Investment Banking puzzles, solved step by step

Puzzles
100
Traced to a firm
36
Topics
12
Hard
29
Topic
All topicsProbability7Mental maths and counting11Growth and compounding9Valuation riddles11Logic and brainteasers11Rates, risk and options9Estimation and market sizing7Accounting riddles9Expected value and games7Enterprise value and dilution6Deal maths6DCF and cost of capital7
Level
AnyWarm upCoreHard
Source
AnyReported at a firmStandard
Showing 51–51 of 51 · filtered from 100Clear filters
  1. 099A company with a 10% WACC and an equity beta of 1.0 is considering an all-equity project in a riskier business, where pure-play peers have an asset beta of 1.5. The risk-free rate is 7% and the equity risk premium is 5%. What discount rate should the project use?DCF and cost of capitalCoreBulge bracket IBMiddle market IB

    Try it first

    Which rate belongs in the project's DCF?

    Show the worked solution

    14.5%, from the project's own beta, not the company's 10% WACC. The project is all-equity, so its discount rate is its cost of equity at the peers' asset beta: 7% + 1.5 x 5% = 14.5%. Using 10% would accept projects that cannot earn their own risk. A project returning 12% looks like a winner at 10% but destroys value at 14.5%.

    Why is the company's own WACC the wrong rate?

    A bank with a low cost of funds still charges a risky borrower a high interest rate, because the rate should reflect the loan, not the bank. Projects work the same way. The discount rate is the return investors demand for the risk of these particular cash flows, so it belongs to the project, not to the company that happens to own it. The company's 10% WACC is the right rate for a project as risky as the company's average business, and this one is riskier.

    Where does the risk come from? Pure-play peers, companies that do only this riskier business, have an asset betaThe beta of a business with its debt stripped out: how much its operating cash flows move with the market, regardless of how it is financed. of 1.5. Because the project is all-equity, its equity beta equals that asset beta. Plug it into CAPM: 7% + 1.5 x 5% = 14.5%. For comparison, the parent's own cost of equity at a beta of 1.0 is 12%, and its WACC is lower still because it blends in cheaper debt.

    Discount the project at its own risk, not its owner'sCompany WACCthe wrong hurdle10.0%Company cost of equity7% + 1.0 x 5%12.0%Project rate, asset beta 1.57% + 1.5 x 5%14.5%project earns 12%At 10%: 12 / 0.10 = 120NPV +20: looks like a winnerWrong rate, wrong decisionAt 14.5%: 12 / 0.145 = 82.8NPV -17.2: destroys valueCost 100, pays 12 a year forever
    The project's own rate is 14.5% from an asset beta of 1.5, against the company's 10% WACC, so a project earning 12% shows an NPV of +20 at the wrong rate and -17.2 at the right one.

    What does the wrong rate cost in practice?

    The relationship
    rproject=rf+βasset×ERP=7%+1.5×5%=14.5%r_{\text{project}} = r_f + \beta_{\text{asset}} \times \text{ERP} = 7\% + 1.5 \times 5\% = 14.5\%
    r_frisk-free rate, 7%
    beta_assetthe pure-play peers' asset beta, 1.5
    ERPequity risk premium, 5%
    What it says in wordsAn all-equity project's rate is the risk-free rate plus its own beta times the market premium.

    Take a project costing 100 that pays 12 a year forever, an IRR of 12%. At 10% it is worth 120, an NPV of +20. At 14.5% it is worth 82.8, an NPV of -17.2. A company that discounts everything at its own WACC systematically accepts risky projects that destroy value and rejects safe ones that would create it. The limitation: peer betas are estimated with error, so use several peers and a median, and if the project were part-funded with debt you would relever the asset beta for that financing.

    Where candidates lose it

    The standard slip is answering 10% because the question opens with the company's WACC. That number is there as bait: the interviewer wants to hear that the discount rate follows the risk of the cash flows.

    The second loss is relevering the 1.5 with the parent's debt when the question says the project is all-equity. Read the financing assumption before adjusting the beta.

    What the interviewer asks next

    • If the project were funded 30% with debt at 9% pre-tax and a 25% tax rate, what rate would you use?
    • How would you find the asset beta if the peers carry debt?
    • Why might a conglomerate's divisions argue for a single company-wide hurdle rate, and what goes wrong?