SOLVAY BUSINESS SCHOOL
MBA
Finance
André Farber
CHEM-CAL CORPORATION
The main issue raised in the case is to find a cutoff rate to be used for the analysis of investment projects. Mr
Cochran is willing to apply what he learned recently in a management program. Unfortunately, there is room for
improvement in his grasp of finance. Moreover, since 1979, academic have gained a better understanding of the
issues raised in the case: they now more cautious about using the textbook weighted average of capital.
The current capital structure of Chem-Cal is the following (to simplify the analysis, preferred stocks are included
in debt):
Exhibit 1: Current capital structure (USD millions)
Book value
Equity
80
Debt
35
Total
115
Market value
50
30
80
%
63%
37%
Notice that the company is not in excellent shape: market value of equity is less then book value.
The first step is to calculate the cost of equity.
A starting point (in the absence of data about the beta of the stocks) is the current stock price ($25) relative to
EPS ($4.25). Assuming that the present value of growth opportunity is zero:
P
EPS
4.25
 rs 
17%
rs
25
There is another way to obtain the same result based on the simplest version of the Dividend Discount Model:
Div
rs  g
g  ROE(1 Payout)
P
If the NPV of new investment is zero (PVGO = 0), then ROE = r and:
P
Div
Div
EPS


rs  rs (1 Payout) rs  Payout
rs
The second step is to find the unlevered cost of capital
We know that the cost of equity of a levered firm is higher than the cost of equity of an unlevered firm (r 0)
because of financial risk. The relation between rS and r0 is (MM Proposition II with corporate taxes):
rS  r0 ( r0  rB )(1Tc )
B
S
With rS = 17%, rB = 10.5%, TC = 50% and B/S= 0.6, we get r0 = 15.5%.
This is the discount rate to use to calculate the value of the projects for an unlevered firm.
The third step is to calculate the NPV of the unlevered projects
To do this we need to know the expected unlevered cash flows of each project. Assume that the UCF of each
project is constant. Then:
NPV(10%) = - Cost + UCF  Annuity factor(10%, Project life)
Project
A
B
C
D
E
F
InvestmentLife
800
3,000
3600
600
4800
1800
8
20
10
2
15
6
NPV(10%) UCF
920 322
4,200 846
1680 859
66 384
1140 781
108 438
NPV(15.5%)
623
2,151
632
20
-342
-164
Project A, B C and D
have all positive
NPVs: they should be
accepted. E and F are
more problematic.
They should be
rejected if financed
through equity.
The fourth step is to incorporate side effect of financing.
Two main approaches:
1) Calculate APV for each project by adding PVTS to NPV
2) Discount UCF at a weighted average cost of capital
1. APV calculations for E and F
Assume that each project is financed with debt and, for simplicity, that the debt is repaid at the end of the project
(other assumptions are, of course, possible but this one is simple to implement). The annual tax shield is :
TS = TC rB Debt
PVTS = TS  Annuity factor(10.5%, Project life)
This leads to the following calculations:
Project
E
F
Debt
Life
4,800
1,800
15
6
Annual tax
shield
252
94.5
NPV
PVTS
APV
-342
-164
1,863
406
1,521
242
Both project have positive APV: they should be undertaken (before a final decision, some additional calculations
might be useful based on the exact timing of repayment).
2. Weighted average cost of capital
The weighted average cost of capital for Chem-Cal as a whole is:
rwacc 17% 
50
30
105
. % (105
. ) 12.6%
80
80
This discount rate could be used to calculate the APV of projects E and F assuming that the funding of these
project is similar to the funding of the firm as a whole
Project
E
F
APV
=NPV(12.6%)
353
- 29
If the financing of each project is not a carbon copy of Chem-Cal financing, another calculation of the weighted
average cost of capital might be used In addition, we might wish to take into account the finite life of the
projects (see Taggart for detailed explanation). We would have to specify a leverage ratio L (=B/V) and, for
instance, we might use Taggart’s formula 2C.3 (valid for finite of perpetual life, debt tax shields uncertain):
rwacc  r0  rBTC L
For L = 0.4, for instance, we obtain rwacc = 15.5 - 10.5  0.5  0.4 = 13.4
Project F would still not be profitable