Bond Valuation and Yield to Maturity Explained: The Finance Student's Complete Guide
Bond valuation is usually the first place finance students apply time value of money to a real security — and it is where a lot of them stall. The formulas look intimidating, the vocabulary piles up (coupon, par, yield, premium, discount), and the inverse relationship between price and interest rates feels backwards until it suddenly does not. This guide builds bond valuation from the ground up with worked examples, then shows you how the same logic connects to the bond accounting you will see in intermediate accounting.
What a Bond Actually Is
A bond is a loan that investors make to a company or government. The borrower promises two kinds of cash flow: regular coupon payments (the face value times the coupon rate) and the face value (also called par, usually $1,000) at maturity. Because those cash flows are fixed by contract, a bond's value depends entirely on how investors discount them — which is exactly the time value of money you already know.
Pricing a Bond: The Core Formula
A bond's price is the present value of an annuity (the coupons) plus the present value of a lump sum (the face value), both discounted at the market's required yield:
C = coupon payment per period | F = face value
r = market yield per period | n = number of periods
The coupon rate determines C. The market yield determines r. Keeping those two rates separate is the most important habit in this entire topic.
Worked Example: Discount, Premium and Par
A 10-year bond has a $1,000 face value and a 6% annual coupon ($60 per year). Price it at three different market yields:
| Market Yield | PV of Coupons | PV of Face Value | Price | Trades At |
|---|---|---|---|---|
| 8% | $402.61 | $463.19 | $865.80 | Discount |
| 6% | $441.61 | $558.39 | $1,000.00 | Par |
| 5% | $463.30 | $613.91 | $1,077.22 | Premium |
On a BA II Plus, the 8% case is: N = 10, I/Y = 8, PMT = 60, FV = 1000, CPT PV → −865.80. (New to the calculator? See our BA II Plus guide.)
The pattern is the rule worth memorising: when the market yield is above the coupon rate, the bond sells at a discount; when it is below, at a premium; when they are equal, at par. A discount compensates buyers for receiving a coupon lower than what new bonds pay.
Semiannual Coupons
Most US corporate and Treasury bonds pay coupons twice a year. Adjust three inputs: halve the coupon, halve the yield, double the periods. For the same bond at an 8% yield: N = 20, I/Y = 4, PMT = 30, FV = 1000 → price $864.10. The small difference from the annual figure comes from compounding more frequently. Exams often state "semiannual" once in the question and nowhere else — underline it.
Yield to Maturity and Current Yield
Yield to maturity (YTM) is the discount rate that makes the present value of a bond's cash flows equal to its current price — in other words, the bond's internal rate of return if you buy today and hold to maturity. It cannot be solved algebraically; you solve it on the calculator.
Example. An 8-year bond with a 5% semiannual coupon trades at $950. N = 16, PMT = 25, FV = 1000, PV = −950, CPT I/Y → 2.89% per half-year, or about 5.79% annual YTM (quoted as twice the semiannual rate).
Current yield is much simpler: annual coupon ÷ current price. For the $865.80 bond above, current yield = 60 ÷ 865.80 = 6.93%. It ignores the gain from the price pulling up to par at maturity, which is why YTM (8%) is higher for a discount bond.
Why Prices Fall When Rates Rise
Imagine you own the 6% bond above. Market rates jump and new bonds now pay 8%. Nobody will pay you $1,000 for $60 a year when $1,000 can buy $80 a year elsewhere. The only way to sell your bond is to lower its price until its total return matches 8% — which is exactly what the $865.80 price does. Higher discount rate, lower present value.
Two refinements matter for exams. First, longer maturities are more sensitive to rate changes, because more cash flows are discounted for longer. Second, pull to par: as maturity approaches, a discount bond's price rises toward $1,000 even if yields do not change. Hold the 8% yield constant and the same bond is worth $875.06 one year later.
How This Connects to Bond Accounting
Everything above is the investor's view. In intermediate accounting, the issuing company records the same bond: the cash it receives is the price you just calculated, and the difference from face value becomes a discount or premium that is amortised over the bond's life using the effective interest method. If you understand valuation, the accounting is just tracking that present value over time. See the bonds payable complete guide and, for the investor's books, accounting for investments.
Bond Problems Making Your Head Spin?
Bond valuation ties together TVM, yields and accounting entries — and one missed conversion wrecks the answer. Work through your homework or exam review with a finance tutor at Accounting Tutor Online.
Book a session →Common Exam Mistakes
- Using the coupon rate as the discount rate. Discount at the market yield; the coupon rate only sets the payment.
- Forgetting semiannual adjustments to N, rate and payment.
- Quoting a semiannual YTM as annual. Double it for the bond-equivalent yield.
- Sign errors when solving for YTM — price must be negative if PMT and FV are positive.
Test Yourself: Bond Valuation
Pick an answer to see the explanation. 4 questions.
Q1. A bond pays a 6% coupon and similar bonds currently yield 8%. The bond trades at:
Q2. A 10-year bond with a $1,000 face value and 6% annual coupon is priced at a 6% market yield. Its price is:
Q3. A bond pays a $60 annual coupon and trades at $865.80. What is its current yield?
Q4. If market interest rates rise, the price of an existing fixed-rate bond will:
Practise Bond Questions With Full Solutions
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