 1 0 1 PV = FV = 133.82 PV = FV = 133.82 100

19. t The previous example had a single payment. Sometimes there is a series of payments. t Annuity: a sequence of equal cash flows, occurring at the end of each period. t When the payments occur at the end of the period, the annuity is also known as an ordinary annuity. t When the payments occur at the beginning of the period, the annuity is called an annuity due. The Value of a Series of Payments

20. What An Annuity Looks Like 01 234

21. t If you borrow money to buy a house or a car, you will pay a stream of equal payments. t That’s an annuity. Example

22. If you invest $1,000 at the end of the next 3 years, at 8%, how much would you have after 3 years? 0 1 2 3 n = 3 i = 8%Pmt. = 1,000 1,000 1,0001,000 Future Value of an Annuity

23. If you invest $1,000 at the end of the next 3 years, at 8%, how much would you have after 3 years? 0 1 2 3 FV A = 1,000 * [value from FV A table, 3yrs. 8%] FV A = 1,000 * 3.2464 = $3,246.40 1,000 1,0001,000 Future Value of an Annuity

24. Future Value of an Ordinary Annuity (Annuity in Arrears) In the previous example, notice that the last payment is deposited on the last day of the last period. That means it doesn’t have time to earn any interest! This type of annuity is called an ordinary annuity, or an annuity in arrears.

25. Future Value of an Annuity Due t Often, when the series of payments applies to money saved, an annuity due is a better description of what happens. t Suppose you decide to save $1,000 each year for three years, starting TODAY!

26. Future Value of an Annuity Due If you invest $1,000 at the beginning of each of the next 3 years, at 8%, how much would you have after 3 years? 0 1 2 3 FV A = 1,000 * [value from FV ADue table, 3yrs. 8%] FV A = 1,000 * 3.50611 = $3,506.11 1,000 1,0001,000 Today Future value

27. How much is $1 received in the future worth today? (COMPOUNDING) Figuring out how much a future amount is worth TODAY is called DISCOUNTING the cash flow. Present Value of a Single Amount ? TODAYFUTURE

28. io i% = 6% N = 1 FV = 100 PV = ?? FV = 100 PV = ?? 0 1 0 1 PV = FV = 100 If you will receive $100 one year from now, what is the PV of that $100 if the relevant interest rate is 6%?

29. PV (1 + 0.06) = 100 (which is the FV) PV = 100 / (1.06) 1 = $94.34 OR PV = FV (PV factor i, n ) PV = 100 (0.9434 ) (from PV of $1 table) PV = $94.34 0 1 PV = 94. 34 FV = 100 If you will receive $100 one year from now, what is the PV of that $100 if the relevant interest rate is 6%?

30. t The previous example had a single payment. Sometimes there is a series of payments. t Annuity: a sequence of equal cash flows, occurring at the end of each period. t When the payments occur at the end of the period, the annuity is also known as an ordinary annuity. The Value of a Series of Payments

31. t Finding the present value of a series of cash flows is called discounting the cash flows. t What is the series of future payments worth today ? 01 234 Present Value of an Annuity

32. i% = 8N = 3 i% = 8N = 3 PMT = 1,000 PV = ?? PMT = 1,000 PV = ?? 0 1 2 3 10001000 1000 10001000 1000 What is the PV of $1,000 at the end of each of the next 3 years, if the interest rate is 8%?

33. PV A = 1,000 (3 yrs., 8% factor from the PVA table) PV A = 1,000 * (2.5771) PV A = $2,577.10 0 1 2 3 10001000 1000 10001000 1000 What is the PV of $1,000 at the end of each of the next 3 years, if the interest rate is 8%? Present Value

34. Agenda t Bonds Payable

35. Characteristics of Bonds Payable t Bonds usually involve the borrowing of a large sum of money, called principal. t The principal is usually paid back as a lump sum at the end of the bond period. t Individual bonds are often denominated with a par value, or face value, of $1,000.

