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LOS b, (Part 2): Explain the limitations and assumptions for traditional yield measures.

When computing the yield to maturity, the implicit reinvestment assumption is that the interest payments are reinvested at the:

A) prevailing yield to maturity at the time interest payments are received.

B) coupon rate.

C) yield to maturity at the time of the investment.

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The reinvestment assumption states that reinvestment must occur at the YTM in order for an investor to earn the YTM.  The assumption also states that payments are received in a prompt and timely fashion resulting in immediate reinvestment of those funds.  

 

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Which of the following describes the yield to worst? The:

A) yield given default on the bond.

B) lowest of all possible yields to call and yields to put.

C) lowest of all possible prices on the bond.

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Yield to worst involves the calculation of yield to call and yield to put for every possible call or put date, and determining which of these results in the lowest expected return.

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When a bond's coupon rate is greater than its current yield, and its current yield is greater than its yield to maturity, the bond is a:

A) discount bond.

B) premium bond.

C) par value bond.

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For a premium bond, coupon rate > current yield > yield to maturity.
For a par bond, coupon rate = current yield = yield to maturity.
For a discount bond, coupon rate < current yield < yield to maturity.

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Calculate the current yield and the yield-to-first call on a bond with the following characteristics:

• 5 years to maturity
• $1,000 face value
• 8.75% semi-annual coupon
• Priced to yield 9.25%
• Callable at $1,025 in two years

Current Yield

Yield-to-Call

A) 8.93% 5.51%

B) 9.83% 19.80%

C) 8.93% 11.02%

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To calculate the CY and YTC, we first need to calculate the present value of the bond: FV = 1,000; N = 5 × 2 = 10; PMT = (1000 × 0.0875) / 2 = 43.75; I/Y = (9.25 / 2) = 4.625; CPT → PV = -980.34 (negative sign because we entered the FV and payment as positive numbers). Then, CY = (Face value × Coupon) / PV of bond = (1,000 × 0.0875) / 980.34 = 8.93%.

And the YTC calculation is: FV = 1,025 (price at first call); N = (2 × 2) = 4; PMT = 43.75 (same as above); PV = –980.34 (negative sign because we entered the FV and payment as positive numbers); CPT → I/Y = 5.5117 (semi-annual rate, need to multiply by 2) = 11.02%.

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A 20-year bond with a par value of $1,000 and an annual coupon rate of 6% currently trades at $850. It has a promised yield of:

A) 7.9%.

B) 7.5%.

C) 6.8%.

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N = 20; FV = 1,000; PMT = 60; PV = -850; CPT → I = 7.5

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What is the yield to call on a bond that has an 8% coupon paid annually, $1,000 face value, 10 years to maturity and is first callable in 6 years? The current market price is $1,100. The call price is the face value plus 1-year’s interest.

A) 7.02%.

B) 7.14%.

C) 6.00%.

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N = 6; PV = -1,100.00; PMT = 80; FV = 1,080; Compute I/Y = 7.02%.

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A $1,000 bond with an annual coupon rate of 10% has 10 years to maturity and is currently priced at $800. What is the bond's approximate yield-to-maturity?

A) 12.6%.

B) 13.8%.

C) 11.7%.

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FV = 1,000, PMT = 100, N = 10, PV = -800

Compute I = 13.8

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An 11% coupon bond with annual payments and 10 years to maturity is callable in 3 years at a call price of $1,100. If the bond is selling today for 975, the yield to call is:

A) 9.25%.

B) 10.26%.

C) 14.97%.

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PMT = 110, N = 3, FV = 1,100, PV = 975

Compute I = 14.97

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A coupon bond pays annual interest, has a par value of $1,000, matures in 4 years, has a coupon rate of $100, and a yield to maturity of 12%. The current yield on this bond is:

A) 11.25%.

B) 9.50%.

C) 10.65%.

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FV = 1,000; N = 4; PMT = 100; I = 12; CPT → PV = 939.25.

Current yield = coupon / current price

100 / 939.25 × 100 = 10.65

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If interest rates and risk factors remain constant over the remainder of a coupon bond's life, and the bond is trading at a discount today, it will have a:

A) negative current yield and a capital gain.

B) positive current yield and a capital gain.

C) positive current yield, only.

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A coupon bond will have a positive current yield. If it is trading at a discount, it will have a capital gain because its value at maturity will be greater than its price today.