Cost of capital

AliceAlice
in Odomirok.22-23-GAAP

cost of capital = required capital x Risk cost of capital(R-i)

Why do we calculate associated risk margin as (discounted) required capital x cost of capital?

also why we calculate risk cost of capital R-i as required return on capital by purchaser - risk free rate - illiquidity premium.

I have hard time to understand these formula in a real situation.

Thank you.

Comments

  • grahamgraham

    It sounds like you're asking why the formulas given in the text are true. This isn't discussed in the text and isn't something you would need to know, but it's still a good question. I'm just guessing, but here's how I might think about it:

    If I understand, your first question is about the risk margin formula:

    • risk margin = (R-i) x required capital

    Recall that this formula is for risk margin portion of the FV(liabilities) is used in calculating goodwill:

    • goodwill = price - [ FV(assets) - FV(liabilities) ]

    Note the following:

    • FV(liabilities) higher => FV(assets) - FV(liabilities) lower => goodwill higher

    Now, according to the risk margin formula:

    • R higher => risk margin higher
    • required capital higher => risk margin higher

    In both cases, FV(liabilities) and therefore goodwill will also be higher. This chain of reasoning implies both R and required capital vary directly with goodwill. You can now ask yourself whether that makes sense. If the purchaser requires a higher return, or if there is more capital required to support the liabilities, this puts the purchaser in a weaker position. Intuitively then for a fixed price, the purchaser's goodwill must be higher (or he would require a lower purchase price) and that matches what the formulas tell us. (The relationship implied by the risk margin formula is linear but why that's true is definitely beyond the scope of the syllabus.)

    Your second question is the rationale for the cost-of-capital formula (R-i). Let's look at the boundary case where R=i. This wouldn't happen in reality but sometimes it helps to look at boundary cases to understand why a formula is true. So, if R=i, then the risk margin would be zero. If the purchaser only required a return equal to the risk-free rate then they could invest the liabilities at the risk-free and by definition there would be no risk.

    There is one extra point to be made here however regarding the illiquidity premium. I would just assume the illiquidity premium is rolled into the risk-free rate since practically any non-cash investment is not going to be completely liquid.

    Anyway, like I said, I don't think any of this is stuff you need to know for the exam but it enhances overall understanding by thinking through it.

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