36. t Bonds usually carry a stated rate of interest. t Interest is normally paid semiannually. t Interest is computed as: Interest = Principal × Stated Rate × Time Characteristics of Bonds Payable

37. Measuring Bonds Payable and Interest Expense The selling price of the bond is determined by the market based on the time value of money. The selling price of the bond is determined by the market based on the time value of money. dates of interest payments... principal payment TodayFuture

38. Who Would Buy My Bond? t $1,000, 6% stated rate. t The market rate of interest is 8%. t Who would buy my bond? t Nobody---so I’ll have to sell (issue) it at a discount. t e.g., bondholders would give me something less for the bond.

39. Who Would Buy My Bond? t $1,000, 6% stated rate. t The market rate of interest is 4%. t Who would buy these bonds? t EVERYONE! t So the market will bid up the price of the bond; e.g., I’ll get a little premium for it since it has such good cash flows. t Bondholders will pay more than the face.

40. Determining the Selling Price t Bonds sell at: u “Par” (100% of face value) u less than par (discount) u more than par (premium) t Market rate of interest vs. bond’s stated rate of interest determines the selling price (market price of the bond) t Therefore, if u market % > stated %: Discount u market % < stated %: Premium

41. The time value of money... Selling price of a bond = present value of future cash flows promised by the bonds, discounted using the market rate of interest

42. Finding The Proceeds Of A Bond Issue t To calculate the issue price of a bond, you must find the present value of the cash flows associated with the bond. t First, find the present value of the interest payments using the market rate of interest. Do this by finding the PV of an annuity. t Then, find the present value of the principal payment at the end of the life of the bonds. Do this by finding the PV of a single amount.

43. Selling Bonds -- Example On May 1, 1991, Clock Corp. sells $1,000,000 in bonds having a stated rate of 6% annually. The bonds mature in 10 years, and interest is paid semiannually. The market rate is 8% annually. Determine the proceeds from this bond issue.

44. First, what are the cash flows associated with this bond? t Interest payments of $60,000 (that’s 6% of the $1 million face value) each year for 10 years. AND t A lump sum payment of $1,000,000 (the face amount of the bonds) in 10 years.

45. The PV of the future cash flows = issue price of the bonds t The present value of these cash flows will be the issue price of the bonds. t That is the amount of cash the bondholders are willing to give TODAY to receive these cash flows in the future.

46. Two parts to the cash flows: INTEREST PAYMENTS PV of an ordinary annuity of $60,000 for 10 periods at an interest rate of 8%: Use a calculator or a PV of an annuity table: 60,000 (PV A,, 8%, 10 )= 60,000 (6.7101) = 402,606 402,606 PRINCIPAL PAYMENT PV of a single amount of $1 million ten years in the future at 8%: Use a calculator or a PV of a single amount table: 1,000,000 (PV,, 8%, 10) = 1,000,000 (.46319)= 463,190

47. Selling Bonds -- Example t The sum of the PV of the two cash flows is $865,796. t The bonds would be described as one that sold for “87.” We’ll round to a whole number just to make the example easier to follow. What does that mean? It means the bonds sold for 87% of their par or face value.

48. Selling Bonds -- Example If the bonds sold for 87% of their face value, the proceeds would be approximately $870,000 (rounded) for $1,000,000-face bonds. If the bonds sold for 87% of their face value, the proceeds would be approximately $870,000 (rounded) for $1,000,000-face bonds.

49. Recording Bonds Sold at a Discount t The balance sheet would show the bonds at their face amount minus any discount. t The discount on bonds payable is called a contra-liability, because it is deducted from the liability. t Cash would be recorded for the difference, that is, the proceeds.

50. Recording Bonds Sold at a Discount t How would the issuance of the bonds at a discount be recorded in the journal? DateTransaction DebitCredit May 1 Cash 870,000 Discount on bond payable130,000 Bonds payable 1,000,000

51. Selling Bonds -- Example On May 1, 1991, Magic Inc. sells $1,000,000 in bonds having a stated rate of 9% annually. The bonds mature in 10 years and interest is paid semiannually. The market rate is 8% annually. Determine the issue price of these bonds.

52. Selling Bonds -- Example To figure out the proceeds from the sale, you either have to calculate the present value of the cash flows (using the market rate of interest) OR Be told that the bonds sold at X, a percentage of par (e.g., 104).

