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?


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