The spot interest rate for a 1-year risk-free investment is 6%, while the forward rate for a risk-free investment between years 1 and 2 is 7:21% (both annualized). What should be the arbitrage-free price of a zero-coupon 2-year corporate bond with € 10 000 face value if the market requires a spread of 250 bp as a risk premium? Could anyone help me to solve this problem ? Thanks !
- Calculate the value of a dollar after 2 years:
Value of a dollar after 2 years = 1 * (1 + SR) * (1 + FR1,1) = 1 * (1 + 0,6) + (1 +0,0721) = 1,136426
- Calculate the annual risk-free yield ®:
1,136426 = (1+r)^2 <=> r = 0,066032833 ~6,6%
- Calculate the PV of the zero-bond incl. risk-premium:
Yield incl. risk-premium = 6,6% + 2,5% = 9,10% PV of zero bond:
FV =10.000; N=2; I/Y=9,1; PMT=0 <=> CPT PV <=> PV = 8.400,87
Regards, Oscar
Thanks !