13.1 Explain the Pricing of Long-Term Liabilities

Long-Term Debt Financing

Long-term debt financing is how businesses raise large amounts of capital for major investments, expansions, or operations. The two main options are long-term loans from banks and bonds sold to investors. Each works differently in terms of structure, flexibility, and cost, and understanding those differences matters for both accounting treatment and financial decision-making.

Long-Term Loans vs. Bonds

Long-term loans are issued by financial institutions like banks. They come with fixed interest rates and set repayment terms. A few key features:

• They often require collateral (assets pledged as security) or personal guarantees to protect the lender
• Repayment happens through periodic payments that include both principal and interest over the life of the loan
• The borrower typically deals with a single lender, and the terms are negotiated directly

Bonds are debt securities issued by corporations or governments. Instead of borrowing from one bank, the issuer essentially borrows from many investors at once. Each bond represents a portion of a larger total debt obligation.

• Bonds have a fixed interest rate called the coupon rate and a maturity date when the principal (face value) must be repaid
• Interest is paid periodically to bondholders, most commonly semi-annually
• Unlike most bank loans, bonds can be traded on secondary markets, giving investors liquidity (the ability to sell before maturity)
• The indenture is the legal contract between the issuer and bondholders that spells out all the terms and conditions, including payment schedules, covenants, and what happens in the event of default

Market Interest Rates and Bond Pricing

The relationship between a bond's coupon rate and the current market interest rate determines whether the bond sells at par, at a premium, or at a discount. This is one of the most tested concepts in this unit.

• Issued at par: The coupon rate equals the market rate. Investors pay exactly face value. For example, a $\$1{,}000$ bond with a 5% coupon when the market rate is also 5% sells for $\$1{,}000$.
• Issued at a premium: The coupon rate is higher than the market rate. Investors are willing to pay more than face value because the bond pays better interest than what's currently available. That same 5% coupon bond might sell for $\$1{,}050$ if the market rate drops to 4%.
• Issued at a discount: The coupon rate is lower than the market rate. Investors will only buy the bond for less than face value to compensate for the below-market interest payments. If the market rate rises to 6%, that 5% coupon bond might sell for $\$950$.

Companies need to consider market rates carefully when setting the coupon rate on a new bond issue:

• A coupon rate set too low means the bond sells at a discount, so the company raises less cash than the face value of the debt it's taking on
• A coupon rate set too high means the company pays more interest than necessary over the bond's life

Yield to maturity (YTM) is the total return an investor can expect if they hold the bond until it matures. It accounts for the bond's current market price, face value, coupon rate, and time remaining to maturity. YTM is especially useful for comparing bonds with different coupon rates and prices on an apples-to-apples basis.

Calculating Interest on Long-Term Liabilities

Interest Calculation Methods

Simple interest is calculated only on the original principal amount. The formula is:

$I = P \times r \times t$

• $I$ = Interest amount
• $P$ = Principal (the original amount borrowed)
• $r$ = Annual interest rate (as a decimal)
• $t$ = Time period (in years)

For example, a $\$10{,}000$ loan at 6% annual interest for 3 years produces $\$10{,}000 \times 0.06 \times 3 = \$1{,}800$ in total interest.

Compound interest is calculated on both the principal and any previously accumulated interest. The formula is:

$A = P \times (1 + r)^n$

• $A$ = Final amount (principal + total interest)
• $P$ = Principal
• $r$ = Interest rate per compounding period (as a decimal)
• $n$ = Total number of compounding periods

Compounding can occur annually, semi-annually, quarterly, or monthly. More frequent compounding produces higher total interest because interest starts earning interest sooner.

Effective interest rate (EIR) captures the actual annual cost of borrowing after accounting for compounding. It's calculated as:

$EIR = \left(1 + \frac{r}{m}\right)^m - 1$

• $r$ = Stated (nominal) annual interest rate
• $m$ = Number of compounding periods per year

The EIR is what lets you make fair comparisons. A loan compounding monthly at a 6% stated rate has a higher true cost than one compounding semi-annually at 6%, because the monthly loan compounds more often. Specifically, 6% compounded monthly gives an EIR of about 6.17%, while 6% compounded semi-annually gives an EIR of about 6.09%.

Valuation and Risk Assessment

Present value calculations are used to determine what future cash flows from a bond or loan are worth today. Since a dollar received in the future is worth less than a dollar today, you discount future interest payments and the principal repayment back to the present using the market interest rate. This is how bond prices are actually determined.

Amortization schedules map out how each payment on a loan or bond breaks down between interest and principal over time. Early payments typically go mostly toward interest, with the principal portion growing as the balance decreases.

Credit ratings, assigned by agencies like Moody's and S&P, assess how likely a bond issuer is to repay its debt. Higher-rated issuers (lower risk) can borrow at lower interest rates, while lower-rated issuers must offer higher rates to attract investors willing to take on more risk.