Risk Analysis in Capital Budgeting – CA Inter FM Study Material

Risk Analysis in Capital Budgeting – CA Inter FM Study Material is designed strictly as per the latest syllabus and exam pattern.

Risk Analysis in Capital Budgeting – CA Inter FM Study Material

Theory Questions

Question 1.
What is certainty equivalent?
Answer:
Certainty equivalent method: The certainty equivalent is a confirmed return that the management would accept rather than accepting a higher but uncertain return. In this approach we use risk less or certain cash flow is generated in place of the original cash flows and discount it with risk free rate of discount to compute present value of cash flow.

Step 1 : Calculate Certain Cash:
Certain Cash = Expected Cash Flow × C.E. Coefficient
Step 2 : Calculate NPV on the basis of certain cash flow and risk free discount rate.

Question 2.
Write two main reasons for considering risk in Capital Budgeting decisions. (2 Marks Nov 2018)
Answer:
There are two main reasons for considering risk in capital budgeting decisions:

1. Funds used in any proposal has their opportunity cost according to level of risk associated with proposal. We have to make adjustment of risk for correct evaluation of project. If return from proposal is appropriate according to risk associated with project then we will accept the offer otherwise reject.
2. To know the real value or present value of cash inflows we have to make adjustment of risk. Higher risk will lead to higher risk premium and also expectation of higher return.

Question 3.
Explain the steps of Sensitivity Analysis. (4 Murks May 2019)
Answer:
Sensitivity Analysis is conducted by following the steps as below:

Step 1: Finding variables, which have an influence on the NPV (or IRR) of the project.
Step 2: Establishing mathematical relationship between the variables.
Step 3: Analysis the effect of the change in each of the variables on the NPV (or IRR) of the project.

Question 4.
What is Risk Adjusted Discount Rate? (2 Marks Nov 2020)
Answer:
It is a sum of risk free rate and risk premium. The Risk Premium is based on degree of risk associated with proposal. It is calculated as:
Risk adjusted discount rate = Risk free rate + Risk premium

Practical Problems

Question 1.
From the following details relating to a project, analyze the sensitivity of the project to changes in initial project cost, annual cash inflow and cost of capital:

Initial Project Cost (₹) 2,00,000
Annual Cash Inflow (₹) 60,00,000
Project Life (Years) 5
Cost of Capital 10%

To which of the three factors, the project is most sensitive if the variable is adversely affected by 10%? (Use annuity factors: for 10% 3.791 and 11% 3.696). (5 Marks Nov 2018)

Answer:

Calculation of NPV through Sensitivity Analysis:
NPV(Base) = 60,00,000 × 3.791 – 2,00,00,000 = 27,46,000

Situation	NPV	Changes in NPV
Base (present)	₹ 27,46,000	–
If initial project cost is varied adversely by 10%	(₹ 2,27,46,000 – ₹ 2,20,00,000) = ₹7,46,000	(₹ 27,46,000 – ₹ 7,46,000)/₹27,46,000 = 72.83%
If annual cash flow is varied adversely by 10%	(₹ 54,00,000 × 3.791) – ₹ 2,00,00,000 = ₹ 4,71,400	(₹ 27,46,000 – ₹ 4,71,400)/₹27,46,000 = 82.83%
If cost of capital is varied adversely by 10% i.e. 11%	(₹ 60,00,000 × 3.696) – ₹ 2,00,00,000 = ₹ 21,76,000	(₹ 27,46,000 – ₹ 21,76,000)/₹ 27,46,000 = 20.76%

Conclusion: Project is most sensitive to ‘annual cash inflow’.

Question 2.
Kanoria Enterprises wishes to evaluate two mutually exclusive projects

The cut off rate is 14%. The discount factor at 14% are:

Year	1	2	3	4	5	6	7	8
DF	0.877	0.769	0.675	0.592	0.519	0.456	0.400	0.351

Advise management about the acceptability of projects X and Y. (5 Marks May 2019)
Answer:
The Possible Outcomes of Project X and Project Y are as follows:

In pessimistic situation project X will be better as it gives low but positive NPV whereas Project Y yield highly negative NPV under this situation. In most likely situation both the project will give same result. However, in optimistic situation Project Y will be better as it will give very high NPV.

So, project X is a risk less project as it gives positive NPV in all the situation whereas Y is a risky project as it will result into negative NPV in pessimistic situation and highly positive NPV in optimistic situation. So acceptability of project will largely depend on the risk taking capacity (Risk seeking/Risk aversion) of the management.

Question 3.
Door Ltd. is considering an investment of ₹ 4,00,000 this investments expected to generate substantial cash inflows over the next five years. Un-fortunately the annual cash flows from this investment is uncertain, but the following probability distribution has been established:

Annual Cash Flow (₹)	Probability
50,000	0.3
1,00,000	0.3
1,50,000	0.4

At the end of its 5 years life, the investment is expected to have a residual value of ₹ 40,000. The cost of capital is 5%.
(1) Calculate NPV under the three different scenarios.
(2) Calculate expected net present value
(3) Advise Door Ltd. on whether the investment is to be undertaken.

