6.2: Bond Valuation Flashcards
(34 cards)
What factors affect the discount rate used in bond valuation?
Market conditions (other market interest rates) and factors specific to the issue and issuer.
How is the price of a bond determined?
The price of a bond equals the present value of the future payments on the bond, which is the present value of the interest payments and the par value repaid at maturity.
What is the formula for pricing a bond (Equation 6.1)?
B = I × [ (1 - 1 / (1 + k_b)ⁿ ) / k_b ] + F × 1 / (1 + k_b)ⁿ
B = bond price
I = interest (or coupon) payments
k_b = bond discount rate (or market rate)
n = term to maturity
F = face (par) value of the bond
How can Equation 6.1 be written more compactly using present value factors?
B = I × PVAF(k_b, n) + F × PVIF(k_b, n)
Example 6.1 - What is the price of a $1,000 par value bond that matures in 10 years, with a 6% coupon rate and a market rate of 7%?
F = $1,000; I = $60; n = 10; k_b = 0.07
B = $60 × [ (1 - 1 / (1 + 0.07)¹⁰) / 0.07 ] + $1,000 × 1 / (1 + 0.07)¹⁰
= ($60 × 7.02358) + ($1,000 × 0.50835) = $421.41 + $508.35 = $929.76
What are the keystrokes for calculating the bond price in Example 6.1 using a financial calculator?
-60 → PMT; 10 → N; -1,000 → FV; 7% → I/Y; CPT → PV = -$929.76
What does it mean when a bond trades at a discount?
A bond trades at a discount when its price is less than its par value.
What does it mean when a bond trades at a premium?
A bond trades at a premium when its price is greater than its par value.
Example 6.2 - What is the price of a $1,000 par value bond that matures in 10 years, with a 6% coupon rate and a market rate of 5%?
F = $1,000; I = $60; n = 10; k_b = 0.05
B = $60 × [ (1 - 1 / (1 + 0.05)¹⁰) / 0.05 ] + $1,000 × 1 / (1 + 0.05)¹⁰
= ($60 × 7.72173) + ($1,000 × 0.61391) = $463.30 + $613.91 = $1,077.21
-60 → PMT; 10 → N; -1,000 → FV; 5% → I/Y; CPT → PV = $1,077.22
Example 6.3 - What is the price of a 15-year bond that pays interest semi-annually, with a 5% coupon rate and a market rate of 6%?
Semi-annual market rate: k_b = 3%
Term to maturity: n = 30
Semi-annual coupons: I = $25
B = $25 × [ (1 - 1 / (1 + 0.03)³⁰) / 0.03 ] + $1,000 × 1 / (1 + 0.03)³⁰
= ($25 × 19.60044) + ($1,000 × 0.41199) = $490.01 + $411.99 = $902.00
-25 → PMT; 30 → N; -1,000 → FV; 3% → I/Y; CPT → PV = $902.00
What is the most important property of fixed income investments, such as bonds, regarding interest rates?
If interest rates decrease, the market prices of bonds increase and vice versa.
What happens to the price of a bond if the yield is less than the coupon rate?
The bond trades at a premium.
What happens to the price of a bond if the yield is greater than the coupon rate?
The bond trades at a discount.
What is the relationship between bond yields and bond prices?
There is an inverse relationship between bond yields and bond prices.
What factors influence the sensitivity of bond prices to interest rate changes?
- For a given change in interest rates, bond prices will increase more when rates decrease than they will decrease when rates increase.
- The curve is steeper for lower interest rates, indicating a greater impact of interest rate changes on bond prices when rates are lower.
What is the price of a bond with a $1,000 par value, a 5% coupon rate, paying interest semi-annually, with market rates at 6%, for terms to maturity of 5 years and 30 years?
For 5 years:
n = 10
B = $25 × PVAF(3%, 10) + $1,000 × PVIF(3%, 10)
= ($25 × 8.53020) + ($1,000 × 0.74409)
= $213.26 + $744.09 = $957.35
For 30 years:
n = 60
B = $25 × PVAF(3%, 60) + $1,000 × PVIF(3%, 60)
= ($25 × 27.67556) + ($1,000 × 0.16973)
= $691.89 + $169.73 = $861.62
for 5 years:
-25 → PMT; 10 → N; -1,000 → FV; 3% → I/Y; CPT → PV = $957.35
For 30 years:
-25 → PMT; 60 → N; -1,000 → FV; 3% → I/Y; CPT → PV = $861.62
Calculate the price of Bond 1 and Bond 2 when market rates are 5% and 6%, given Bond 1 has a $1,000 par value, a 5% coupon rate, and Bond 2 has a 6% coupon rate.
For market rate 5%:
Bond 1:
B = $1,000 (trades at par since market yield = coupon rate)
Bond 2:
B = $30 × PVAF(2.5%, 30) + $1,000 × PVIF(2.5%, 30)
= ($30 × 20.93029) + ($1,000 × 0.47674)
= $627.91 + $476.74 = $1,104.65
For market rate 6%:
Bond 1:
B = $25 × PVAF(3%, 30) + $1,000 × PVIF(3%, 30)
= ($25 × 19.60044) + ($1,000 × 0.41199)
= $490.01 + $411.99 = $902.00
Bond 2:
B = $1,000 (trades at par since market yield = coupon rate)
For Bond 1:
-25 → PMT; 30 → N; -1,000 → FV; 3% → I/Y; CPT → PV = $902.00
For Bond 2:
-30 → PMT; 30 → N; -1,000 → FV; 2.5% → I/Y; CPT → PV = $1,104.65
What is interest rate risk?
The sensitivity of bond prices to changes in interest rates.
What is duration?
An important measure of interest rate risk that incorporates several factors.
What factors increase the duration of a bond?
Durations will be higher when:
1. Market yields are lower,
2. Bonds have longer maturities,
3. Bonds have lower coupons.
What are the components of a bond quote in Table 6.2?
The components include the issuer, coupon rate, maturity date, price, and yield.
What are Canada T-Bills, and what do they typically represent?
Canada T-Bills are short-term debt securities issued by the government, typically representing maturities from 1 month to 1 year.
Example: Canada 1-Month T-Bill, maturity Jun 2019, price 99.87, yield 1.68%
What are Canada Benchmarks, and what do they typically represent?
Canada Benchmarks are government bonds with longer maturities, typically ranging from 2 years to 30 years.
Example: Canada 2-Year Benchmark, maturity 2021, price 100.34, yield 1.57%
What do Provincial bonds represent, and how do their coupons compare?
Provincial bonds are issued by Canadian provinces, and their coupons can vary.
Examples from Table 6.2 show coupons ranging from 1.25% to 3.50%.
