BUSF_A01.qxd

Cost of individual capital elements

10.2 Cost of individual capital elements

An economic asset (which loan stocks, equities, and so on, are to their owners) has a

current value equal to the value of the future cash benefits from ownership of the asset

discounted at a rate commensurate with the timing and risk of each of those cash

benefits, that is:

v 0 =∑Cn/(1 +r)n (10.1)

where C is the cash flow associated with the asset, rthe rate of return and nthe time

of each cash flow. To a loan creditor or shareholder, the future cash flows, at any given

moment, will be the future interest or dividend receipts (payable annually, biannually,

or perhaps quarterly) and, perhaps, a repayment of the principal at some future

specified date.

Logically, a rate of return to the investors represents a cost to the business con-

cerned. Therefore we can make the general statement that:

p 0 =∑Cn/(1 +k)n (10.2)

where kis the cost of capital to the business and p 0 is the security’s current market

price.

Loan notes (or loan stocks or debentures)

With Stock Exchange listed loan notes we should know the current market value of the

loan notes, the contracted interest payments and dates, and the contracted amount

and date of the repayment of the principal. Thus, in the valuation expression above,

we should know all of the factors except k. Solving for kwill give us the cost of cap-

ital figure that we require.

Loan notes that were originally issued at par are currently quoted in the capital market at £93

per £100 nominal value, repayment of the nominal value in full is due in exactly five years’

time, and interest at 10 per cent on the nominal value is due for payment at the end of each

of the next five years. What is the cost of the loan notes?

Assume a 30 per cent rate of corporation tax.

Example 10.1

Since we are seeking to deduce a rate that can be used to discount after-tax cash flows, we

need an after-tax cost of capital. The loan notes interest would attract tax relief, but the cap-

ital repayment would not because it is not an expense.

The following statement holds true:

93 = + + + + +

where kLis the after-tax cost of the loan notes.

100

(1 + kL)^5

10(1 −0.30)

(1 + kL)^5

10(1 −0.30)

(1 + kL)^4

10(1 −0.30)

(1 + kL)^3

10(1 −0.30)

(1 + kL)^2

10(1 −0.30)

(1 + kL)

Solution

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