Year	1	2	3	4	5
DF @ 5%	0.952	0.907	0.864	0.823	0.784

(5 Marks Nov 2019)
Answer:
(1) NPV under different scenarios:
NPV = PV of inflow – Initial Investment
Situation I = 50,000 × 4.33 + 40,000 × 0.784 – 4,00,000 = (1,52,140)
Situation 2 = 1,00,000 × 4.33 + 40,000 × 0.784 – 4,00,000 = 64,360
Situation 3 = 1,50,000 × 4.33 + 40,000 × 0.784 – 4,00,000 = 2,80,860

(2) Expected NPV:
Expected NPV = PV of expected inflow – Initial Investment
= 1,05,000 × 4.33 + 40,000 × 0.784 – 4,00,000 = 86,010
Expected Inflow = 50,000 × 0.3 + 1,00,000 × 0.3 + 1,50,000 × 0.4 = 1,05,000

(3) Advise: Door Ltd. should accept the proposal having positive expected NPV.

Question 4.
A Ltd. is considering two mutually exclusive projects X and Y. You have been given below the Net Cash Flow probability distribution of each project:

(1) Compute the following:

(а) Expected Net Cash Flow of each project.
(b) Variance of each project.
(c) Standard Deviation of each project.
(d) Coefficient of variation of each project.

Answer:

(a) Expected Net Cash Flow:

ENCF (X) = Σfx
= 50,000 × 0.30 + 60.000 × 0.30 + 70,000 × 0.40
= 61,000
ENCF (Y) = 1,30,000 × 0.20 + 1,10,000 × 0.30 + 90,000 × 0.50
= 1,04,000

(b) Variance:

Variance (X) = (50,000 – 61,000)² (0.3) + (60,000 – 61,000)² (0.3) + (70,000 – 61,000)² (0.4)
= 6,90,00,000
Variance (Y) = (1,30,0001,04,000)²(0.2) + (1,10,0001.04,000)²(0.3) + (90,000 – 1,04,000)² (0.5)
= 24,40,00,000

(c) Standard Deviation:

Standard Deviation (X) = \(\sqrt{6,90,00,000}\) = 8,306.62
Standard Deviation (Y) = \(\sqrt{24,40,00,000}\) = 15,620.50

(d) coefficient of variation:

Coefficient of variation (X) = \(\frac{8,306.62}{61,000}\) = 0.1362
Coefficient of variation (Y) = \(\frac{15,620.50}{1,04,000}\) = 0.1502

(2) Identify which project do you recommend? Give reason. (10 Marks Nov 2020)
Answer:
In project X risk per rupee of cash flow is 0.1362 while in project Y it is 0.1502. Therefore, Project X is better than Project Y.

Question 5.
A project requires an initial outlay of ₹ 3,00,000. The company uses certainty equivalent method approach to evaluate the project. The risk free rate is 7%.

Following information is available:

PV factor at 7%

Year	1	2	3	4	5
PV Factor	0.935	0.873	0.816	0.763	0.713

Evaluate the above. Is investment in the project beneficial? (5 Marks Jan 2021)
Answer:
Statement Showing the Net Present Value of Project

Important Questions

Question 1.
Probabilities for net cash flows for 3 years a project are as follows:

Calculate the expected net cash flows. Also calculate the net present value of the expected cash flow, using 10 per cent discount rate. Initial Investment is ₹ 10,000.
Answer:

The net present value of the expected value of cash flow at 10 per cent discount rate has been determined as follows:
Expected NPV = 6,000 × 0.909 + 4,800 × 0.826 + 4,200 × 0.751 – 10,000
= ₹ 2,573

Question 2.
Calculate Variance, Standard Deviation and Coefficient of Variation on the basis of figure given below:

Answer:
Project A:
Variance = (8,000 – 12,000)² (0.1) + (10,000 – 12,000)² (0.2) + (12,000 – 12,000)² (0.4) + (14,000 – 12,000)² (0.2) + (16,000 – 12.000)² (0.1) = 48,00,000
Standard Deviation = \(\sqrt{48,00,000}\) = 2,190.90
Coefficient Variation = 2,190.90 ÷ 12,000 = 0.1826

Project B:
Variance = (24,000 – 16,000)² (0.1) + (20,000 – 16,000)² (0.15) + (16,000 – 16,000)² (0.5) + (12,000 – 16,000)² (0.15) + (8,000- 16000)² (0.1) = 1,76,00,000
Standard Deviation = \(\sqrt{1,76,00,000}\) = 4,195.23
Coefficient of variation = 4,195.23 ÷ 16,000 = 0.2622

