Question

Threw has recently issued two bonds with semi-annual payments of R50. One bond has maturity of 2 years and the other one has a maturity of 10 years. Both bonds currently sell at par R1 000, with a yield-to-maturity (YTM) of 9%.

Required:

3.1. Calculate the price of each bond if the YTM drops to 6%. [4]

3.2. Calculate the price of each bond if the YTM rises to 10%. [4]

3.3. Comment on the pattern observed as a result of these changes. [2]

Answer 1

3.1) If YTM drops to 6%

Price of bond having maturity of 2 years

Here face value = 1000 ,
Interest = 50
n = no of coupon payments= 2 x 2 = 4
YTM = 6%/2 = 3%
Price of bond = Interest x PVIFA(YTM%,n) + redemption value x PVIF(YTM%,n)
PVIFA(YTM%,n) = [1-(1/(1+r)^n / r ]
PVIFA(3%,4) = [1-(1/(1+3%)^4 / 3%]
=[1-(1/(1+0.03)^4 / 0.03]
=[1-(1/(1.03)^4 / 0.03]
=[1-0.888487 / 0.03]
=0.111513/0.03
=3.717098
PVIF(3%,4) = 1/(1+3%)^4
=1/(1.03)^4
= 0.888487
Price of bond = 50 x 3.7171 + 1000 x 0.888487
=185.85 + 888.49
= 1074.34 R

Price of bond having maturity of 10 years

Here face value = 1000 ,
Interest = 50
n = no of coupon payments= 10 x 2 = 20
YTM = 6%/2 = 3%
Price of bond = Interest x PVIFA(YTM%,n) + redemption value x PVIF(YTM%,n)
PVIFA(YTM%,n) = [1-(1/(1+r)^n / r ]
PVIFA(3%,20) = [1-(1/(1+3%)^20 / 3%]
=[1-(1/(1+0.03)^20 / 0.03]
=[1-(1/(1.03)^20 / 0.03]
=[1-0.55368 / 0.03]
=0.44632/0.03
=14.8775
PVIF(3%,20) = 1/(1+3%)^20
=1/(1.03)^20
= 0.55368
Price of bond = 50 x 14.8775 + 1000 x 0.55368
=743.87 + 553.68
= 1297.55 R

3.2) If YTM rises to 10%

Price of bond having maturity of 2 years

Here face value = 1000 ,
Interest = 50
n = no of coupon payments= 2 x 2 = 4
YTM = 10%/2 = 5%
Price of bond = Interest x PVIFA(YTM%,n) + redemption value x PVIF(YTM%,n)
PVIFA(YTM%,n) = [1-(1/(1+r)^n / r ]
PVIFA(5%,4) = [1-(1/(1+5%)^4 / 5%]
=[1-(1/(1+0.05)^4 / 0.05]
=[1-(1/(1.05)^4 / 0.05]
=[1-0.82270 / 0.05]
=0.17730/0.05
=3.54595
PVIF(5%,4) = 1/(1+5%)^4
=1/(1.05)^4
= 0.82270
Price of bond = 50 x 3.54595 + 1000 x 0.82270
=177.30 + 822.70
= 1000 R

Price of bond having maturity of 10 years

Here face value = 1000 ,
Interest = 50
n = no of coupon payments= 10 x 2 = 20
YTM = 10%/2 = 5%
Price of bond = Interest x PVIFA(YTM%,n) + redemption value x PVIF(YTM%,n)
PVIFA(YTM%,n) = [1-(1/(1+r)^n / r ]
PVIFA(5%,20) = [1-(1/(1+5%)^20 / 5%]
=[1-(1/(1+0.05)^20 / 0.05]
=[1-(1/(1.05)^20 / 0.05]
=[1-0.37689 / 0.05]
=0.62311/0.05
=12.4622
PVIF(5%,20) = 1/(1+5%)^20
=1/(1.05)^20
= 0.37689
Price of bond = 50 x 12.4622 + 1000 x 0.37689
=623.11 + 376.89
= 1000 R

3.3) Bond having larger maturity is more sensitive to interest rate risk than bond having shorter maturity