ICAEW focus PQ
A weighty issue (part 2)
Rob Stephens looks at the cost of
debt and the WACC calculation
Illustration: the market price today of a 7%
bond is £90, its redemption value is £105 in five
years’ time (tax rate is 30%).
Although it is possible to take an accurate
guess at the overall cost of debt (comprised of
both the interest cost and capital cost to the
company), I would suggest using 10% as an
initial estimate (see table below left).
If you repeat the step above at another
discount rate (I chose 5% as a positive/
negative NPV will always tell me that the rate
I’m looking for will be higher/lower than my
first estimate), you will be able to interpolate.
At 5%, NPV = 13.53.
Via interpolation, the cost of debt equals:
a + {NPVa/(NPVa-NPVb) x (b-a)} ➞ 5%
+ {13.53/19.74 x 5%} ➞ 8.43%
I
n a previous article we introduced the term
‘weighted average cost of capital’, or WACC
(PQ, February 2012). We have already
shown the various ways to calculate the cost of
equity (ke) and shall now draw our attention to
the cost of debt (kd) before pulling it all together
in a WACC calculation.
Cost of debt.
When we talk about the cost of debt we are
usually talking about the company’s cost of
servicing its own debt (bonds/loan stock) rather
than bank loans. The easiest type of debt of this
type to deal with and calculate is irredeemable
debt – it is calculated in an almost identical way
to cost of equity (dividend model with zero
growth) since interest is fixed per annum. So in
principle it is:
kd = interest/P0 (interest paid divided by the market price
of the bond) instead of
ke = dividend/P0 (dividend paid divided by the market
price of the share)
Then there is one other adjustment to make –
when companies pay interest, they save tax on
the amount paid. In order to show a net (of tax
relief) cost of debt we multiply interest by (1-tax
rate). The irredeemable cost of debt now
becomes:
Kd = interest (1-t)/P0
Time
Market Price
Interest
Redemption
Cash flow
Redeemable debt.
Rather than issue irredeemable debt, a company
may choose to issue redeemable debt. This
simply means that the company will pay interest
each period (typically every year) for a set
amount of time before redeeming (paying off) the
bond. This will be designed to suit the
company’s financial position/needs.
When calculating the cost of redeemable debt,
we must remember that ‘the market price of the
bond today always equals the present value of
the future payments by the company
discounted at their cost of debt’.
Discount
factor (10%)
Discounted
Cashflow
0
(90)
1.0
(90)
1-5
7 x (1-0.3)
3.791
18.58
5
105
0.621
65.21
Net Present Value
-6.21
WACC.
Finally, once you have the costs of your various
components of long term finance we can average
those costs.
Imagine a company has £2m market value of
equity and ke = 10%
Also, imagine if the above company had
market value of £1m (as shown, kd = 8.43%).
The WACC is a weighted average of the two ie
2/3 of our finance is in the form of equity which
carries a cost of 10%, 1/3 is in the form of debt
which carries a cost of 8.43%:
WACC = (ke x E/(E+D)) + (kd x D/(E+D)) ➞
(10% x 2/3) + (8.43% x 1/3) ➞ WACC = 9.48%
This completes the picture and gives the rate
we would base our hurdle rate within project
appraisal (NPV) on. In reality and in the exam
additional, long term finance costs could be
added to our calculation – this could include
preference shares and bank loans which are less
complex than equity and bonds. PQ
• Rob Stephens is a Partner at First Intuition
Reading
on the
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