Reading 6: Discounted Cash Flow Applications - LOS d, (Par black, style

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1、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)   1.00%.

B)   1.01%.

C)   9.00%.

D)   9.60%.

2、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)   3.95%.

B)   4.07%.

C)   4.26%.

D)   2.04%.

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

A)   4.93%.

B)   4.56%.

C)   5.06%.

D)   5.12%.

4、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)   9.37%.

D)   1.00%.

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

A)   3.81%.

B)   3.84%.

C)   3.87%.

D)   3.98%.

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答案和详解如下：

1、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)   1.00%.

B)   1.01%.

C)   9.00%.

D)   9.60%.

The correct answer was D)    

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%.

2、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)   3.95%.

B)   4.07%.

C)   4.26%.

D)   2.04%.

The correct answer was C)    

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

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

A)   4.93%.

B)   4.56%.

C)   5.06%.

D)   5.12%.

The correct answer was A)

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) = .04927

4、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)   9.37%.

D)   1.00%.

The correct answer was B)    

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.

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

A)   3.81%.

B)   3.84%.

C)   3.87%.

D)   3.98%.

The correct answer was B)    

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%.