Discount rates for project
appraisal
We know that we have to discount
cash flows in order to value
projects
We can identify the cash flows
BUT
What discount rate should we use?
1
The Discount Rate and Capital
Budgeting
Weighted Average Cost of Capital
Method
Adjusted Present Value (APV)
Flow-to-equity (FTE)
Example
Summary and Conclusions
2
Method 1: Weighted Average
Cost of Capital (WACC)
We use a discount rate that reflects
the average returns that the
company should be making to
satisfy
(a) its bondholders
(b) its shareholders
(c ) the proportion of debt in its
capital structure
3
Component costs
Cost of bonds = interest rate
expected by bond holders
Bonds are cheaper for companies
because the interest paid can
offset tax
Cost of shares = dividends + capital
gain expected by shareholders
4
WACC calculation
E D
r
=r
+r
(
1
T
)
WACC
e
d
C
V V
E = Value of shares (equity) = 500
D = Value of Debt (bonds) = 500
Note V = Value of firm = E+D = 1000
Tc=Corporate tax=30%
re = return expected by shareholders
rd = return expected by bondholders
5
Note on Miles and Ezzell
formula
• M&M assumed perpetuities for their cash flows.
M&E looked at the case of finite projects where
the leverage was adjusted to be a constant of
the remaining value.
• The complication is that V depends on the
amount of debt which depends on the value of
the project…
WACC(M & E) r0
where r0
Tc .rD
D (1 r0 )
V (1 rD )
the cost of capital of the firm if it had no debt
(the all - equity cost of capital) and rD
the cost of debt
Example: WACC calculation
Cost of equity = 13.5%, If firm were all-equity,
the WACC would be 10% (see later)
Cost of Debt = 5%
Corporate Tax rate = 30%
D/V= 0.5
So WACC = 0.5 x13.5 + 0.5 x 5 x 0.7
= 8.5%
WACC(M&E) = 9.21%
The two WACCs differ because future tax shields
are less valuable if uncertain.
7
Example: Project with cash flows
of -1000, 400, 400, 600, 500
-£1,000
0
£400
£400
£600
£500
1
2
3
4
After tax cash flows (pre-tax cash flows x 0.7)
-1,000
280
280
420
350
8
Valuation using WACC
To find the value of the project, discount the
after-tax cash flows at the weighted
average cost of capital.
NOTE: we do not include the interest
payments.
280
280
420
35
NPV
1
,
000
2
3
4
(
1
.
085
)
(
1
.
085
)
(
1
.
085
)
(
1
.
08
)
NPV
77
.3
8
.5
% £
9
How is WACC affected by changing level of debt?
As debt rises, shareholders demand higher
returns because their investment is riskier
Debt is cheaper than equity
But the average will either
(a) stay constant (if no tax effect of debt)
(b) become lower as the advantage of debt
becomes more important
(c ) rise as cost of bankruptcy rises
Note: Shareholders will always get a higher
return if debt increases...
10
WACC
Very popular but not always relevant.
Companies that finance their projects
using very different debt packages
should not use the WACC.
Not the method used in property
investment.
11
Method 2: Adjusted Present
Value (APV)
This method identifies the precise
financing package for the project and
adds in the tax advantages of the
financing directly.
The discount rate used is the rate that
would apply if the company were
entirely financed by equity. (r0 )
12
Adjusted Present Value Approach
The value of a project to the firm can be thought of
as the value of the project to an –all-equity
financed firm (NPV) plus the present value of the
financing side effects (NPVF):
There are four side effects of financing:
The Tax Subsidy to Debt
The Costs of Issuing New Securities
The Costs of Financial Distress
Subsidies to Debt Financing
APV
NPV
NPVF
13
The cost of capital for an allequity firm (ro)
We can use the formula
r0 = WACC/(1-TcD/V)
= 8.5%/(1-0.3x0.5) = 10%
Again we use the after-tax cash flows
without taking the interest into
account.
14
APV cont.
280
280
420
350
PV10 = 1,000 +
+
+
+
2
3
4
(1.10) (1.10) (1.10) (1.10)
PV10 = £40.60
But we also look at the benefits of having
the tax shield for interest payments
We assume that we issue a bond at 10%
which matures at the end of the fourth
year.
15
APV cont.
Treat loan as a project
500
.05
(
1
.3
) 500
NPV
=
500 t
loan
4
(
1.05
)
(
1.05
)
t
=
1
NPV
=
£
26.60
loan
4
or just calculate the tax saved.5% of 500 = £25 p.a. So
saves 25x.3 = 7.5 p.a for 4 years.
PV(loan) = 7.5/1.05+7.5/1.052+7.5/1.053+7.5/1.054
= 26.60 (note discount rate is the before tax cost
of debt)
So APV = 26.60 + 40.60 = £67.20
16
APV cont.
Note that the PV is not quite the same as calculated by the
WACC approach.
Useful because we can calculate the benefits of specific
loans attached to projects.
See discussion paper on APV approach in property
investment
Much proposed by text books, not used much in practice
partly because of the use of r0 – a difficult concept.
17
Method 3:
Flow to Equity approach (FTE)
We take the viewpoint of the
shareholders and discount their
cash flows at the cost of equity
after taking the cash flows for the
loan, interest and tax have been
taken into account.
To calculate the cost of equity, we
use...
18
Another formula!
re = r0 + (r0-rd)(1-Tc)D/E
Here r0 is the cost of equity if there is
no debt in the company (as before).
r0 = the all-equity cost of capital
The discount rate (re) will be higher
than either WACC or r0 but the cash
flows are after financing charges so
will be lower.
19
Calculation of re
r0= 10%,rd = 5%, Tc=.3 and D/E=1
re = 10% +(10%-5%)(0.7)1
= 10% + 3.5%
= 13.5%
20
Example using FTE
Debt = 500, re = 13.5%
CF
-1000
Interest
Tax
0
Loan
500
CFE
-500
NPV(13.5%)
400
400
600
500
-25
-25
-25
-25
-112.5
-112.5
-172.5
-142.5
-500
262.5
262.5
£109.40 IRR
402.5
-167.5
27.2%
21
Notes on FTE
Investment = 500 because debt is used to
finance half of the investment cost
Cash flows include paying interest and paying
back loan at end of period.
NPV = highest of all methods but assumptions
are not quite right because D/E too low, thus
re too low. To get a similar NPV as the other
two methods, re ≈ 18%
But this is nearest to the methods used in
property development appraisal
22
Summary of WACC, APV, FTE
WACC used commonly
APV more flexible but little used
FTE used in Property Development
23