﻿ Ken Szulczyk's Lecture Notes for Accounting 1 - Installment Notes Payable and Bonds

# Lecture #11:  Installments Notes Payable and Bonds

Although some promissory notes require a single lump-sum payment of the amount borrowed plus interest, most long-term notes require a series of payments and are called installment notes.  Each payment on an installment note includes interest and usually includes a partial repayment of the amount originally borrowed.

Installment Notes Payable.

When an installment note is used to borrow money, the borrower records the note just like a single-payment note.  For example, a company borrows \$60,000 by signing a 12% installment note that requires six annual payments.  The borrower records the note as follows:

 1990 Dec 31 Cash \$60,000 Notes Payable \$60,000 Borrowed by signing a 12% note.

(a)  Installment Payments of Accrued Interest plus Equal Amounts of Principal.

The borrower pays an equal amount of principal each month, plus the interest.  Using the last example, the company pays \$10,000 of principal, plus accrued interest at the end of each year.  The journal entry:

 1991 Dec. 31 Notes Payable (\$60,000 / 6) \$10,000 Interest Expense (\$60,000 X 0.12) 7,200 Cash \$17,200 To record first installment payment. 1992 Dec.31 Notes Payable (\$60,000 / 6) \$10,000 Interest Expense (\$50,000 X 0.12) 6,000 Cash \$16,000 To record second installment payment.

As the company pays off this loan, the interest expense becomes smaller and smaller, causing the company’s total loan payments to decrease over time.

(b)  Installment Payments that are Equal in Total Amount.

Many installment notes require a series of payments where the total amount of each payment is equal to each of the other payments.  Since the payments are equal in amount, they consist of changing amounts of interest and principal.  To do the calculation, you have to use the present value formula:

PV t = FV t / ( 1 + i )  +  FV t+1 / ( 1 + i ) 2 + FV t+2 / ( 1 + i ) 3  +          + FV t+n / (1 + i ) n+1

PV t :     The present value of all future payments that you will either pay or receive.
FV t :     The future payment.
i :            The interest rate.

For example, you will receive \$100 a year for the next three years and the market interest rate is 10%.

PV t =100 / ( 1 + 0.1 )  + 100 / ( 1 + 0.1 ) 2 + 100 / ( 1 + 0.1) 3  = \$248.68

The value of these future payments to you is worth \$248.68 to you today.  If you put \$248.68 in a bank account today at 10% interest, after the first year, you earn: 0.1 X 248.68 = \$24.87

Then you withdraw a \$100 and your remaining balance is \$173.55.  After the second year, you earn: 0.1 X 173.55 = \$17.36  Then  you withdraw a \$100 and your remaining balance is \$90.91.

After the third year, you earn:0.1 X \$90.91 = \$9.09 And withdraw the last \$100 out of the bank.  Using this same concept, you apply it to the six-year installment note of \$60,000 at 12% interest.  The formula:

\$60,000 = X / ( 1 + 0.12 )  +  X / ( 1 + 0.12) 2 +X / ( 1 + 0.12 ) 3  +          + X / (1 + 0.12 ) 6

X is the future payment of the loan and each payment is equal in amount.  Therefore X = \$14,594.  Each year you pay \$14,594 on your loan.

(c)  Allocating the Interest and Principal of Each Payment.

 Payment Interest Principal Paid Loan Balance Year 0 - - - \$60,000 Year 1 \$14,594 \$7,200 \$7,394 \$52,606 Year 2 \$14,594 \$6,313 \$8,281 \$44,325 Year 3 \$14,594 \$5,319 \$9,275 \$35,050 Year 4 \$14,594 \$4,206 \$10,388 \$24,662 Year 5 \$14,594 \$2,959 \$11,635 \$13,027 Year 6 \$14,594 \$1,563 \$13,027 \$0

We call this chart an installment note amortization schedule.  The journal entry to record the first payment:

 1991 Dec. 31 Notes Payable \$7,394 Interest Expense \$7,200 Cash \$14,594 To record the first installment payment

## Borrowing by Issuing Bonds.

Corporations often borrow money by issuing bonds.  Just like a notes payable, a bond is a written promise to pay interest and principal.  For example:

 Bond \$1,000 10% February 1, 1999

This bond matures on February 1, 1999.  Who holds this bond will receive \$1,000 on the date.  The bondholder will also receive \$100 ( 0.1 X \$1,000) a year in interest.  Most bonds pay the interest twice a year, which is \$50 every six months for this example.

