Question

(a) Wojewodzki Corporation issued a 5-year bond at a coupon rate of 5%. The coupon is paid annually. The face value of the bond is $1,000. At the day of issuance, the bond was trading at yield to maturity of 8%. Calculate the price of this bond.

(b) Calculate this bond’s current yield.

(c) Is this bond a discount or a premium bond? Shortly explain

(d) Calculate the price of the bond issued by Wojewodzki Corporation, if the coupons are paid semi-annually.

(e) Shortly explain why as interest rates increase, bonds’ prices fall and as interest rates fall, bonds’ prices increase?

Answer 1

No of periods (N) = 5
YTM =8%
Coupon amount = 1000 x 5%= 50
Par value = 1000

The price of the bond = coupon amount x PVAF(YTM, N) + Par value× PVIF (YTM, N)

=50 x PVAF(8%, 5) + 1000× PVIF (8%,5 )
= $880.21

The price of the bond = $880.21

(Note:
PVAF = present value annuity factor.
PVIF = present value interest factor.) .

a. Current yield= coupon amount per annum/current price of the bond.
=1000x5%/880.21
= 5.68%

b. Bond is trading at a discount because the current price of the bond is below the face value of the bond.

c. No of periods (N) = 5 x 2 = 10
YTM for half year 8/2 = 4%
Coupon amount (semi annual )= 1000×5%×(0.5) = 25
Par value = 1000

The price of the bond = coupon amount x PVAF(YTM, N) + Par value× PVIF (YTM, N)

=25 x PVAF(4%, 10) + 1000× PVIF (4%,10)
= $878.34

The price of the bond = $878.34

(Note:
PVAF = present value annuity factor.
PVIF = present value interest factor.)

d. Price of the bond is calculated by discounting all the future cash flows from Bond including coupon amount and face value. As interest rate increases discounting factor increases and hence the present value of future cash flow decreases, due to which price of the bond decreases.

*Example for reference purpose:

Part 1

Price of the 30 years bond with face value of $1000 after 1 year, with a yield of 8% and coupon rate of 8%.

No of periods (N) = 30-1= 29
YTM for half year= 8%
Coupon amount = 80 (C)
Par value = 1000 (Po)

The price of the bond = coupon amount x PVAF(YTM, N) + Par value× PVIF (YTM, N)

=80 x PVAF(8%, 29) + 1000× PVIF (8%,29)
= $1000

The price of the bond after 1 year (P1)= $1000

(Note:
PVAF = present value annuity factor.
PVIF = present value interest factor.)

Part 2:

Price of the bond after 1 year, with a yield of 8.5%

No of periods (N) = 30-1= 29
YTM for half year= 8.5%
Coupon amount = 80 (C)
Par value = 1000 (Po)

The price of the bond = coupon amount x PVAF(YTM, N) + Par value× PVIF (YTM, N)

=80 x PVAF(8.5%, 29) + 1000× PVIF (8.5%,29)
= $946.70

The price of the bond after 1 year (P1)= $946.70

(Note:
PVAF = present value annuity factor.
PVIF = present value interest factor.)