Topic Capital On Budgeting.pdf

As Project “A” has a higher Net Present Value, it has to be taken up... It represent the same relationship of investment and cash inflows in case of payback calculation : F = I/C WhereF

Practice Problem on Capital Practice Problem on Capital Budgeting Budgeting

1

1 Initial Investment = Rs 1,00,000Initial Investment = Rs 1,00,000

Expected future cash inflows Rs 20,000, Rs 40,000, Rs 60,000, Rs 70,000 From the above compute Pay-back period

Solution:

Calculation of Pay Back period

Year Cash Cash Inflows Inflows (Rs.) (Rs.) Cumulatige Cash Cumulatige Cash Inflows Inflows (Rs.)(Rs.)

The initial investment is recovered between the 2nd and the 3rd year

Balance of Unrecovered Initial Balance of Unrecovered Initial Investm Investment ent

× 12

∴  Pay back Preiod = 2 years 

Cash Inflows during the year

Initial Investment − Cumulative

=

= 2 2 Cash Inflows at the end of 2

×  12

 years 

Cash Cash Inflows in the 3rd year Inflows in the 3rd year

1,00,000 − 60,000

× 12

= 2 years 

60,000 40,000

× 12

= 2 years 

60,000

= 2 years 8 months.

2

2 Victory Ltd decided to purchase a machine to increase th installed capacity.Victory Ltd decided to purchase a machine to increase th installed capacity TheThe company has four machines under consideration The relevant details including estimated yearly expenditure and sales are given below All sales are for cash Corporate Tax Rate @ 33.99% (inclusive

Corporate Tax Rate @ 33.99% (inclusive of Surcharge @ 10%, Deduction less @ 2% of Surcharge @ 10%, Deduction less @ 2% andand Secondary & Higher Education less @ 1%) Calculate Pay-back Period

Initial

Initial Investment Investment (Rs (Rs lacs) lacs) 30.00 30.00 40.00 35.00 Estimated

Estimated Annual Annual Sales Sales (Rs (Rs lacs) lacs) 50.00 40.00 45.00 48.00 Cost

Cost of of Production Production (Estd) (Estd) (Rs (Rs lacs) lacs) 18.00 14.00 16.70 21.00 Economic

Scrap

Scrap Values Values (Rs (Rs lacs) lacs) 4.00 2.50 3.00 5.00 Solution:

Statement Showing Payback for four machines

(1)Initial

(1)Initial Investm Investment ent (Rs (Rs lacs) lacs) 30.00 30.00 40.00 35.00

(2)

(2) Estd Estd Annual Annual Cost Cost of of Production Production (Rs (Rs Lacs) Lacs) 50.00 50.00 40.00 45.00 48.00 (3)Estd

(3)Estd Cost Cost of of Production Production (Rs (Rs lacs) lacs) 18.00 14.00 16.70 21.00

(4)Deprecia

(4)Depreciation tion (Rs (Rs lacs) lacs) 13.00 9.17 9.17 12.33 12.33 7.50

(5) Profit

(5) Profit Before Tax (PBT) [2 Before Tax (PBT) [2 –   – 3 3 –   – 4] 4] 19.00 16.83 15.97 19.50

(6)

(6) Tax Tax @ @ 33.99% 33.99% (Rs (Rs lacs) lacs) 6.4581 5.721 5.428 6.628

(7) Profit

(7) Profit After Tax (PAT) [5 After Tax (PAT) [5 –   – 6] 6] (Rs (Rs lacs) lacs) 12.5419 11.109 10.542 12.872 (8)

(8) Net Net Cash Cash Flow Flow [7+4] [7+4] 25.5419 20.279 22.872 20.372

M 1

M

2

M

3 M

4

Pay back Period (Years)  30.00  30.00  40.00  35.00

25.5419 20.279 22.872 20.372 Initial

Initial Investm Investment ent

=

= 1.17 1.17 = = 1.48 1.48 = = 1.74 1.74 = = 1.72 1.72  Net Annual Ca

 Net Annual Cash Flow sh Flow

Analysis : Machine 1 is more profitable, as it has the lowest payback period.

3 A project costing Rs 10 lacs EBITD (Earnings before Depreciation, Interest and

Taxes) during the first five years is expected to be Rs 2,50,000; Rs 3,00,000; Rs

3,50,000; Rs 4,00,000 and Rs 5,00,000 Assume 33.99% tax and 30% depreciation

on WDV Method Compute Accounting Rate of Return

Computation of Project ARR :

Less : Depreciation 3,00,000 2,10,000 1,47,000 1,02,900 72,030 1,66,386

(50,000) 76,404 1,34,000 1,96,116 2,82,503 1,27,805

Book Value of Investment :

Begining 10,00,000 7,00,000 4,90,000 3,43,000 2,40,100

Average EBIT (1 − t) 1,27,805

ARR = Average Investment ×100 =4,71,427 ×100

= 27.11%

Note : Unabsorbed depreciation of Yr 1 is carried forward and set-off against profits of Yr 2 Tax is

calculated on the balance of profits

= 33.99% (90,000 –  50,000)

=

4 Z Ltd has two projects under consideration A & B, each costing Rs 60 lacs

The projects are mutually exclusive Life for project A is 4 years & project B is 3 years Salvage value NIL for both the projects Tax Rate 33.99% Cost of Capital is 15% Compute Net Present Value

 Net Cash Inflow (Rs Lakhs)

At the end of the year Project A Project B P.V @ 15%

Computation of Net Present Value of the Projects

10 P.V of Cash outflow (Initial Investment) = 60.00

Net Present Value = 117.18

Project B

(PAT+Dep.)

