Debt Capital Markets puzzles, solved step by step

Puzzles
100
Traced to a firm
16
Topics
13
Hard
30
Topic
All topicsLeverage, coverage and cash flow9Mental maths and numeracy8Estimation and market sizing7Logic and brainteasers8Cost of capital and valuation riddles7Bond pricing and yield7Compounding, PIK and fees6Issuance and refinancing arithmetic8Credit spreads and default probability8Duration and convexity8Capital structure and recovery8Probability and expected value10Yield curve and forward rates6
Level
AnyWarm upCoreHard
Source
AnyReported at a firmStandard
Showing 1–1 of 1 · filtered from 100Clear filters
  1. 060Pitching for a bond mandate costs Rs 50 lakh of team time. You estimate a 30% chance of winning a mandate worth Rs 4 crore in fees. Should you pitch, and what win probability makes the pitch break even?Probability and expected valueWarm upSyndicate desks

    Try it first

    What is the expected value of pitching, net of the cost?

    Show the worked solution

    Yes, pitch: the expected value is plus Rs 70 lakh, and the pitch breaks even at a 12.5% win probability. A 30% chance of Rs 4 crore is worth Rs 1.2 crore in expectation, against a certain Rs 50 lakh cost. Break-even is where the probability times Rs 4 crore equals Rs 50 lakh: 0.5 divided by 4, or 12.5%. The 30% estimate clears that by a wide margin, so even a rough probability supports pitching.

    How do you compare an uncertain fee with a certain cost?

    A shopkeeper deciding whether to print Rs 500 of flyers asks how much extra business they might bring, times how likely that is. Expected value multiplies each outcome by its probability and adds them up, so a 30% chance of Rs 4 crore is worth Rs 1.2 crore before costs. The cost of pitching is paid whether you win or lose, so it comes off in full: Rs 1.2 crore minus Rs 0.5 crore is plus Rs 0.7 crore.

    The relationship
    EV=0.30×4.0−0.5=+0.7 crorep∗=0.54.0=12.5%EV = 0.30 \times 4.0 - 0.5 = +0.7\ \text{crore} \qquad p^{*} = \frac{0.5}{4.0} = 12.5\%
    0.30your estimated chance of winning
    4.0the fee if you win, Rs crore
    0.5the cost of pitching, paid either way, Rs crore
    p*the break-even win probability
    What it says in wordsExpected fee less the certain cost; break-even is the cost divided by the prize.
    The pitch is worth it when the expected fee clears a cost you pay either wayExpected fee: 30% x Rs 4 croreRs 1.2 croreCertain cost of pitching- Rs 0.5 croreNet expected value+ Rs 0.7 crore01.6cost Rs 0.5 crorebreak-even 12.5%your 30% estimate: Rs 1.2 croreExpected fee, Rs crore0%10%20%30%40%Chance of winning the mandate
    The expected fee of Rs 1.2 crore less the Rs 0.5 crore cost leaves plus Rs 0.7 crore, and the expected fee line crosses the cost at a 12.5% win probability, well below the 30% estimate.

    What win probability makes the pitch worth it, and how robust is the answer?

    Break-even is the probability at which the expected fee just covers the cost: Rs 50 lakh over Rs 4 crore, 12.5%. The 30% estimate is more than twice that, so the decision survives a lot of error in the estimate. That is the useful part of the calculation: you rarely know a win probability precisely, but you often know whether it is comfortably above or below the break-even.

    Name what the simple sum leaves out. Losing is the most likely outcome, 70% of the time, so a desk that pitches only once can easily end Rs 50 lakh down; expected value pays off across many pitches. The team's time also has an opportunity cost if it could pitch a better mandate instead, and a win may bring follow-on business that the Rs 4 crore does not capture. Each of those shifts the break-even; none reverses this answer.

    Where candidates lose it

    The trap is anchoring on the most likely outcome. You lose 70% of the time, so candidates say the pitch loses money. Expected value is not the most likely outcome; it is the probability-weighted average, and here that is plus Rs 70 lakh.

    The second loss is forgetting to subtract the cost and answering Rs 1.2 crore, or dividing the wrong way for break-even. Say break-even as cost over prize, then check it: 12.5% of Rs 4 crore is Rs 50 lakh.

    What the interviewer asks next

    • If you win you must share the mandate with a second bank, halving your fee. Does the answer change?
    • You can pitch three mandates like this but can only staff two. How do you choose?
    • How would you estimate the 30% win probability in the first place?