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Fixed Income【Reading 57】Sample

By purchasing a noncallable, nonputable, U.S. Government 30-year bond, an investor is entitled to:
A)
full recovery of face value at maturity or when the bond is retired.
B)
annuity of coupon payments.
C)
annuity of coupon payments plus recovery of principal at maturity.



Bond investors are entitled to two distinct types of cash flows: (1) the periodic receipt of coupon income over the life of the bond, and (2) the recovery of principal (or face value) at the end of the bond’s life.

Answering an essay question on a midterm examination, a finance student writes these two statements:
Statement 1: The value of a fixed income security is the sum of the present values of all its expected future coupon payments.
Statement 2: The steps in the bond valuation process are to estimate the bond’s cash flows, determine the appropriate discount rate, and calculate the present value of the expected cash flows.
With respect to the student's statements:
A)
only one is correct.
B)
both are correct.
C)
both are incorrect.



Statement 1 is incorrect. The value of a fixed income security is the sum of the present values of its expected future coupon payments and its future principal repayment. Statement 2 is correct. The three steps in the bond valuation process are to estimate the cash flows over the life of the security; determine the appropriate discount rate based on the risk of the cash flows; and calculate the present value of the cash flows using the appropriate discount rate.

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Assume a city issues a $5 million bond to build a new arena. The bond pays 8% semiannual interest and will mature in 10 years. Current interest rates are 9%. What is the present value of this bond and what will the bond's value be in seven years from today?
Present ValueValue in 7 Years from Today
A)
4,674,8024,871,053
B)
4,674,8024,931,276
C)
5,339,7584,871,053



Present Value:
Since the current interest rate is above the coupon rate the bond will be issued at a discount. FV = $5,000,000; N = 20; PMT = (0.04)(5 million) = $200,000; I/Y = 4.5; CPT → PV = -$4,674,802
Value in 7 Years:
Since the current interest rate is above the coupon rate the bond will be issued at a discount. FV = $5,000,000; N = 6; PMT = (0.04)(5 million) = $200,000; I/Y = 4.5; CPT → PV = -$4,871,053

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A corporate bond with the following data is issued:
  • $1,000 par value.
  • 8% coupon payments.
  • 5 years to maturity with semiannual coupon payments.
  • Market interest rates are 10%.

What is the total interest expense?
A)
923.
B)
545.
C)
477.



Total interest expense is the difference between the amount paid by the issuer and the amount received from the bondholder.
Present value of the bond is computed as follows: FV = 1,000; PMT = [(1,000)(0.08)] / 2 = 40; I/Y = 5; N = 10; CPT → PV = -923
[($40 coupon payments)(10 periods) + $1,000 par value] – $923 present value of the bond = 477

TOP

A bond is issued with the following data:
  • $10 million face value.
  • 9% coupon rate.
  • 8% market rate.
  • 3-year bond with semiannual payments.

What is the present value of the bond?
A)
$10,138,754.
B)
$10,000,000.
C)
$10,262,107.



FV = 10,000,000; PMT = 450,000; I/Y = 4; N = 6; CPT → PV = -10,262,107

TOP

It is easier to value bonds than to value equities because:
A)
the future cash flows of bonds are more stable.
B)
Both of these choices are correct.
C)
there is no maturity value for common stock.



Bonds pay out a specified periodic cash flow (coupon payment) throughout the life of the bond and pay out a lump sum at the maturity date.  Common stocks don't have a maturity date and have more volatility than bonds.

TOP

Which of the following characteristics would create the least difficulty in estimating a bond’s cash flows?
A)
Noncallable bond.
B)
Variable coupon rate.
C)
Putable bond.


Normally, estimating the cash flow stream is straightforward for a high quality, option-free bond due to the high degree of certainty in the timing and amount of the payments. The following four conditions could lead to difficulty in forecasting the bond’s future cash flow stream:
  • increased credit risk;
  • the presence of embedded options (i.e., call/put features or sinking fund provisions);
  • the use of variable rather than fixed coupon rate; and
  • the presence of a conversion or exchange privilege.

TOP

Which of the following characteristics would create the most difficulty in estimating a bond's cash flows?
A)
Fixed coupon rate.
B)
Noncallable bond.
C)
Exchange privilege.



Normally, estimating the cash flow stream is straightforward for a high quality, option-free bond due to the high degree of certainty in the timing and amount of the payments. The following four conditions could lead to difficulty in forecasting the bond’s future cash flow stream: (1) increased credit risk, (2) the presence of embedded options (i.e., call/put features or sinking fund provisions), (3) the use of variable rather than fixed coupon rate, and (4) the presence of a conversion or exchange privilege.

TOP

Which of the following characteristics would create the least difficulty in estimating a bond’s cash flows?
A)
Sinking fund provisions.
B)
Conversion privilege.
C)
Fixed coupon rate.



Normally, estimating the cash flow stream is straightforward for a high quality, option-free bond due to the high degree of certainty in the timing and amount of the payments. The following four conditions could lead to difficulty in forecasting the bond’s future cash flow stream:
  • increased credit risk;
  • the presence of embedded options (i.e., call/put features or sinking fund provisions);
  • the use of variable rather than fixed coupon rate; and
  • the presence of a conversion or exchange privilege.

TOP

Today an investor purchases a $1,000 face value, 10%, 20-year, semi-annual bond at a discount for $900. He wants to sell the bond in 6 years when he estimates the yields will be 9%. What is the estimate of the future price?
A)
$1,079.
B)
$1,152.
C)
$946.



In 6 years, there will be 14 years (20 − 6), or 14 × 2 = 28 semi-annual periods remaining of the bond's life So, N = (20 − 6)(2) = 28; PMT = (1,000 × 0.10) / 2 = 50; I/Y = 9/2 = 4.5; FV = 1,000; CPT → PV = 1,079.
Note: Calculate the PV (we are interested in the PV 6 years from now), not the FV.

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