1.  The difference between notes payable and bonds.

When a business borrows money by signing a notes payable, the lender is usually a single creditor such as a bank.  A bond is usually issued in denominations of \$1,000, \$2,000, etc. and sold to many different lenders.  After bonds are issued, investors can buy and sell these bonds on the financial markets before the bonds mature.

2.  Difference between stocks and bonds.

A share of stock represents ownership in a corporation.  For example, if a person owns 1,000 shares out of 10,000, then he owns 10% of the corporation’s equity.  He also will receive 10% of the corporation’s earnings, when dividends are declared.

When a person buys a bond, he has given a loan to a corporation.  Therefore, a bond represents a debt or a liability to the corporation.  For example, a person owns a \$1,000, 11%, 20 year bond issued by the corporation.  This person has two rights.  First, the right to receive 11% or \$110 interest each year the bond is outstanding. Second, the right to be paid \$1,000 when the bond matures in 20 years.

3.  Why issue bonds instead of stock?

A corporation that needs long-term funds may consider issuing additional shares of stock or issuing bonds.

• If the corporation issues new shares of stock to new shareholders, the old shareholders lose part of their control over the corporation.  If the corporation issues bonds,  bondholders do not share in the management or earnings of the corporation. There is one disadvantage of issuing bonds.  The interest on the bonds must be paid, whether or not there are any profits.

• Corporations in the U.S. usually pay about 40% of their net income in taxes.  When a corporation issues bonds and pays the interest, this interest payment is an expense, which lowers the corporation’s net income.  With a lower net income, the corporation pays less taxes.

• A potential advantage of issuing bonds instead of stock is that if bonds are issued, the result may be increased earnings for the common stockholders.  For example, a corporation has 200,000 shares of common stock outstanding and needs \$1 million to expand its operations.  Management estimates that after the expansion, the company can earn \$900,000 annually.      There are two plans.

 Plan A Plan B Earnings before bond interest and income taxes \$900,000 \$900,000 Deduct interest expense (100,000) Income before corporation income taxes \$900,000 \$800,000 Deduct income taxes (assumed 40% rate) (360,000) (320,000) Net income \$540,000 \$480,000 Plan A income per share (300,000 shares) \$1.80 Plan B income per share (200,000 shares) \$2.40

Plan A:  The corporation issues 100,000 new shares of the corporation’s stock at \$10 per share.

Plan B:  The corporation issues \$1 million of 10% bonds.

Looking at these two plans, plan B will result in a higher income per share.

## Characteristics of Bonds

Corporations have created a variety of bonds.

1.  Coupon bonds.

Bond

\$1,000

10%

February 1, 1999

These types of bonds have coupons at the bottom of the certificate.  When it is time to receive an interest payment, the bondholder detaches one coupon and mails it to the corporation.  The corporation will send a check to the bondholder.

2.  Registered Bonds, Bearer Bonds, and Debentures.

1. Registered bonds - Most bonds are registered, which means that the corporation has the names and addresses of all the bondholders.  This offers some protection from loss or theft of the bonds.

2. Bearer Bonds - Who ever holds the bonds will receive the interest payment.  Coupon bonds tend to be bearer bonds.

3. Debentures (i.e. unsecured). - The corporation does not pledge assets for the bond issues.  These bonds depend on the credit standing of the corporations.  A corporation has to be strong to issue this type of bonds.

## The Process of Issuing Bonds

A corporation has authorized to sell \$8 million of 9%, 20-year bonds on Jan. 1, 1990.  The corporation pays the interest semiannually.

 Jan. 1 Cash \$8,000,000 Bonds Payable \$8,000,000 Sold 9%, 20-year bonds at par on their interest date.

