Question

Please show formula and workings

New South Wales Treasury has issued $1,000 face value, 25-year bonds that pay a coupon of 9.875 per cent semi-annually.

The current market rate for similar securities is 11 per cent.

Required

a What is the bond’s current market value?

b What will be the bond’s price if rates in the market (i) decrease to 9 per cent; (ii) increase to 12 per cent?

Suppose the bonds were to mature in 12 years. How would the interest rate changes in part b affect the bond prices?

Answer 1

Price of a bond is mathematically represented as:

where P is price of bond with periodic coupon C, periodic YTM i, n periods to maturity and M face value.

For bond in question, M = $1000, n = 25 * 2 = 50 semi-annual periods, C = 9.875% * $1000/2 = $49.375 (semi-annually)

a) i = 11%/2 = 5.5% (semi-annually)

P = $835.99 + $68.77 = $904.76

b) i) i = 9%/2 = 4.5% (semi-annually)

P = $975.75 + $110.71 = $1086.46

(ii) i = 12%/2 = 6% (semi-annually)

P = $778.24 + $54.29 = $832.53

c) If n = 12 years = 12 * 2 = 24 semi-annual periods

Original price for bond when i = 5.5% (semi-annualy):

P = $649.37 + $276.66 = $926.02

when i = 4.5% semi-annually

P = $715.71 + $347.70 = $1063.42

when i = 6% semi-annually

P = $619.67 + $246.98 = $866.65