Chapter 6: Pricing Fixed-Income Securities

If you invest $2,000 today at 9% compounded interest for two years, the value of the investment to the nearest dollar at the end of the two years will be:

$2,376 Future Value = $2,000(1 + .09) 2 = $2,376

If you invest $3,000 today at 8% compounded interest for three years, the value of the investment to the nearest dollar at the end of the three years will be:

$3,779 Future Value = $3,000(1 + .08)³ = $3,779

To the nearest dollar, what is the value today of an investment that pays $1,000,000 in 15 years, assuming an annual opportunity cost of 8%?

$315,242 Present Value = $1,000,000/(1.08)¹⁵ = $315,242

To the nearest dollar, what is the value today of an investment that pays $10,000 in five years, assuming an annual opportunity cost of 6%?

$7,473 Present Value = $10,000/(1.06)⁵ = $7,473

How much would you pay for a security that pays $150 at the end of each of the next three years plus another $500 at the end of the third year if the relevant interest rate is 9%?

$765 Present Value = $150/(1.09)¹ + $150/(1.09)² + $650/(1.09)³ = $765

To the nearest dollar, what is the value today of an investment that pays $15,000 in seven years, assuming an annual opportunity cost of 9%?

$8,206 Present Value = $15,000/(1.09)⁷ = $8,206

A bank buys a $10,000 Treasury bill with a maturity of 1 year. Current market rates are 8%. If interest rates rise to 8.25%, what is the approximate change in the price of the T-bill?

-0.23% ΔP/P = -[Duration/(1+i)]*Δi = [1/(1+.08)]*.0025 = -.00231

Sources of a bond's total return?

-Coupon interest -Reinvestment income -Capital gains or losses realize at maturity

A bond that with a 12% coupon rate (paid semi-annually) has two years to maturity. If the current discount rate is 10%, what is the bond's Macaulay's duration?

1.73 years Semi-annual Discount Rate5.00% 01234 Cash Flows120$ 120$ 120$ 1,120$ t*CF120.00$ 240.00$ 360.00$ 4,480.00$ PV(t*CF)$114.29$217.69$310.98$3,685.71 ΣPV(t*CF)$4,328.66 Price$1,248.22 Macaulay's Duration = ΣPV(t*CF)/Price 3.47Semi-Annual Periods 1.73Years

A bond that has an annual coupon rate of 15% has two years to maturity. If the current discount rate is 8%, what is the bond's Macaulay's duration?

1.88 years Discount Rate 8.00% 0 1 2 Cash Flows $150 $1,150 t*CF $150.00 $2,300.00 PV(t*CF) $138.89 $1,971.88 ΣPV(t*CF) $2,110.77 Price $1,124.83 Macaulay's Duration = ΣPV(t*CF)/Price 1.88Years

What is the Macaulay's duration of a 10 year zero-coupon bond with a face value of $1,000 and a market rate of 8%, compounded annually is:

10 years

What is the effective annual cost of a credit card that charges 18%, compounded monthly?

19.56% Effective Rate = (1 + .18/12)¹² - 1 = .1956

A bond that has an annual coupon rate of 11% has three years to maturity. If the current discount rate is 16%, what is the bond's Macaulay's duration?

2.69 years Discount Rate 16.00% 0 1 2 3 Cash Flows $110 $110 $1,110 t*CF$110.00 $220.00$3,330.00 PV(t*CF)$94.83$163.50$2,133.39 ΣPV(t*CF)$2,391.71 Price$887.71 Macaulay's Duration = ΣPV(t*CF)/Price 2.69 Years

A 90-day Treasury bill is quoted as having a price of $987.50. What is its bond equivalent yield?

5.13% BEY = (Pf - P₀ )/P₀ * (365/h) = (1000 - 987.50)/987.50 * 365/90 = .0513

A 90-day Treasury bill is quoted as having a 6% bond equivalent yield. What is the effective annual yield?

6.14% i* = [1 + i/(365/h)]³⁶⁵/h - 1 = [1 + .06/(365/90)]³⁶⁵/⁹⁰ - 1 = .0614

A bank quotes you a rate of 7% on a CD, compounded quarterly. What is the effective annual rate?

