1.A company issued an annual-pay bond with a face value of $135,662, maturity of 4 years, and 7.00 percent coupon, while the market interest rates are 8.00 percent

What is the present value of the interest payments on the date when the bonds are issued?

A)   $131,164.

B)   $49,857.

C)   $31,453.

D)   $18,992.

2.What is the unamortized discount on the date when the bonds are issued?

A)   $1,748.

B)   $499.

C)   $15,729.

D)   $4,493.

3.What is the unamortized discount at the end of the first year?

A)   $3,495.

B)   $1,209.

C)   $538.

D)   $2,247.

4.A company issued a bond with a face value of $67,831, maturity of 4 years, and 7 percent coupon, while the market interest rates are 8 percent.

What is the unamortized discount when the bonds are issued?

A)   $498.58.

B)   $15,726.54.

C)   $2,246.65.

D)   $1,748.07.

5.What is the unamortized discount at the end of the first year?

A)   $1,209.61.

B)   $538.46.

C)   $1,748.07.

D)   $2,246.65.

答案和详解如下：

1.A company issued an annual-pay bond with a face value of $135,662, maturity of 4 years, and 7.00 percent coupon, while the market interest rates are 8.00 percent

What is the present value of the interest payments on the date when the bonds are issued?

A)   $131,164.

B)   $49,857.

C)   $31,453.

D)   $18,992.

The correct answer was C)

Present value of the interest payments on the date of issue is $31,453 = [I/Y = 8.00%, N = 4, PMT = $9,496.34 ($135,662 * 0.07 ), FV = $0 ].

2.What is the unamortized discount on the date when the bonds are issued?

A)   $1,748.

B)   $499.

C)   $15,729.

D)   $4,493.

The correct answer was D)

The unamortized discount rate at the time bonds are issued will be $4,493.

Face value of bonds = $135,662.
Proceeds from bond sale = $131,168.70 [I/Y = 8.00%, N = 4, PMT = $9,496.34 ($135,662 * 0.07 ), FV = $135,662 ].
Unamortized discount = $4,493 = ($135,662 - $131,169).

3.What is the unamortized discount at the end of the first year?

A)   $3,495.

B)   $1,209.

C)   $538.

D)   $2,247.

The correct answer was A)    

The unamortized discount will decrease by $998 at the end of first year and will be $3,495.

Interest expense = ($131,169)(0.08) = $10,493.52, or $10,494.
Coupon payment = ($135,662)(0.07) = $9,496.
Change in discount = ($10,494 - $9,496) = $998.
Discount at the end of first year = $4,493 - $998 = $3,495.

4.A company issued a bond with a face value of $67,831, maturity of 4 years, and 7 percent coupon, while the market interest rates are 8 percent.

What is the unamortized discount when the bonds are issued?

A)   $498.58.

B)   $15,726.54.

C)   $2,246.65.

D)   $1,748.07.

The correct answer was C)

Coupon payment = ($67,831)(0.07) = $4,748.17.
Present value of bond: FV = $67,831, N = 4, I = 8, PMT = $4,748.17, CPT PV = $65,584.35.
Discount = $67,831 - $65,584.35 = $2,246.65.

5.What is the unamortized discount at the end of the first year?

A)   $1,209.61.

B)   $538.46.

C)   $1,748.07.

D)   $2,246.65.

The correct answer was C)

Interest expense = ($65,584.35)(0.08) = $5,246.75.
Coupon payment = ($67,831)(0.07) = $4,748.17.
Change in discount = $5,246.75 - 4,748.17 = $498.58.
Discount at the end of the first year = $2,246.65 - 498.58 = $1,748.07.