The valuation of Junior and Senior debts (Stulz,ch18)

[Yun chiang Tai]

Hello David:
I have a question as follows
A junior bond with a face value of 200 matures in 5 years. A senior bond on the same firms also
matures in 5 years, and has a face value of 100. Assume -A=0.5 and the riskfree rate =0.4. Firm value
is equal to 400. Using the Merton model, what is the value of junior bond?
with the following information that some are strictly wrong
d1 d2 N(d1) N(d2)
1.978 0.860 0.9761 0.8051
1.978 0.860 0.8051 0.9761
0.9952 -.1228 0.8413 0.5478
0.9952 -1.505 0.8413 0.0661
0.9952 -.1228 0.8413 0.4522
and the result of junior debt is 99.07. How to solve it?
My idea is to follow the lecture note (1) First to obtain the value of senior debt
(2) then deduct it to obtain the junior debt
but how to know that which one in the five column information is right and which one is wrong?
Thank you so much
chris

 

[David Harper CFA FRM]

Hi Chris,

To save time, I input this into my Merton XLS.
See this XLS
(I assume you mean the riskfree rate = 4% = 0.04 rather than 0.4? Please check my input assumptions)

Re: the five column, you can probably deduce per normal probabilities (e.g., d1 = 1.978 must be > 80%), but it is a strange question

See red cell for answer near to yours. Per Stulz, price two call options
1. Equity as call option on $400 firm with strike of $100 (just LT debt) = $324.50
2. Equity as call option on $400 firm with strike of $300 (LT debt + Sub debt) = $225.27
Difference is value of subord debt = $99.23.

David