7.19% Effective Rate = (1 + .07/4)⁴ - 1 = .0719

A bond's Macaulay duration is 7.95 years. If the current annual interest rate is 7%, what is the modified duration of this bond?

7.43 years Modified Duration = Macaulay's Duration/(1+i) = 7.95/1.07 = 7.43

What is the effective annual rate of an investment that offers 8%, compounded quarterly?

8.24% Effective Rate = (1 + .08/4)⁴ - 1 = .0824

If $1,500 is invested today, the initial investment plus interest will be worth $2,700 in seven years. What is the annual interest rate on the investment?

8.76% Interest = [$2,700/$1,500] ¹/⁷ - 1 = 8.76%

A three-year 9% bond is trading at par of $5,000. If you buy the bond expecting to hold it to maturity and believe you can reinvest the $225 semi-annual coupon payments at a 3.5% semi-annual rate through maturity. The total return on this investment is _____ annually.

8.80% Future value = $225[(1.035)⁶ - 1]/0.035 = $1,473.78 + $5,000.00 = $6,473.78 Total return = [$6,473.78/$5,000.00]¹/⁶ - 1= 1.043994 - 1 = .043994 x 2 = 8.80%

If $2,500 is invested today, the initial investment plus interest will be worth $5,000 in eight years. What is the annual interest rate on the investment?

9.05% Interest = [$5,000/$2,500] ¹/⁸ - 1 = 9.05%

A bank quotes you an effective annual rate of 10% on a semi-annual investment. What is the annual simple interest rate?

9.76% Effective Rate = .10 = (1 + NOM/2)² - 1 and solve for NOM. .10 + 1 = (1 + NOM/2)² 1.1 = (1 + NOM/2)² 1.1¹/² = 1 + NOM/2 1.0488 = 1 + NOM/2 1.0488 - 1 = NOM/2 .0488 = NOM/2 2 * .0488 = NOM .0976 = NOM

Everything else the same, if the yield to maturity decreased 1 percentage point, which of the following bonds would have the largest percentage increase in value?

A 25-year zero-coupon bond.

The Macaulay's duration of a 10-year, 10% bond with a face value of $1,000 and a market rate of 8%, compounded annually is: a. 10 years b. 11 years c. 12 years d. 13 years e. None of the above

None of the above Since this is a coupon bond, the duration must be less than the maturity.

All other things the same, longer maturity bonds have greater relative price volatility than shorter maturity bonds.

True

All other things the same, low coupon bonds have greater relative price volatility than high coupon bonds.

True

The duration of any security with interim cash flows will be less than the security's maturity.

True

The effective annual interest rate will never be less than the simple interest rate.

True

The greater the compounding frequency, the higher the future value, everything else the same.

True

For the same change in interest rates bondholder's will realize:

a greater capital gain when rates fall than capital loss when rates rise

If the holder of a bond can demand that the issuer convert the bond into common stock of a different company at a predetermined price at a set time in the future, the bond has a(n) ______________ option.

exchange

Duration:

is a measure of how price sensitive a bond is to a change in interest rates.

Cash in your possession today:

is worth more than the same amount of cash received in the future.

If the holder of a bond can demand redemption of the bond at a predetermined price at a set time in the future, the bond has a(n) ______________ option.

put

A stripped security:

should sell as a package of zero coupon bonds.

Bond prices and interest rates move in the same direction.

False

For a given absolute change in interest rates, the percentage increase in an option free bond's price will be less than the percentage decrease.

False

T/F As interest rates rise, bond prices rise, everything else the same.

False

The greater the compounding frequency, the higher the present value, everything else the same.

False

There is an inverse relationship between a bond's duration and its price volatility.

False

Using a 360-day year results in higher returns than using a 365-day year.

False

Two bonds with different coupon amounts are priced to yield the same yield to maturity. For a given change in market rate:

the bond with the lower coupon will always change more in price than the bond with the higher coupon.

If a bond is a par bond, then:

the yield to maturity is equal to the coupon rate.

If a bond is a discount bond, then:

the yield to maturity is greater than the coupon rate

If a bond is a premium bond, then:

the yield to maturity is less than the coupon rate.