When the semiannual interest is paid on these bonds, the transaction is recorded as follows:

 July 1 Interest Expense \$360,000 Cash \$360,000 Paid the semiannual interest on the bonds.

When the bonds are paid at maturity, an entry like the following is made:

 Jan. 1 Bonds Payable \$8,000,000 Cash \$8,000,000 Paid bonds at maturity.

## Bonds Sold at a Discount

For example, we have a \$1,000 bond with an 8%.  This interest rate is 8% on the bond.  The company is obligated to pay this rate as the bond remains outstanding. What if the market interest rate is 12%?  The company will not sell this bond, because the creditors can earn a higher rate than 8%.

What can the company do?  The company can sell this bond for a price that is less than \$1,000 to compensate the creditors for the higher market interest rate.  This is the market value of the bond.  To calculate the bond’s market value, you have to use the present value formula.  For example:

• A \$1,000 bond.
• The bond pays interest twice a year.
• The interest on the bond is 8%, which is \$80 a year or \$40 every six months.
• The bond matures in two years and the market interest rate is 12% a year, which is 6% for a payment period.

P Bond =\$40 / ( 1 + 0.06 )  + \$40 / ( 1 + 0.06 ) 2 + \$40 / ( 1 + 0.06) 3  +  \$40 / ( 1 + 0.06) 4  +  \$1,000 / ( 1 + 0.06) 4  =  \$930.76

At a market price of \$930.76 for this bond, the creditors will earn an average return of 12% a year, when you look at future cash flows.

Important Law:  As the market interest rate increases, the bond’s market price decreases, and vice-versa.

If the company sold a 100 bonds for this market price, the journal entry is:

 1997 Jan. 1 Cash \$93,076 Discount on Bonds Payable 6,924 Bonds Payable \$100,000 Sold 8%, two-year bonds at a discount on their date of issue.

If you were to prepare a balance sheet, then:

 Long-term liabilities: Bonds payable, 8%, due Jan. 1, 1999 \$100,000 Discount Bonds Payable at 12% 6,924 \$93,076

The corporation accepted \$93,076 in cash, but in two years, the corporation must pay \$100,000 for the bonds.  The difference of \$6,924 is the cost of borrowing the funds.  This cost has to be transferred to the interest expense account.  We will use the straight-line method.  The bonds mature in two years and the company pays interest twice a year, so there are four interest payments.  For each period: \$6,924 / 4 = \$1,731  The journal entry to record the interest payment:

 July 1 Interest Expense \$5,731 Discount on Bonds Payable \$1,731 Cash \$4,000 To record payment of six month’s interest and amortization of the discount.

## Bonds Sold at a Premium

Using the same example in the last topic, what if the market interest rate is 4%?  If the company has bonds with a stated interest rate of 8% on them, the company will not sell these bonds for a \$1,000 each.  The company can borrow more cheaply from the market.  What the company will do is sell these bonds for a higher market price.  Therefore, the company is compensated for the lower interest rate.  You have to use the Present Value Formula.

P Bond =\$40 / ( 1 + 0.02 )  + \$40 / ( 1 + 0.02 ) 2 + \$40 / ( 1 + 0.02) 3  +  \$40 / ( 1 + 0.02) 4  +  \$1,000 / ( 1 + 0.02) 4  = \$1,076.19

If the company sells 100 bonds, then the journal entry is:

 May 1 Cash \$107,619 Premium on bonds payable \$7,619 Bonds Payable \$100,000 Sold bonds at a premium on their date of issue.

Each period, when the company pays the interest, it benefits by \$7,619 / 4 = \$1,905.  The premium lowers the company’s interest cost.  The journal entry to record the payment of interest:

 Nov. 1 Interest Expense \$2,095 Premium on Bonds Payable \$1,905 Cash \$4,000

If you prepared the balance sheet after the first interest payment, then:

 Long-term liabilities: Bonds payable, 8%, due Jan. 1, 1999 \$100,000 Premium on Bonds Payable  at 4% 5,714 \$105,714