Question

Suppose that 6-month, 12-month, 18-month, and 24-month zero rates are 3.8%, 4%, 4.3%, and 4.6% per annum with continuous compounding respectively. Estimate the cash price of a bond with a face value of 100 that will mature in 24 months and pays a coupon of 10% per annum semiannually. approx. $112.37 approx. $104.56 approx. $110.17 approx. $99.85

Answer 1

Please refer to below spreadsheet for calculation and answer. Cell reference also provided.

A В C D E 1 Bond Face value Annual Coupon rate Coupon frequency Years to maturity $100.00 2 10% 2 2 6 Cash Flow of PV of CF Year Zero rates Coupon bond $5.00 7 $4.91 8 0.5 3.80% $5.00 $4.80 9 1 4.00% $5.00 $4.69 10 1.5 4.30% $105.00 $95.77 11 4.60% 2 12 $110.17 Cash Price of Bond 13 14 15 16 LLU

Cell reference -

А В C D E 1 Bond Face value Annual Coupon rate 2 100 0.1 2 Coupon frequency Years to maturity 4 2 6 Cash Flow of PV of CF Year Zero rates Coupon bond -$C$2*$C$3/2 -$C$2*$C$3/2 -$C$2*$C$3/2 -$C$2*$C$3/2+C2 D11/EXP (B11*C11) 7 0.5 D8/EXP(B8*C8) 0.038 8 D9/EXP(B9*C9) D10/EXP (B10*C10) 1 0.04 10 1.5 2 0.043 11 0.046 12 =SUM(E8:E11) Cash Price of Bond 13 14 15 16 Lr LC LO

Hope this will help, please do comment if you need any further explanation. Your feedback would be highly appreciated.