interest rate impact on credit spread

Hi schweser says " as interest rates increase the expected value of the firm at maturity increases which inturn decreases the risk of default , a reduction in risk will narrow credit spreads" However , as per merton model Vt = Dt + St [value of firm = value of debt + equity value] if interest rates increase value of debt decreases right ? thereby decreasing the value of firm and widening the credit spread Please help me , Am I missing something here

The value of the equity is like a call option. The strike of that option is the value of the debt; everything above and beyond the present debt value belongs to the stockholders. Now, if the present value of the debt declines because of rising interest rates, then it’s like owning a call option whose strike is going down => good for you.

Here is another way to look at it: Imagine you get a 30 year 1 million mortgage at 5 % interest, no money down. Right after you lock in that rate the interest rates jump to 10 %. This means that the PV of your mortgage just went down a lot. Let's assume it trades at 70 % of its original value in the market. You could now issue a 700,000 bond at 10 % coupon to retire the original 1 million debt. Your annual interest obligation went up, but your absolute level of debt went down by 30 %. If the house is still worth 1 million you just increased your equity from 0 to 300,000.

@Factor hedge: Do you mind posting the reference, i.e. what book/page in Schweser and which article/text?

@Karlsolo thank you , excellent explanation . so the equation in simple terms are St = St - max (St- Pv of Dt , 0 ) if the Pv of debt decreases the call option value increases there by in the equation (merton) Vt = Dt + St [value of firm = value of debt + equity value] my St value increases , I hope its right . @wat it is mentioned in schweser book 4 (Credit risk measurement and management) pg 98 AIM 86.2

Actually, I’m not quite sold on the explanation. @Klarsolo - I think you did a great job explaining why the value of a firm’s equity increases as interest rates increase: interest rate increase --> debt value (or “strike price”) decreases --> equity increase, assuming Vt has stayed the same. What the reading seems to imply, though, is that Vt is what’s increasing as a result of an increase in the risk-free rate, which I’m not entirely sold on yet. Based solely on the credit spread formula, I can see why credit spreads decrease/narrow if the risk-free rate increases (you’re subtracting a larger number), but I’m not readily seeing why an increase in the risk free rate implies that the value of Vt should increase. (This is straight from the core text - Stulz, Ch 18)