12/05/2023
Scenario 1 – Projects are Divisible and Constraints is a Single
Period One
Solution:
Scenarios of Capital
Rationing
The following steps may be adopted by solving the problem under this
situation:
a. Calculate the profitability index for each project
b. Rank the projects on basis of profitability index calculated in a above.
c. Choose the optimal combination of projects.
41
43
Scenario 1 – Projects are Divisible and Constraints is a Single
Period One
XYX Company is considering five independent projects.
Scenario 1 – Projects are Divisible and Constraints is a Single
Period One
Solution:
Project
Required Initial
Investment
NPV at the Appropriate
Cost of Capital
Project Required Initial NPV at the Appropriate
Investment
Cost of Capital
(1)
(2)
(3)
A
P1,000,000
P20,000
Profitability
Index (3/2)
(4)
0.02
Rank
A
P1,000,000
P20,000
B
3,000,000
35,000
C
500,000
16,000
B
3,000,000
35,000
0.0117
5
D
E
2,000,000
1,000,000
25,000
30,000
C
500,000
16,000
0.032
1
D
2,000,000
25,000
0.0125
4
E
1,000,000
30,000
0.03
2
The fund available is P3,000,000. Determine the optional combination of
projects assuming that the projects are divisible.
42
(5)
3
44
1
12/05/2023
Scenario 1 – Projects are Divisible and Constraints is a Single
Period One
Solution:
Rank of
Investment
Project
Required
Initial Outlay
1
C
P 500,000
2
E
1,000,000
3
A
1,000,000
4
Total
¼ of D
500,000
P3,000,000
45
Scenario 2 – Projects are Indivisible and Constraints is a Single
Period One
Solution: Feasible Combination
Aggregate of NPVs
A, C
P36,000
A, D
45,000
A, E
50,000
C, D
41,000
C, E
46,000
D, E
55,000
A, C, E
66,000
By a careful inspection of the feasible combinations constructed in the
above table, we can conclude that the optimal project mix is A, C, and E
because the aggregate of their NPVs is the maximum.
47
Scenario 2 – Projects are Indivisible and Constraints is a Single
Period One
Using the same data, used in previous illustration, determine the optimal
project mix on the basis of the assumption that the projects are
indivisible.
Scenario 3 – Projects are Divisible and Constraints is Multi-period
One
Under this scenario, the problem of capital rationing can be solved with
the help of linear programming. It is a mathematical programming
approach.
Solution:
The following steps to be followed for solving the problem under the
situation are:
a. Construct a table using the visible combination of the project (whose
aggregate of initial outlay does not exceed the fund available for
investment).
b. Choose the combination whose aggregate NPV is maximum and
consider it as the optimal project mix.
Harrah Corporation has considered seven independent projects, namely,
A, B, C, D, E, F, and G for implementation. The company has a capital
budget of P400 million. The minimum acceptable rate of return is 7%.
Let us now consider the capital rationing problem.
46
48
2
12/05/2023
Scenario 3 – Projects are Divisible and Constraints is Multi-period
One
Ranking Based on the NPV
Project
Investments
In millions
NPV @ 7%
In millions
A
100
54.73
B
100
40.47
C
200
87.014
D
200
283.007
E
200
62.23
F
50
4.76
G
50
26.08
Scenario 3 – Projects are Divisible and Constraints is Multi-period
One
Ranking Based on the Profitability Index
Project
The optimum set comprise of projects D and C. by implementing them
with an investment of P400 million (P200 million+P200 million), the
company would earn returns whose present value is P370.021 million
(P283.007+87.014 million).
A
B
C
D
E
F
G
PV of Outflows PV of Inflows Profitability
In millions
In millions
Index
100
154.73
1.547
100
140.47
1.405
200
287.01
1.435
200
483.01
2.415
200
262.23
1.311
50
54.76
1.095
50
76.08
1.522
49
51
Scenario 3 – Projects are Divisible and Constraints is Multi-period
One
Ranking Based on the IRR
Scenario 3 – Projects are Divisible and Constraints is Multi-period
One
Ranking Based on the Profitability Index
Under the profitability ranking projects D, A, and G has scored the first
three ranks with a total funds commitment of P350 million. Obviously,
Projects C. B, and E which are next in the sequence of decreasing PI,
cannot be accommodated from the balance of funds ie. P50 million
(P400 million – P350 million) available for investment. Hence, Project F
is selected to complete the optimum set. The sum of NPVs of Projects D,
A, G, and F amounts to P368.58 million. As seem from the above
illustration, the decision regarding choice of set of projects which best
meets the corporate financial objective in a capital rationing situation
upon checking the criterion used for selection.