Working note:
Expected Cash Flow = Σfx
Project A = 8,000(0.1) + 10,000 (0.2) + 12,000(0.4) + 14.000(0.2) + 16,000 (0.1) = 12,000
Project B = 24,000 (0.1) + 20,000 (0.15) + 16,000 (0.5) + 12,000(0.15) + 8,000(0.1) = 16,000

Question 3.
Following information have been retrieved from the finance department of Corp Finance Ltd. relating to Projects X, Y and Z:

You are required to determine the risk adjusted net present value of the projects considering that the Company selects risk-adjusted discount on the basis of the coefficient of variation:

Answer:
Statement showing the determination of the risk adjusted net present value

Question 4.
X Ltd is considering its New Product with the following details of three years project:


1. Calculate the NPV of the project.
2. Find the impact on the project’s NPV of a 2.5 per cent adverse variance in each variable. Which variable is having maximum effect.
Answer:
1. Calculation of Net Cash Inflow per year:

Calculation of Net Present Value (NPV) of the Project:

Here NPV represent the most likely outcomes and not the actual out-comes. The actual outcome can be lower or higher than the expected outcome.

2. Sensitivity Analysis considering 2.5% Adverse Variance in each variable

The above table shows that by varying one variable at a time by 2.5% while keeping the others constant, the impact in percentage terms on the NPV of the project. Thus it can be seen that the change in selling price has the maximum effect on the NPV by 24.82%.

Question 5.
PNR Ltd. is considering a project with the following cash flows:

The cost of capital is 12%. Measure the sensitivity of the project to changes in this levels of plant cost, running cost and savings (considering each factor at a time) such that the NPV becomes zero. The P.V. factors at 12% are as under:

Year	0	1	2	3
PV factor@12%	1	0.892	0.797	0.711

Determine the factor which is the most sensitive to affect the accept lability of the project?
Answer:
Present value (PV) of Cash Flows

Determination of the most Sensitive factor:

(i) Sensitivity Analysis w.r.t. Plant cost:
NPV of the project would be zero when the cost of the plant is increased by ₹ 5,86,40,000
∴ Percentage change in the cost
= 5,86,40,000 ÷ (4,00,000 × 0.892) + (5,00,000 × 0.797) + (6,00,000 × 0.711) × 100 = 49.61%

(ii) Sensitivity Analysis w.r.t. Running cost:
NPV of the project would be zero when the running cost is increased by ₹ 5,86,40,000
∴ Percentage change in the cost
= {5,86,40,000 ÷ (4,00,00,000 × 0.892) + (5,00,00,000 × 0.797) + (11,00,00,000 × 0.711)} × 100 = 49.61%

(iii) Sensitivity Analysis w.r.t. Savings:
NPV of the project would be zero when the savings decreased by ₹ 5,86,40,000
∴ Percentage change in the savings
= {5,86,40,000 ÷ (12,00,00,000 × 0.892) + (14,00,00,000 × 0.797) + (11,00,00,000 × 0.711)} × 100 = 19.75%
The Savings factor is the most sensitive as only a change beyond 19.75% in savings makes the project unacceptable.

Question 6.
A&R Ltd. has under its consideration a project with an initial investment of ₹ 90,00,000. Three probable cash inflow scenarios with their probabilities of occurrence have been estimated as below:

Annual cash inflow (₹)	20,00,000	30,00,000	40,00,000
Probability	0.2	0.7	0.1

The project life Is 5 years and the desired rate of return is 18%. The estimated terminal values for the project assets under the three probability alternatives, respectively, are ₹ 0, ₹ 20,00,000 and ₹ 30,00,000.

You are required to:

(a) Calculate the probable NPV:
(b) Calculate the worst-case NPV and the best-case NPV; and
(c) State the probability occurrence of the worst case, if the cash flows are perfectly positively correlated over time.

Answer:

(a) Calcualation of probable NPV.’
NPV = PV of inflows – PV of outflows
= [{20,00,000 × 0.2) + (30,00,000 × 0.7) + (40,00,000 × 0.1) × 3.127 + {(0 × 0.2) + (20,00,000 × 0.7) + (30,00,000 × 0.1)}] × 0.437 – 90,00,000
= 29,00,000 × 3.127 + 17,00,000 × 0.437 – 90,00,000
= 8,11,200

(b) Calculation of worst-case and best-case NPV:
Worst-case NPV = PV of inflows – PV of outflows
= 20,00,000 × 3.127 – 90,00,000
= (27,46,000)
Best-case NPV PV of inflows – PV of outflows
= 40,00,000 × 3.127 + 30,00,000 × 0.437 – 90,00,000
= 48,19,000

The cash flows are perfectly positively correlated over time means cash flow in first year will be cash flows in subsequent years. The cash flow of ₹ 20,00,000 is the worst case cash flow and its probability is 20%, thus, possibility of worst case is 20% or 0.2.