1215

An investor has the following options available to them:

• They can buy a 10% semi annual coupon, 10-year bond for $1,000.
• The coupons can be reinvested at 12%.
• They estimate the bond will be sold in 3 years $1,050.

Based on this information, what would be the average annual rate of return over the 3 years?

A) 13.5%.

B) 11.5%.

C) 9.5%.

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1. Find the FV of the coupons and interest on interest:

N = 3(2) = 6; I = 12/2 = 6; PMT = 50; CPT → FV = 348.77

2. Determine the value of the bond at the end of 3 years:

1,050.00 (given) + 348.77 (computed in step 1) = 1,398.77

3. Equate FV (1,398.77) with PV (1,000) over 3 years (N = 6); CPT → I = 5.75(2) = 11.5%

1215

What is the present value of a three-year security that pays a fixed annual coupon of 6% using a discount rate of 7%?

A) 92.48.

B) 100.00.

C) 97.38.

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This value is computed as follows:

Present Value = 6/1.07 + 6/1.07² + 106/1.07³ = 97.38

The value 92.48 results if the coupon payment at maturity of the bond is neglected. The coupon rate and the discount rate are not equal so 100.00 cannot be the correct answer.

1215

Assume an option-free 5% coupon bond with annual coupon payments has two years remaining to maturity. A putable bond that is the same in every respect as the option-free bond is priced at 101.76. With the term structure flat at 6% what is the value of the embedded put option?

A) 1.76.

B) -3.59.

C) 3.59.

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The value of the embedded put option of the putable bond is the difference between the price of the putable bond and the price of the option-free bond.

The value of the option-free bond is computed as follows: PMT = 5; N = 2; FV = 100; I = 6; CPT → PV = -98.17(ignore sign).

The option value = 101.79 ? 98.17 = 3.59.

1215

An investor gathered the following information on three zero-coupon bonds:

• 1-year, $600 par, zero-coupon bond valued at $571
• 2-year, $600 par, zero-coupon bond valued at $544
• 3-year, $10,600 par, zero-coupon bond valued at $8,901

Given the above information, how much should an investor pay for a $10,000 par, 3-year, 6%, annual-pay coupon bond?

A) $10,000.

B) Cannot be determined by the information provided.

C) $10,016.

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A coupon bond can be viewed simply as a portfolio of zero-coupon bonds. The value of the coupon bond should simply be the summation of the present values of the three zero-coupon bonds. Hence, the value of the 3-year annual-pay bond should be $10,016 (571 + 544 + 8,901).

1215

An investor gathered the following information on two zero-coupon bonds:

• 1-year, $800 par, zero-coupon bond valued at $762
• 2-year, $10,800 par, zero-coupon bond valued at $9,796

Given the above information, how much should an investor pay for a $10,000 par, 2-year, 8%, annual-pay coupon bond?

A) $9,796.

B) $10,558.

C) $10,000.

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A coupon bond can be viewed simply as a portfolio of zero-coupon bonds. The value of the coupon bond should simply be the summation of the present values of the two zero-coupon bonds. Hence, the value of the 2-year annual-pay bond should be $10,558 ($762 + $9,796).

1215

What is the present value of a 7% semiannual-pay bond with a $1,000 face value and 20 years to maturity if similar bonds are now yielding 8.25%?

A) $879.52.

B) $1,000.00.

C) $878.56.

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N = 20 × 2 = 40; I/Y = 8.25/2 = 4.125; PMT = 70/2 = 35; and FV = 1,000.

Compute PV = 878.56.

1215

Given a required yield to maturity of 6%, what is the intrinsic value of a semi-annual pay coupon bond with an 8% coupon and 15 years remaining until maturity?

A) $1,196.

B) $1,095.

C) $1,202.

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This problem can be solved most easily using your financial calculator. Using semiannual payments, I = 6/2 = 3%; PMT = 80/2 = $40; N = 15 × 2 = 30; FV = $1,000; CPT → PV = $1,196.

1215

Assuming the risk-free rate is 5% and the appropriate risk premium for an A-rated issuer is 4%, the appropriate discount rate for an A-rated corporate bond is:

A) 1%.

B) 5%.

C) 9%.

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The yield on a risky bond = appropriate risk-free rate + appropriate risk premium.

1215

Which of the following statements about a bond’s cash flows is most accurate? The appropriate discount rate is a function of:

A) the risk-free rate plus the risk premium.

B) only the return on the market.

C) the risk-free rate plus the return on the market.

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The return on the market would be used only when discounting the cash flows of the market. The risk premium reflects the cost of any incremental risk incurred by the investor above and beyond that of the risk-free security.