Q34. A firm issues a $5 million zero coupon bond with a maturity of four years when market rates are 8%. Assuming semiannual compounding periods, the total interest on this bond is:

A)   $1,200,000.

B)   $1,600,000.

C)   $1,346,549.

Q35. A company issued an annual-pay bond with a face value of $135,662, maturity of 4 years, and 7% coupon, while the market interest rates are 8%.

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.

Q36. What is the unamortized discount on the date when the bonds are issued?

A)   $499.

B)   $1,748.

C)   $4,493.

Q37. What is the unamortized discount at the end of the first year?

A)   $1,209.

B)   $538.

C)   $3,495.

Q38. When bonds are issued at a premium:

A)   earnings of the firm increase over the life of the bond as the bond premium is amortized.

B)   coupon interest paid decreases each period as bond premium is amortized.

C)   earnings of the firm decrease over the life of the bond as the bond premium is amortized.

Q39. Assume a city issues a $5 million bond to build a hockey rink. The bond pays 8% semiannual interest and will mature in 10 years. Current interest rates are 6%. What is the present value of this bond?

A)   $5,743,874.

B)   $5,000,000.

C)   $3,363,478.

答案和详解如下：

Q34. A firm issues a $5 million zero coupon bond with a maturity of four years when market rates are 8%. Assuming semiannual compounding periods, the total interest on this bond is:

A)   $1,200,000.

B)   $1,600,000.

C)   $1,346,549.

Correct answer is C)

The interest paid on the bond will be the difference between the future value of the bond of $5,000,000 and the proceeds of the bond when it was originally issued.

First find the present value of the bond found by N = 8; FV = 5,000,000; I = 4; PMT = 0; CPT → PV = −3,653,451.  This is the amount of money the bond generated when it was originally issued.

Then take the difference between the $5,000,000 future price and the $3,653,451 from the proceeds  = $1,346,549 which is the interest paid on the bond.

Q35. A company issued an annual-pay bond with a face value of $135,662, maturity of 4 years, and 7% coupon, while the market interest rates are 8%.

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.

Correct answer is 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; CPT → PV].

Q36. What is the unamortized discount on the date when the bonds are issued?

A)   $499.

B)   $1,748.

C)   $4,493.

Correct answer is C)

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; CPT → PV].
Unamortized discount = $4,493 = ($135,662 − $131,169).

Q37. What is the unamortized discount at the end of the first year?

A)   $1,209.

B)   $538.

C)   $3,495.

Correct answer is C)

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.

Q38. When bonds are issued at a premium:

A)   earnings of the firm increase over the life of the bond as the bond premium is amortized.

B)   coupon interest paid decreases each period as bond premium is amortized.

C)   earnings of the firm decrease over the life of the bond as the bond premium is amortized.

Correct answer is A)

As bond premium is amortized, interest expense will be successively lower each period, thus increasing earnings over the life of the bond.

Q39. Assume a city issues a $5 million bond to build a hockey rink. The bond pays 8% semiannual interest and will mature in 10 years. Current interest rates are 6%. What is the present value of this bond?

A)   $5,743,874.

B)   $5,000,000.

C)   $3,363,478.

Correct answer is A)

Since current interest rates are lower than the coupon rate the bond will be issued at a premium. FV = $5,000,000 N = 20 I/Y = 3 PMT = (0.04)($5,000,000) = $200,000. Compute PV = $-5,743,874

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