53. First, what are the cash flows associated with this bond? t Interest payments of $90,000 (that’s 9% of the $1 million face value) each year for 10 years. AND t A lump sum payment of $1,000,000 (the face amount of the bonds) in 10 years.

54. The PV of the future cash flows = issue price of the bonds t The present value of these cash flows will be the issue price of the bonds. t That is the amount of cash the bondholders are willing to give TODAY to receive these cash flows in the future.

55. Two Parts To The Cash Flows INTEREST PAYMENTS PV of an ordinary annuity of $90,000 for 10 periods at an interest rate of 8%: Use a calculator or a PV of an annuity table: 90,000 (PV A,, 8%, 10 )= 90,000 (6.7101) = $ 603,909 PRINCIPAL PAYMENT PV of a single amount of $1 million ten years in the future at 8%: Use a calculator or a PV of a single amount table: 1,000,000 (PV,, 8%, 10) = 1,000,000 (.46319) = $ 463,190

56. Bonds Issued At A Premium t The total PV of the two cash flows is $1,067,099. This is more than the face, so these bonds are being issued at a premium. t Again, we’ll round the number to make the example easier to follow. Let’s say these bonds were issued at 107, or 107% of par. t That would make the proceeds $1,070,000 (rounded).

57. Recording Bonds Sold at a Premium t How would the issuance of the bonds at a premium be recorded in the journal? DateTransaction DebitCredit May 1 Cash 1,070,000 Premium on bond payable 70,000 Bonds payable 1,000,000

58. Measuring and Recording Interest on Bonds Issued at a Discount t The discount must be amortized over the outstanding life of the bonds. t The discount amortization increases the periodic interest expense for the issuer. t Two methods are commonly used: u Effective-interest amortization u Straight-line amortization

59. t Clock corp. Sold their bonds on May 1, 1991 at 87. The bonds have a 10-year maturity and $30,000 interest is paid semiannually. t Why would the bonds sell for 87? u The market rate of interest was greater than the rate on the face on the date of issue. u So clock corp. Had to offer the bonds at a “discount” to get buyers. Recall the Facts of the Problem

60. t Clock Corp. sold their bonds on May 1, 1991 at 87. The bonds have a 10-year maturity and $30,000 interest is paid semiannually. t Where did the $30,000 come from? u 1,000,000 x.06 x 1/2 u The interest payments are always calculated by the terms and amounts stated on the face of the bonds. Problem, Continued

61. Effective Interest Method For Amortizing A Bond Discount If we prepared a balance sheet on the date of issue, the bond would be reported like this: Bonds Payable $ 1,000,000 less Discount on B/P (130,000) less Discount on B/P (130,000) Net Bonds Payable 870,000 Net Bonds Payable 870,000

62. Effective Interest Method For Amortizing A Bond Discount t The discount is a contra-liability (and is deducted from the face value of the bond to give the “book value.”) t In order to get the book value to equal the face value at maturity, we’ll have to get rid of the balance in the discount account. t Each time we pay interest to our bondholders, we’ll amortize a little of the discount.

63. Effective Interest Method For Amortizing A Bond Discount t Each time we pay interest to our bondholders, we’ll amortize a little of the discount--how much? t On the first interest date, the amount we’ve actually “borrowed” from the bondholders is $870,000. t The market rate at the time we borrowed--the rate we had to pay to get the bondholders to buy our bonds--was 8%. t 870,000 x.08 x 1/2 = 34,800 (This will be the interest expense for the first 6 months.)

64. Effective Interest Amortization of Bond Discount We know the cash payment to the bondholders is $30,000: We know the cash payment to the bondholders is $30,000: 1,000,000 x.06 x 1/2 1,000,000 x.06 x 1/2 par value interest 6-month period par value interest 6-month periodrate

65. Effective Interest Amortization of Bond Discount The difference between the interest expense of $34,800 and the cash payment to the bondholders of $30,000 is the amount of discount amortization. The difference between the interest expense of $34,800 and the cash payment to the bondholders of $30,000 is the amount of discount amortization.$34,800 - 30,000 $ 4,800 This amount will be deducted $ 4,800 This amount will be deducted from the discount. from the discount.