Project
Investments
In millions
NPV @ 7%
In millions
A
100
13.6
B
100
15.1
C
200
22.1
D
200
20.7
E
200
12.0
F
50
11.9
G
50
16.7
Among the seven projects, Project C has the highest IRR of 22.1% and,
hence, this project is selected as first and its commitment of funds is
P200 million, the project having next best IRR is Project D with 20.7%
and its commitment of funds is also P200 million.
50
52
3
12/05/2023
Effects of Inflation to Capital Budgeting Analysis
Inflation
Effects on
Capital
Budgeting
Computations under the two approaches are presented below:
Reconciliation of the Market-Based and Real Costs of Capital
The real cost of capital
The inflation factor
The combined effect (12%x10%)
The market-based cost of capital
12.0%
10.0
1.2
23.2%
55
Effects of Inflation to Capital Budgeting Analysis
Effects of Inflation to Capital Budgeting Analysis
Inflation affects the numbers that are used in the analysis but does not
affect the results of the analysis if certain condition is satisfied.
To illustrate, we use the following data:
Marvex Corp. wants to purchase a new equipment that cost P360,00.
The equipment would provide annual net cash flows from operations of
P200,000 and it would have a three-year life with no salvage value. For
each of the next three years, the company expects a 10% inflation rate
in the cash flows associated with the new machine. If the company’s real
cost of capital is 12% or market based cost of capital of 23.2%, should
the equipment be purchased.
54
Solution A: Inflation Not Considered
Items
Initial Investment
Annual cost savings
NPV
Years(s)
Amount of
Cash Flows
12%
Factor
PV of Cash
Flows
Present
(P360,000)
1.000
(P360,000)
1-3
200,000
2.402
480,400
P120,400
56
4
12/05/2023
Effects of Inflation to Capital Budgeting Analysis
Solution B: Inflation Considered
Items
Years(s)
Amount of
PI
Cash
Number
Flows
Initial
Investment
Present
(P360,000)
1
2
3
Annual cost
savings
Price –
Adjusted
Cash Flows
2.3%
Factor
PV of Cash Flows
1.000
(P360,000)
1.000
(P360,000)
200,000
1.100
220,000
0.812
178,640
200,000
1.210
242,000
0.659
159,480
200,000
1.331
266,200
0.535
142,420
P120,540
*Computation of the price-index number, assuming a 10% inflation rate
each year: (1+r)n
*Discount formula is computed as 1/(1+r)n
*the amount of the total might be different because of rounding off error 57
Financial
Breakeven
Point
Effects of Inflation to Capital Budgeting Analysis
Financial Breakeven Point
Solution B: Inflation Considered
It will be noted that the net present value obtained in solution B, where
inflation is explicitly taken into account is the same within rounding error
to the obtained in Solution A, where the inflation effects were not
considered. This result may seem surprising but it is logical because we
have adjusted both the cash flow and the discount rate so that they are
consistent and these adjustments cancel each other out across the two
solutions. (with and without the inflation considered)
This occurs when the NPV of the project is zero. The financial BEP is
thus:
58
60
Where the OCF is the level of the OCF that results in a zero NPV. A
project that breaks even on a financial basis has a discounted payback
equal to its life, a zero NPV, and an IRR just equal to the required return.
5
12/05/2023
Sensitivity Analysis
If the NPV estimate turns out to be very sensitive to relatively small
changes in the projected value of some component of project cash flows,
then the forecasting risk associated with that variable is high that may
require further study or market research
Sensitivity
Analysis
63
Sensitivity Analysis
This is the determination of what happen to the Net Present Value (NPV)
estimates when we ask “what if” questions or in response to a given
change in an input variable other things held constant.
This is useful in pinpointing the areas where forecasting risk is especially
severe.
In this technique, each variable is changed by several specific
percentage points above and below the expected value, holding other
things constant; then a new NPV is calculated for each of these values.
62
6