# Distribution of value at horizon

This is taken from the textbook Risk Management in Banking, and is in Chapter 18.2

So I'm confused at the Value at Horizon column in this particular table. How do I get 1004.7 ... ? Also, am I missing out key information for this understanding?

The scenario is: a facility has a current rating of B and has transition probabilities to:

• B to A at 10% with risky rate 5.1%
• B to B at 75% with risky rate 6.0%
• B to C at 7% with risky rate 7.0%
• B to D at 5% with risky rate 9.0%
• B to E at 2% with risky rate 13.0%
• B to Default at 1%

The facility face value is 1000 and has a coupon of 6.5%. The risk-free rate is 5% and the current market rate applicable for valuation of the facility is 6%. The horizon is 1 year.

So the current value of the facility is the PV of the next 2 cashflows: 65 and 1065 at the credit risk-adjusted market rate of 6%:

$$\frac{65}{1+6\%} + \frac{1065}{(1+6\%)^2} = 1009.2$$

However, why is it that the value at horizon, as stated in the textbook is 1004.7? Am I missing out a discounting formula that is missing from the textbook?