66. Recording the First Interest Payment on Bonds Sold at a Discount t How would the first interest payment be recorded in the journal? DateTransaction DebitCredit Nov 1 Interest expense 34,800 Discount on bond payable 4,800 Cash 30,000

67. Next Time -- t When we calculate the amount of interest expense for the second interest payment, our principal balance has changed. t Instead of 870,000, we now have a principal balance of 874,800. Why? t 874,800 x.08 x 1/2 = $34,992 t This is the interest expense for the second six-month period.

68. Effective Interest Amortization of Bond Discount interest expense$34,992 interest expense$34,992 cash payment 30,000 cash payment 30,000 discount amortization 4,992 discount amortization 4,992 After this payment, the new book value of the bonds will be 874,800 + 4,992 = $879,792.

69. Recording the Second Interest Payment on Bonds Sold at a Discount t How would the second interest payment be recorded in the journal? DateTransaction DebitCredit May 1 Interest expense 34,992 Discount on bond payable 4,992 Cash 30,000

70. Effective Interest Amortization of Bond Discount t Carrying value of bonds is defined as the par or face value of the bonds minus any unamortized discount (or plus any unamortized premium). t In this example, the discount has now been reduced from 130,000 to 120,208. The carrying value of the bonds is the face ($1,000,000) minus the unamortized discount ($120,208) = $879,792. t The book value of the bonds is increasing.

71. What’s Happening? t Each time we pay the bondholders $30,000, we are not paying the full amount of the true interest expense for the $870,000 loan. t The amount we don’t pay gets added to the carrying value of the bond. (Reducing the discount increases the carrying value of the bond.) t So, the bond’s carrying value is increasing from $870,000 to the face value of $1,000,000 over the life of the bond.

72. Straight-Line Amortization of Bond Discount t The other method is not as accurate, but the calculations are easier. t Identify the amount of the bond discount. t Divide the bond discount by the number of interest periods. t Include the discount amortization amount as part of the periodic interest expense entry. t The discount will be reduced to zero by the maturity date.

73. Here’s a review of the facts of the problem: Here’s a review of the facts of the problem:  Clock Corp. sold their bonds on May 1, 1991 at 87. The bonds have a 10-year maturity and $30,000 interest is paid semiannually.  Why would the bonds sell for 87? The market rate of interest is greater than the rate on the face. The market rate of interest is greater than the rate on the face.  Where did the $30,000 come from? 1,000,000 x.06 x 1/2 Straight-Line Amortization of Bond Discount

74. The discount of $130,000 is divided by 20. (10-year bonds with interest paid twice each year) The discount of $130,000 is divided by 20. (10-year bonds with interest paid twice each year) $6,500 will be amortized from the discount every time the interest payment is made. So, interest expense will be $36,500 every time the $30,000 payment is made. Straight-Line Amortization of Bond Discount

75. t How would the interest payments be recorded in the journal? DateTransaction DebitCredit All Interest expense 36,500 Discount on bond payable 6,500 Cash 30,000

76. Measuring and Recording Interest on Bonds Issued at a Premium t The premium must be amortized over the term of the bonds. t The premium amortization decreases the periodic interest expense for the issuer. t Two methods are commonly used: u Effective-interest amortization u Straight-line amortization

77. t Magic Inc. sold their bonds on May 1, 1991 at 107. There were $1,000,000 worth of bonds with a stated rate of 9% annually. The bonds mature in 10 years and $45,000 interest is paid semiannually. The market rate is 8% annually. t Why would the bonds sell for 107? u The market rate of interest is less than the rate on the face. t Where did the $45,000 come from? u $1,000,000 x 9% x 1/2 = 45,000 Recall the Facts of the Problem

78. Effective Interest Method For Amortizing A Bond Premium If we prepared a balance sheet on the date of issue, the bond would be reported like this: Bonds Payable $ 1,000,000 plus Premium on B/P 70,000 plus Premium on B/P 70,000 Net Bonds Payable $1,070,000 Net Bonds Payable $1,070,000

79. Effective Interest Method For Amortizing A Bond Premium t The premium carries a credit balance (and is added to the face value of the bond to give the “book value.”) t In order to get the book value to equal the face value at maturity, we’ll have to get rid of the balance in the premium account. t Each time we pay interest to our bondholders, we’ll amortize a little of the premium.

