Probability Approach to NPV National Paper Mills is considering expansion

into manufacture of glazed paper or craft paper.

Though both the projects can be undertaken but

due to capital constraints only one of them can

be implemented now. The glazed paper project

involves an outlay of Rs 25 crore while craft

paper project can be implemented with Rs 20

crore. The markets are uncertain and the

estimates of NPV for both the projects with

corresponding probabilities are as below:

Rs Lacs

Glazed paper Craft paper

Probability NPV Probability NPV

0.20 400.00 0.10 250.00

0.30 650.00 0.40 500.00

0.30 850.00 0.30 750.00

0.20 155.00 0.20 250.00

i) What is the expected NPV of each project?

ii) What is the risk of each project, as

measured from standard deviation and co-

efficient of variation

iii) What is the profitability index of each

project?

iv) What conclusion would you draw based on

expected NPV, its standard deviation, and co-

efficient of variation?

v) If firm faces constraint of capital which

project should be undertaken

Scenario Analysis A firm is considering a capital investment of Rs

40 lacs fro a project that has life of 5 years The

cash flows are dependent upon the general

economic conditions. The project team has

considered 4 different scenarios of poor, average,

good and excellent with respective probabilities

of 20%, 30%, 30% and 20% respectively. the cash

flows fro three years under 4 different scenarios

are given below:

Rs lacs

Scenario Prob. Year 1 Year 2 Year 3

Poor 0.20 12.00 15.00 18.00

Average 0.30 15.00 19.00 24.00

Good 0.30 20.00 25.00 35.00

Excellent 0.20 27.00 35.00 44.00

Assuming cost of capital at 12% find out the

following:

i) The NPV of the project under different

scenarios of poor, average, good and excellent.

ii) The expected NPV of the project.

iii) Risk as assessed from standard deviation

and co-efficient of variation.

iv) Find out the probabilities of NPV being

a) negative b) 80%, c) 90%, d) 100%, e) 110%

and f) 120% of the expected NPV.

v) The management does not accept any

proposal that has more than 20% chance of

providing negative NPV. Under such condition

what is your recommendation regarding

acceptance of the project?

Sensitivity Analysis Sensitive Controls Limited have a project on

hand costing Rs 20 crore with a life of 10 years

The expected revenue id Rs 21 crore per annum

with variable cost estimated at 50%. The fixed

cost are Rs 2 crore while depreciation is on the

basis of SLM. The tax rate is 40% and the cost

of capital for the firm is 14%.

The management of the Sensitive Controls

Limited is apprehensive of the cash flow

estimates. The apprehension emanates from

uncertainty of revenue and the proportion of

the variable cost. Due to inherent risk in the

projections the management also believes that

the suppliers of capital for the project may not

be very comfortable with the returns equal to

the current cost of capital.

Find out the following:

i) The estimated annual cash flows of the

project.

ii) Assuming uniform cash flows of the project

for entire life and current cost of capital as

appropriate discount rate find the net present

value of the project.

iii) Find out the NPV of the project assuming

the revenues can change from 70% to 130% of

the expected revenue and plot the NPV with

respect to the level of revenue. Find out from

the plot the approximate minimum revenue that

the project must generate so as to keep the

NPV positive.

iv) Find out the NPV of the project assuming

that the variable cost can change from 35% to

65% of the expected revenue and plot the NPV

with respect to the variable cost as proportion

of expected revenue. What is the maximum

proportion of variable cost the project can

afford?

v) Find out the NPV of eth project for cost of

capital ranging between 11% and 17% and plot

the NPV with respect to cost of capital. What is

the maximum cost of capital that would keep

the project acceptable?

Decision Tree

Child Entertainment Ltd. (CEL) are in the

business of developing fancy toys that last

normally no more than 2 - 3 years They have

come out with another fancy toy that is

expected to last for two years The capital

investment is Rs 275 lacs.

During the first year CEL expects the post tax

cash flows of Rs 150 lacs with probability of 60%

or Rs 180 lacs with probability of 40% depending

upon the demand for the new toy.

During the second year the probabilities of

demand being low, medium and high are 40%,

40% and 20% respectively. If initial demand

during first year is high then the second year cash

flows are expected to be Rs 200 lacs, Rs 240 lacs

and Rs 290 lacs respectively.

However, if initial demand during first year is

low then the second year cash flows are

expected to be Rs 160 lacs, Rs 200 lacs and Rs

250 lacs respectively.

For the kind of business CEL is into the

appropriate discount rate for investment is 15%.

Advise whether CEL should go ahead with the

investment.

Risk Adjusted Discount Rate:

Refer to the previous example: If the firm

faces a capital constraint of Rs 500 lacs which

of the project would be accepted under a)

NPV criterion, b) PI criterion. What would be

the addition to the NPV in each case? Use cost

of capital as per CAPM for calculating NPVs.

Assume that projects can be implemented in

parts.

Certainty Equivalent