I have a bond with coupon rate 10% and annual coupon payments with maturity 3 years, face value 1000 and yield to maturity 8%. The bond pays the first coupon with 20% probability and nothing with 80% of probability. If it pays the first coupon, then with 75% probability it also pays the other coupons + face value and with 25% it does not. What is the price?
I tried to solve it this way:
annual coupon pmts: 100, face value + last coupon: 1100 Present value of first coupon: 100/1.08 = 93 Pres. value of the last 2 coupons (+face value): 100/1.08^2 + 1100/1.08^3 = 959 Price = 80% * 0 + 20% * (93 + 75% * 959) = 163
However, the solution differs from my result. Where is the mistake?