80. Effective Interest Method For Amortizing A Bond Premium t Each time we pay interest to our bondholders, we’ll amortize a little of the premium--how much? t On the first interest date, the amount we’ve actually “borrowed” from the bondholders is $1,070,000. t The market rate at the time we borrowed--the rate we had to pay to get the bondholders to buy our bonds--was 8%. The face rate is 9% t 1,070,000 x.08 x 1/2 = 42,800 (This will be the interest expense for the first 6 months.)

81. t If we pay the bondholders $45,000 cash and the interest expense is $42,800*, the difference will be the amount of the premium amortization. t Notice that the interest expense is LESS than the payment to the bondholders when bonds are issued at a premium. (It is just the opposite when bonds are issued at a discount.) *1,070,000 x.08 x 1/2=42,800 Effective Interest Method For Amortizing A Bond Premium

82. Recording the First Interest Payment on Bonds Sold at a Premium t How would the first interest payment be recorded in the journal? DateTransaction DebitCredit Nov 1 Interest expense 42,800 Premium on bond payable 2,200 Cash 45,000

83. Next Time -- t When we calculate the amount of interest expense for the second interest payment, our principal balance has changed. t Instead of 1,070,000, we now have a principal balance of 1,067,800. Why? t Because we amortized $2,200 of the premium. Now it’s only $67,800. t 1,067,800 x.08 x 1/2 = $42,712 t This is the interest expense for the second six- month period.

84. t The payment to the bondholders is the same each time a payment is made-- $45,000. t Interest expense for the second payment is $42,712 t The difference between the payment and the expense is the amount of amortization of the premium--$2,288. t The new carrying value is $1,067,800 - 2,288 = $1,065,512. Effective Interest Method For Amortizing A Bond Premium

85. Recording the Second Interest Payment on Bonds Sold at a Premium t How would the first interest payment be recorded in the journal? DateTransaction DebitCredit May 1 Interest expense 42,712 Premium on bond payable 2,288 Cash 45,000

86. t Carrying value is defined as the face value plus any unamortized premium. t In this case, the premium started at 70,000 and has been reduced by 2,200 and by 2,288, for a balance of 65,512. t The face of $1,000,000 plus the unamortized premium of 65,512 gives a carrying value of $1,065,512 after the second interest payment. Effective Interest Method For Amortizing A Bond Premium

87. What’s Happening? t Each time we pay the bondholders $45,000, we are paying the full amount of the true interest expense for the $1,070,000 loan, plus some of the principal. t The amount we pay in excess of the interest expense gets deducted from the carrying value of the bond. (Reducing the premium decreases the carrying value of the bond.) t So, the bond’s carrying value is decreasing from $1,070,000 to the face value of $1,000,000 over the life of the bond.

88. Straight-Line Amortization of Bond Premium t Identify the amount of the bond premium. t Divide the bond premium by the number of interest periods. t Include the premium amortization amount as part of the periodic interest expense entry. t The premium will be reduced to zero by the maturity date.

89. Straight-Line Amortization of Bond Premium Interest payment is always $45,000. Premium amortization is 70,000 = 3,500. 20 That means that the premium will be amortized by 3,500 every time a payment is made. Interest expense will be $41,500 each time a payment is made.

90. Straight-Line Amortization of Bond Premium t How would the interest payments be recorded in the journal? DateTransaction DebitCredit All Interest expense 41,500 Premium on bond payable 3,500 Cash 45,000

91. Carrying Value Of BONDS PAYABLE While the specific long-term liability Bonds Payable is always recorded (and kept) at face value, the Discount or Premium (on Bonds Payable) will be either subtracted (discount) or added (premium) to the BP amount to get the carrying value of the bond at any given date.

92. Understanding Notes to Financial Statements t Effective-interest method of amortization is preferred by GAAP. t Straight-line amortization may be used if it is not materially different from effective interest amortization. t Most companies do not disclose the method used for bond interest amortization.

93. Financial Analysis t The debt-equity ratio is an important measure of the state of a company’s capital structure. t When a company’s debt-equity ratio is excessive, a large amount of fixed debt payments may cause problems in tight cash flow periods. Debt-Equity Ratio = Total Debt ÷ Total Equity