Question

Bond Valuation

All bonds have a $1,000 face or par value unless otherwise stated. k_c is the coupon rate and k_dis the market cost of debt.

Value a 20yr bond with 14 years to go before maturity. Its par value is 1000, annual coupon is 7.5% and the applicable interest rate is currently 11%. What would be your total rate of return if you sold this bond in one year (a) if Interest rates remained unchanged, (b) Interest rates rose to 15%?

Answer 1

Purchase Price

Value of Bond =

Where r is the discounting rate of a compounding period i.e. 11%

And n is the no of Compounding periods 14 years

Coupon 7.5%

=

= 755.63

a) IF Rate remains unchanged.

Value of Bond =

Where r is the discounting rate of a compounding period i.e. 11%

And n is the no of Compounding periods 13 years

Coupon 7.5%

=

= 763.75

Return = Coupon + Capital Gain / Purchase Price

= 75 + (763.75 - 755.63) / 755.63

= 11%

b)

If Rates changed to 15%

Value of Bond =

Where r is the discounting rate of a compounding period i.e. 15%

And n is the no of Compounding periods 13 years

Coupon 7.5%

=

= 733.53

Return = Coupon + Capital Gain / Purchase Price

= 75 + (733.53 - 755.63) / 755.63

= 7%

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