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Introduction to Finance

What is a bond really worth?

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Address: Burnaby, BC, CA
Telephone: +1-604-916-5838
Price range: C$30–C$129

Discount the coupons and the face value, find the yield hidden in a price, handle the days between coupon dates, and read the yield curve the way the market does.

Part 1 · Pricing a bond · Step 1 of 14

A bond is a loan you can sell

Cash flows to the bondholder · face value $1,000.00

couponface value (plus the last coupon)

Part 1 · Pricing a bond · Step 1 of 14

A bond is a loan you can sell

A bond is a tradable loan. The issuer (a government, a city, a company) borrows; whoever buys the bond lends, and can sell it to someone else before it matures. Its terms are fixed on day one: the face value F (principal or par value) repaid at maturity, the coupon rate, the yearly coupon C = coupon rate × F, and the frequency m. A bond that pays m times a year pays c = C ÷ m each time.

Try it: Switch between the four kinds of bond. Only the zero pays nothing before maturity; only the perpetual bond never repays its face value.

Kind of bond

Coupon rate (per year)6%

Years to maturity3

Annual coupon, C

$60.00

Each payment

$30.00

Payments

Most Canadian government bonds pay twice a year: c = C ÷ 2 = $30.00 every six months, so a 3-year bond makes 6 payments.

Think first

A bond matures in 1.5 years, has a $500 face value and pays a $40 coupon once a year. What does it pay, and when?

$40 in six months and $540 in 1.5 years. Coupon dates count back from maturity, so the first coupon comes after only half a year.

Question 1 of 6Challenge

A government bond from timeline to a yield change

Today Anika Sharma buys a Government of Canada bond with a face value of $5,000.00 and a coupon rate of 6.4% a year, paid semiannually. There are 30 coupon payments left until maturity, and its yield to maturity is 7% a year, compounded semiannually. The last coupon was paid 61 days ago, in a coupon period that is 182 days long. Treat all the cash flows as risk-free, assume the yield curve is flat at 7% (compounded semiannually) and that there is no arbitrage. Use the simplified whole-period clean price, then add accrued interest. For the yield change, ignore the one day of elapsed time; exact-date pricing gives different answers.

Draw the timeline of the cash flows still to come, and show where today sits.
Find the clean price, the accrued interest and the dirty price. Explain the difference between the clean and dirty prices.
Find the face value of a zero-coupon bond that matures on the same day (semiannual compounding) and whose price today equals the clean price from (b).
Assume a perpetual bond pays its first coupon exactly six months from today, then every six months forever. What coupon makes its price equal that clean price?
The day after Anika buys, news changes the bond's yield to 8.2%. What happens to its clean price, by how much in percent, and why?

Given

The bond

Face value$5,000

Coupon rate (per year, paid twice a year)6.40%

Coupon periods left to maturity30

Yield to maturity (per year, compounded twice a year)7%

Today

Days since the last coupon61

Days in this coupon period182

Part (e)

Yield after the news8.20%

Solution

today

last coupon
(period 0)next coupon
(period 1)

Read the question and the givens first. Try the first part yourself, then press Start solving and open the working to check.

a. Cash flows to come

b. Clean price

b. Accrued interest

b. Dirty price

c. Face value of the zero

d. Perpetual coupon

e. New clean price

e. Price change

Midterm coming up and bond pricing still feels slippery?

Bring your problem sets. We work through them together until every type feels routine.

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What is a bond really worth?

A bond is a loan you can sell

A bond is a loan you can sell

A government bond from timeline to a yield change

Midterm coming up and bond pricing still feels slippery?

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