Reading 66: Yield Measures, Spot Rates, and Forward Rates-LOS 2011, face, interpret, measures, selling

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Session 16: Fixed Income: Analysis and Valuation
Reading 66: Yield Measures, Spot Rates, and Forward Rates

LOS b: Calculate and interpret the traditional yield measures for fixed-rate bonds and explain their limitations and assumptions.

 

 

A bond is selling at a discount relative to its par value. Which of the following relationships holds?

A) yield to maturity < coupon rate < current yield.

B) current yield < coupon rate < yield to maturity.

C) coupon rate < current yield < yield to maturity.

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When a bond is selling at a discount, it means that the bond has a larger YTM (discount rate that will equate the PV of the bond's cash flows to its current price) than its current yield (coupon payment/current market bond price) and coupon payment.

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PG&E has a bond outstanding with a 7% semiannual coupon that is currently priced at $779.25. The bond has remaining maturity of 10 years but has a first put date in 4 years at the par value of $1,000. Which of the following is closest to the yield to first put on the bond?

A) 14.46%.

B) 7.73%.

C) 14.92%.

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To compute yield to first put, enter: FV = $1,000; N = 2 × 4 = 8; PMT = $35; PV = -$779.25; CPT → I/Y = 7.23%, annualized as (7.23)(2) = 14.46%.

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Harmon Moving has a 13.25% coupon semiannual coupon bond currently trading in the market at $1,229.50. The bond has eight years remaining until maturity, but only two years until first call on the issue at 107.50% of $1,000 par value. Which of the following is closest to the yield to first call on the bond?

A) 4.72%.

B) 5.16%.

C) 9.14%.

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To compute yield to first call, enter: FV = $1,075; N = 2 × 2 = 4; PMT = $66.25; PV = –1,229.50, CPT → I/Y = 2.36%, annualized as (2.36)(2) = 4.72%.

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Suppose that IBM has a $1,000 par value bond outstanding with a 12% semiannual coupon that is currently trading at 102.25 with seven years to maturity. Which of the following is closest to the yield to maturity (YTM) on the bond?

A) 11.52%.

B) 11.21%.

C) 11.91%.

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To find the YTM, enter PV = –$1,022.50; PMT = $60; N = 14; FV = $1,000; CPT → I/Y = 5.76%. Now multiply by 2 for the semiannual coupon payments: (5.76)(2) = 11.52%.

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A five-year bond with a 7.75% semiannual coupon currently trades at 101.245% of a par value of $1,000. Which of the following is closest to the current yield on the bond?

A) 7.65%.

B) 7.53%.

C) 7.75%.

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The current yield is computed as: (Annual Cash Coupon Payment) / (Current Bond Price). The annual coupon is: ($1,000)(0.0775) = $77.50. The current yield is then: ($77.50) / ($1,012.45) = 0.0765 = 7.65%.

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The yield to call is a less conservative yield measure than the yield to maturity whenever the price of a callable bond is quoted at a value:

A) equal to or greater than par value plus one year's interst.

B) equal to par value less one year's interest.

C) more than par.

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The more conservative yield measure is the one that results in a lower yield. The YTM on a discount bond will always be less than its yield to call.

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Consider a 5-year, semiannual, 10% coupon bond with a maturity value of 1,000 selling for $1,081.11. The first call date is 3 years from now and the call price is $1,030. What is the yield-to-call?

A) 7.28%.

B) 7.82%.

C) 3.91%.

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N = 6; PMT = 50; FV = 1,030; PV = $1,081.11; CPT → I = 3.91054

3.91054 × 2 = 7.82

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A 12% coupon bond with semiannual payments is callable in 5 years. The call price is $1,120. If the bond is selling today for $1,110, what is the yield-to-call?

A) 11.25%.

B) 10.25%.

C) 10.95%.

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PMT = 60; N = 10; FV = 1,120; PV = 1,110; CPT → I = 5.47546

(5.47546)(2) = 10.95

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If a bond sells at a discount its:

A) coupon rate is less than the market rate of interest.

B) current yield is greater than its YTM.

C) coupon rate is greater than its current yield.

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When a bond sells at a discount, the market rate goes above the coupon rate and the bond's price falls below par. The current yield is the coupon rate / price, so as price falls below 1000 the current yield rises above the coupon rate. The YTM considers the current yield plus the capital gain associated with the discount.

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Consider the purchase of an existing bond selling for $1,150. This bond has 28 years to maturity, pays a 12% annual coupon, and is callable in 8 years for $1,100.

What is the bond's yield to call (YTC)?

A) 10.55%.

B) 10.05%.

C) 9.26%.

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N = 8; PMT = 120; PV = -1,150; FV = 1,100; CPT → I/Y.

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What is the bond's yield to maturity (YTM)?

A) 10.55%.

B) 9.26%.

C) 10.34%.

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N = 28; PMT = 120; PV = -1,150; FV = 1,000; CPT → I/Y.

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What rate should be used to estimate the potential return on this bond?

A) 10.34%.

B) the YTC.

C) the YTM.

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The yield to call should be used since the bond could be called in the future. Because the bond is callable using yield to maturity would give a falsely increased rate of return.