Question

Use the bond term's below to answer the question
Maturity 7 years
Coupon Rate 4%
Face value $1,000
Annual Coupons
YTM 3%

Assuming the YTM remains constant throughout the bond's life, what is percentage capital gains/loss between periods 2 and 3 ?

-0.8496%

-0.7931%

-0.8328%

-0.8248%

Answer 1

Price of the Bond in Year 2

Face Value of the bond = $1,000

Semi-annual Coupon Amount = $40 [$1,000 x 4%]

Yield to Maturity = 3%

Maturity Period = 5 Years [7 Years – 2 Year]

Price of the Bond = Present Value of the Coupon Payments + Present Value of the face Value

= $40[PVIFA 3%, 5 Years] + $1,000[PVIF 3%, 5 Years]

= [$40 x 4.57971] + [$1,000 x 0.86261]

= $183.19 + $862.61

= $1,045.80

Price of the Bond in Year 3

Face Value of the bond = $1,000

Semi-annual Coupon Amount = $40 [$1,000 x 4%]

Yield to Maturity = 3%

Maturity Period = 4 Years [7 Years – 3 Year]

Price of the Bond = Present Value of the Coupon Payments + Present Value of the face Value

= $40[PVIFA 3%, 4 Years] + $1,000[PVIF 3%, 4 Years]

= [$40 x 3.71710] + [$1,000 x 0.88849]

= $148.68 + $888.49

= $1,037.17

Change in Bond Price

Change in Bond Price = Price of the Bond in Year 3 - Price of the Bond in Year 2

= $1,037.17 - $1,045.80

= -$8.63

Percentage capital gains/loss between periods 2 and 3

Percentage capital gains/loss between periods 2 and 3 = [Change in Price of the Bond / Price of the Bond in Year 2] x 100

= [-$8.63 / $1,045.80] x 100

= -0.8248%

“Hence, the Percentage capital gains/loss between periods 2 and 3 would be -0.8248%”

NOTE

-The formula for calculating the Present Value Annuity Inflow Factor (PVIFA) is [{1 - (1 / (1 + r)ⁿ} / r], where “r” is the Yield to Maturity of the Bond and “n” is the number of maturity periods of the Bond.

--The formula for calculating the Present Value Inflow Factor (PVIF) is [1 / (1 + r)ⁿ], where “r” is the Yield to Maturity of the Bond and “n” is the number of maturity periods of the Bond.