Rx bond math question - struggling with understanding the question
Prepping for an Rx interview. From the recruiter, this is verbatim, the technical question he sent me that will show up in my interview:
"What is the IRR for Rate of Return for a bond trading at $400, now trading at 50% with a coupon of 10%? (Candidate should calculate compound interest in your head)"
How is this calculated without a maturity? Makes no sense to me. assuming i'd do YTM = (coupon + price appreciation/n)/((face+price)/2)
There's no way this is verbatim (for a start it's not even consistent/accurate English).
But yeah you need maturity to calculate YTM or vice versa, and it's not clear what's even going on in the question (par value uncertain, possibly 2 distinct current trading prices).
I agree...it makes no sense to me. I tried to clarify the question with the recruiter again and this is what he sent me.
I'm not sure there's anything more you can do here, if you keep pushing it you'll look weird - is this recruiter the one interviewing you?
Bond math guide from restructuringinterviews covers everything pretty well, you'll be fine with actual questions.
Good luck!
You need to know time to maturity - but if you assume 5-year hold period:
You pay $400 for a security that pays $80 per year (10% coupon on $800 face value), thats a 20% IRR.
At maturity in 5 years you’ll receive double your money (face value of the security) - 2x in 5 years is about a 15% IRR.
Add those together and you get a 30-35% IRR, probably closer to 30%.
Thank you. If they give me a maturity, I'll follow this. Why closer to 30% IRR even though you get 35%?
The rule of thumb for 2x money over 5 years is 15%, but that comes from basically equal installments of cash flows over the 5 years. Because this component of the IRR is occurring all at the end of the 5 years (the return of principal), it needs to get discounted back more.
Hence closer to 30 than 35
Probably asking for IRR so you should calculate YTM. Generally, for bond math questions, when they're asking for the return on a bond, it's just YTM. To calculate this, you also need to know the years to maturity, and let's just assume 5 years to maturity here.
For bond math, I've always thought it was more "impressive" to walk through the rationale of YTM by splitting the calculation into 1) return from appreciation and 2) return from coupon payments.
1) Appreciation: You're getting (FV-PV)/PV = 100% appreciation over 5 years. Since it's doubling, you could use rule of 72 and say 14.4% appreciation. compounded)
2) Coupons: Your current yield is Coupon/PV = 20%.
Putting that together, you're looking at around a 34.4% YTM. Looks like the actual YTM is around 31%, so we're not too far.
Thank you! Is there a manual way to calculate the IRR on appreciation instead of rule of 72? Just curious
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