Reading 64: Introduction to the Valuation of Debt Securities 2010, face, discount, investor, change

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LOS c: Compute the value of a bond and the change in value that is attributable to a change in the discount rate.

An investor buys a 25-year, 10% annual pay bond for $900 and will sell the bond in 5 years when he estimates its yield will be 9%. The price for which the investor expects to sell this bond is closest to:

A) $1,091.

B) $964.

C) $1,122.

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This is a present value problem 5 years in the future.
N = 20, PMT = 100, FV = 1000, I/Y = 9
CPT PV = -1,091.29
The $900 purchase price is not relevant for this problem.

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A year ago a company issued a bond with a face value of $1,000 with an 8% coupon. Now the prevailing market yield is 10%. What happens to the bond? The:

A) bond is traded at a market price higher than $1,000.

B) bond is traded at a market price of less than $1,000.

C) bond price is not affected by the change in market yield, and will continue to trade at $1,000.

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A bonds price/value has an inverse relationship with interest rates.  Since interest rates are increasing (from 8% when issued to 10% now) the bond will be selling at a discount.  This happens so an investor will be able to purchase the bond and still earn the same yield that the market currently offers. 

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Suppose the term structure of interest rates makes an instantaneous parallel upward shift of 100 basis points. Which of the following securities experiences the largest change in value? A five-year:

A) zero-coupon bond.

B) floating rate bond.

C) coupon bond with a coupon rate of 5%.

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The duration of a zero-coupon bond is equal to its time to maturity since the only cash flows made is the principal payment at maturity of the bond. Therefore, it has the highest interest rate sensitivity among the four securities.

A floating rate bond is incorrect because the duration, which is the interest rate sensitivity, is equal to the time until the next coupon is paid. So this bond has a very low interest rate sensitivity.

A coupon bond with a coupon rate of 5% is incorrect because the duration of a coupon paying bond is lower than a zero-coupon bond since cash flows are made before maturity of the bond. Therefore, its interest rate sensitivity is lower.

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Randy Harris is contemplating whether to add a bond to his portfolio. It is a semiannual, 6.5% bond with 7 years to maturity. He is concerned about the change in value due to interest rate fluctuations and would like to know the bond’s value given various scenarios. At a yield to maturity of 7.5% or 5.0%, the bond’s fair value is closest to:

7.5%

5.0%

A) 974.03 1,052.36

B) 946.30 1,087.68

C) 1,032.67 959.43

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Given a YTM of 7.5%, calculate the value of the bond as follows:
N = 14; I/Y = 7.5/2 = 3.75%; PMT = 32.50; FV = 1,000; CPT → PV = 946.30

Given a YTM of 5.0%, calculate the value of the bond as follows:
N = 14; I/Y = 5/2 = 2.5%; PMT = 32.50; FV = 1,000; CPT → PV = 1,087.68

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What value would an investor place on a 20-year, 10% annual coupon bond, if the investor required a 10% rate of return?

A) $1,104.

B) $1,000.

C) $920.

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N = 20; I/Y = 10; PMT= 100; FV = 1,000; CPT → PV = 1,000

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An investor plans to buy a 10-year, $1,000 par value, 8% semiannual coupon bond. If the yield to maturity of the bond is 9%, the bond’s value is:

A) $1,067.95.

B) $934.96.

C) $935.82.

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N = 20, I = 9/2 = 4.5, PMT = 80/2 = 40, FV = 1,000, compute PV = $934.96

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Deep discount bonds have:

A) less call protection than bonds selling at par.

B) greater price volatility than bonds selling at par.

C) greater reinvestment risk than bonds selling at par.

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A deep discount bond is a bond selling at a discount of at least 20%.  This means that a $1000 face value bond will be selling at $800.  Using the duration method to show risk, a deep discount bond will have a significantly greater duration than the bond selling at par.  Thus having a duration higher than the face value duration means there is more price volatility for the deep discount bond.  

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The price and yield on a bond have:

A) positive relation.

B) inverse relation.

C) no relation.

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Interest rates and a bond's price have an inverse relationship. If interest rates increase the bond price will decrease and if interest rates decrease the bond price will increase.

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Value a semi-annual, 8% coupon bond with a $1,000 face value if similar bonds are now yielding 10%? The bond has 10 years to maturity.

A) $1,373.87.

B) $875.38.

C) $1,000.00.

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Using the financial calculator: N = 10 × 2 = 20; PMT = $80/2 = $40; I/Y = 10/2 = 5%; FV = $1,000; Compute the bond’s value PV = $875.38.

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What value would an investor place on a 20-year, 10% annual coupon bond, if the investor required an 11% rate of return?

A) $879.

B) $1,035

C) $920.

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N = 20, I/Y = 11, PMT = 100, FV = 1,000, CPT PV