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

1215

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%.

---

 

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

1215

A Treasury bill with a face value of $1,000,000 and 45 days until maturity is selling for $987,000. The Treasury bill’s bank discount yield is closest to:

A) 10.54%.

B) 10.40%.

C) 7.90%.

---

The actual discount is 1.3%, 1.3% × (360 / 45) = 10.4%

The bank discount yield is computed by the following formula, r = (dollar discount / face value) × (360 / number of days until maturity) = [(1,000,000 ? 987,000) / (1,000,000)] × (360 / 45) = 10.40%.

1215

What is the effective annual yield for a Treasury bill priced at $98,853 with a face value of $100,000 and 90 days remaining until maturity?

A) 1.16%.

B) 4.64%.

C) 4.79%.

---

HPY = (100,000 ? 98,853) / 98,853 = 1.16%

EAY = (1 + 0.0116)^365/90 ? 1 = 4.79%

1215

A T-bill with a face value of $100,000 and 140 days until maturity is selling for $98,000. What is the effective annual yield (EAY)?

A) 2.04%.

B) 5.41%.

C) 5.14%.

---

The EAY takes the holding period yield and annualizes it based on a 365-day year accounting for compounding. HPY = (100,000 ? 98,000) / 98,000 = 0.0204. EAY = (1 + HPY)^365/t ? 1 = (1.0204)^365/140 ? 1 = 0.05406 = 5.41%.

1215

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%.

---

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%.

1215

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%.

---

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%.

1215

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

A) 5.41%.

B) 4.18%.

C) 5.14%.

---

Actual discount is 2%, annualized discount is: 0.02(360 / 140) = 5.14%

1215

A Treasury bill (T-bill) with a face value of $10,000 and 219 days until maturity is selling for 97.375% of face value. Which of the following is closest to the holding period yield on the T-bill if held until maturity?

A) 2.63%.

B) 2.81%.

C) 2.70%.

---

The formula for holding period yield is: (P₁ ? P₀ + D₁) / (P₀), where D₁ for a T-bill is zero (it does not have a coupon). Therefore, the HPY is: ($10,000 ? $9,737.50) / ($9,737.50) = 0.0270 = 2.70%.

Alternatively (100 / 97.375) ? 1 = 0.02696.

1215

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%.

---

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%

1215

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%.

---

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%.