Reading 6: Discounted Cash Flow Applications-LOS e 习题精选 2011, effective, interpret, discount, holding

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Session 2: Quantitative Methods: Basic Concepts
Reading 6: Discounted Cash Flow Applications

LOS e: Calculate and interpret the bank discount yield, holding period yield, effective annual yield, and money market yield for a U.S. Treasury bill.

 

 

A 10% coupon bond was purchased for $1,000. One year later the bond was sold for $915 to yield 11%. The investor's holding period yield on this bond is closest to:

A) 9.0%.

B) 1.5%.

C) 18.5%.

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HPY = [(interest + ending value) / beginning value] ? 1
= [(100 + 915) / 1,000] ? 1
= 1.015 ? 1 = 1.5%

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The bank discount of a $1,000,000 T-bill with 135 days until maturity that is currently selling for $979,000 is:

A) 5.6%.

B) 6.1%.

C) 5.8%.

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($21,000 / 1,000,000) × (360 / 135) = 5.6%.

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A Treasury bill (T-bill) with a face value of $10,000 and 137 days until maturity is selling for 98.125% of face value. Which of the following is closest to the bank discount yield on the T-bill?

A) 4.56%.

B) 5.06%.

C) 4.93%.

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The formula for bank discount yield is: (D / F) × (360 / t). Actual discount is 1 ? 0.98125 = 0.01875. Annualized is: 0.01875 × (360 / 137) = 0.04927

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What is the yield on a discount basis for a Treasury bill priced at $97,965 with a face value of $100,000 that has 172 days to maturity?

A) 2.04%.

B) 4.26%.

C) 3.95%.

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($2,035 / $100,000) × (360 / 172) = 0.04259 = 4.26% = bank discount yield.

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A Treasury bill has 40 days to maturity, a par value of $10,000, and is currently selling for $9,900. Its effective annual yield is closest to:

A) 9.60%.

B) 1.00%.

C) 9.00%.

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The effective annual yield (EAY) is based on a 365-day year and accounts for compound interest. EAY = (1 + holding period yield)^365/t ? 1. The holding period yield formula is (price received at maturity ? initial price + interest payments) / (initial price) = (10,000 ? 9,900 + 0) / (9,900) = 1.01%. EAY = (1.0101)^365/40 ? 1 = 9.60%.

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A Treasury bill (T-bill) with a face value of $10,000 and 44 days until maturity has a holding period yield of 1.1247%. Which of the following is closest to the effective annual yield on the T-bill?

A) 12.47%.

B) 8.76%.

C) 9.72%.

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The formula for the effective annual yield is: ((1 + HPY)^365/t) ? 1. Therefore, the EAY is: ((1.011247)^(365/44)) ? 1 = 0.0972, or 9.72%

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A Treasury bill (T-bill) with 38 days until maturity has a bank discount yield of 3.82%. Which of the following is closest to the money market yield on the T-bill?

A) 3.81%.

B) 3.84%.

C) 3.87%.

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The formula for the money market yield is: [360 × bank discount yield] / [360 ? (t × bank discount yield)]. Therefore, the money market yield is: [360 × 0.0382] / [360 ? (38 × 0.0382)] = (13.752) / (358.548) = 0.0384, or 3.84%.

Alternatively: Actual discount = 3.82%(38 / 360) = 0.4032%.

T-Bill price = 100 ? 0.4032 = 99.5968%.

HPR = (100 / 99.5968) ? 1 = 0.4048%.

MMY = 0.4048% × (360 / 38) = 3.835%.

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A Treasury bill has 40 days to maturity, a par value of $10,000, and was just purchased by an investor for $9,900. Its holding period yield is closest to:

A) 9.00%.

B) 1.01%.

C) 1.00%.

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The holding period yield is the return that the investor will earn if the bill is held until it matures. The holding period yield formula is (price received at maturity ? initial price + interest payments) / (initial price) = (10,000 ? 9,900 + 0) / (9,900) = 1.01%. Recall that when buying a T-bill, investors pay the face value less the discount and receive the face value at maturity.

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A T-bill with a face value of $100,000 and 140 days until maturity is selling for $98,000. What is the money market yield?

A) 5.41%.

B) 2.04%.

C) 5.25%.

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The money market yield is equivalent to the holding period yield annualized based on a 360-day year. = (2,000 / 98,000)(360 / 140) = 0.0525, or 5.25%.

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A T-bill with a face value of $100,000 and 140 days until maturity is selling for $98,000. What is its holding period yield?

A) 5.25%.

B) 2.04%.

C) 5.14%.

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The holding period yield is the return the investor will earn if the T-bill is held to maturity. HPY = (100,000 – 98,000) / 98,000 = 0.0204, or 2.04%.