Financial Mathematics Text

Wednesday, December 17, 2014

Some Ambiguities Regarding the Cost of Capital

So I'd like to suggest there's an ambiguity in measuring the cost of capital. As far as I can tell, there isn't always a straight forward consensus on how this should be handled. There are a number of arguments in favor of particular positions.

Today I'm going to very briefly present the issue.

Real versus Nominal

So the first issue is whether the "cost of capital" should we use a "real" rate or a "nominal" rate?

For instance, it's possible to earn a 10% interest rate on bonds but inflation over the period might be, say, 15%. In that case, my "real" rate of return is actually negative.

So is my cost of capital 10% or -5%? (compounded continuously; it would be -4.35% compounded annually.)

Return to the Investor versus Cost to the Company

The second issue becomes a bit more clear when we consider debt.

Suppose I borrow money at a 10% interest rate. The cost to me will be 10%.

But what rate of return can an investor expect to receive by loaning me that money?

Well, that investor will receive 10% (nominal) minus any losses due to default. So either the investor will get the full 10%, or I will be unable to pay my loan in which case they may get a much lower figure (including losses that result in receiving pennies on the dollar.)

Based on the probability of my defaulting and the losses that would occur in such an event, the expected rate of return on a loan to me might be only, 8%.

So is the cost of debt 8% or 10%?

Some Considerations

It's possible that the "right" answer will depend upon whose perspective you're looking at and what it's being used for.

For example, are you the borrower or the investor? That may make a difference between whether we look at the expected return versus the actual cost (assuming no default.)

Regarding the real versus nominal, I often like to think in terms of asset-liability matching.

For example, if I'm saving for retirement, then what I'm concerned with are going to be my real expenses. In that case, I want to use a real cost of capital.

On the other hand, if I borrow money (most loans are in nominal, not real terms), then whatever income I receive I want it to be able to pay back the loan. There's no sense in considering real income increases, especially in a deflationary environment. It's possible to have a real income increase while deflation offsets it enough to result in a nominal loss of income. The result is that your debt level relative to your income would actually increase. So I would want to know what sort of income stream I would get (in nominal terms) to pay back my loan.

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