# How do I solve this exercise with bond and probabilities?

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?

• Is this a homework question? – JTP - Apologise to Monica Jan 13 '19 at 15:04
• I would compute the expected value for each period by multiplying the probability with the payoff (coupon/notional) and then discount the results to get the present value, instead of starting with the present values. – 0xFEE1DEAD Jan 13 '19 at 18:26