9 Total P.V of Cash Inflows = 160.621

10 P.V of Cash Outflows = 60.00

Initial Investment

5 As Project “A” has a higher Net Present Value, it has to be taken up

Cash Inflows :

Calculate the Internal Rate of Return

Solution:

Internal Rate of Return will be calculated by the trial and error method The cash flow is not uniform To have an approximate idea about such rate, we can calculate the “Factor” It represent the same relationship of investment and cash inflows in case of payback calculation :

F = I/C  WhereF = Factor

I = Original investment

C = Average Cash inflow per annum

= 110,000=

Factor for the project 3.14 35,000

The factor will be located from the table “P.V of an Annuity of Rs 1” representing number of years corresponding to estimated useful life of the asset

The approximate value of 3.14 is located against 10% in 4 years

We will now apply 10% and 12% to get (+) NPV and ( –) NPV [Which means IRR lies in between]

Year Cash Inflows P.V @ 10% DCFAT P.V @ 12% DCFAT

 Net Profit  —  10,000 10,000 10,000 10,000 10,000 Depreciation Add back  —   —  8,000 8,000 8,000 8,000

Capital

 Net Cash inflow (26,000) (2,000) 14,000 14,000 16,000 9,200 Discount factor @ 10% 1.000 0.9091 0.8264 0.7513 0.6830 0.6209 Present Value (26,000) (1,819) 11,570 10,570 10,928 5,712

Suggestion: Since NPV is Rs.10,910; it is suggested to accept the proposal

15 Following are the data on a capital project being evaluated by the Management of X Ltd.:

Project M

Find the missing values considering the following table of discount factor only :

Calculation of Cost of Projecti.e., Initial Cash Outlay of Project M

At 15% I.R.R., the total present value of cash inflows is equal to initial cash outlay Total present value of cash inflows @ 15% for 4 years is 2.855

= Rs 40,000 × 2.885 = Rs 1,14,200

∴ Project Cost is Rs 1,14,200

Calculation of Payback period of Project M

1,14,000

= 2.855 years or 2 years 11 months Calculation of Cost of Capital

Discounted Cash inflows Profitability Index =

Cost of Project

Discounted Cash Inflows = 1.064 x 1,14,200 = 1,21,509

Cumulative Discount Factor for 4 years

= Present value of cash inflows  1,21,509 =3.038

Annual cost saving 40,000 Looking at present value table at discount compound discount factor for 4 years is 3.038 ∴

Cos of capital = 12%

Calculation Net Present Value of Project

 N.P V = Present Value of Total Cash Inflows - Cost of Project

= 1,21,509 –  1,14,200 = Rs 7,309

16 Xpert Engineering Ltd is considering buying one of the following two mutually exclusive investment projects:

Project A: Buy a machine that requires an initial investment outlay of Rs

1,00,000 and will generate the cash flows after tax (CFAT) of Rs 30,000 per year for 5 years

Project B: Buy a machine that requires an initial investment outlay of Rs

1,25,000 and will generate ‘cash flows after tax’ (CFAT) of Rs 27,000 per year for 8 years

Which project should be undertaken? The company uses 10% cost of capital to evaluate the projects

Note: Present value of Re 1 for eight years @10% - 0.9091, 0.8264, 0.7513, 0.6830, 0.6209, 0.5645, 0.5132, and 0.4665

Solution:

Calculation of Net Present Value

NPV

Equivalent Annual NPV

Project A = 13,730/3.791 = Rs 3.622 Project B = 19,045/5.335 = Rs 3.570

Analysis

If it is one-time Project, Project B suggested, since its NPV is greater than Project A

If a Project is to be replaced every time after the end of economic life of earlier Project, then Project A is preferable, since its equivalent annual NPV is higher than Project B

17 XYZ Ltd., an infrastructure company is evaluating proposal to build, operate and transfer a section of 35 kms of road at a projcet cost of Rs 200 crores to be financed as follows:

Equity Share Capital Rs 50 crores, loan at the rate of interest of 15% p.a from financial institutions Rs 150 crores The Project after completion will be opened to traffic and a toll will be collected for a period of 15 years from the vehicles using the road

The company is also required to maintain the road during the above 15 years and after the completion of that period, it will be handed over to the Highway Authorities at zero value It is estimated that the toll revenue will be Rs 50 crores per annum and the annual toll collection expenses including maintenance of the roads will amount to 5% of the project cost

The company considers to write off the total cost of the project in 15 years on a straight line basis For Corporate Income-tax purposes the company is allowed to take depreciation @ 10% on WDV basis The financial institutions are agreeable for the repayment of the loan in 15 equal annual instalments –consisting of principal and interest

Solution:

Calculate Project IRR and Equity IRR Ignore Corporate taxation Explain the differences in Project IRR and Equity IRR

Financed by :

Term Loan from financial institutions @ 15% p.a = Rs 150 crores

= Rs 40 crores

Calculation of IRR

Factor to be located = Original investment =

Rs 200

Average annual cash inflow Rs 40 crores

Project’s operating and terminal value cash flows over its 5-year life (Rs.)

Savings

Reduction in clerks salaries (4×50,000) 2,00,000

Less : Expenses

Cash flow = Profit After Tax – Depreciation = 18,600 + 60,000 = Rs 78,600

The cash flows are the same for the years 1 to 5

(i)Evaluation of the Project by using Net Present Value (NPV) Method:

Years Cash flow PV of Annuity of Rs 1 Total present value

 After tax (Rs.) at 12% for five years (Rs.)

Since NPV is negative, therefore, the project is unviable

(ii)Evaluation fo the Project by using PI Method

Profitability Index (PI) = PV of cash inflows/Initial outlay

= 2,83,353/3,00,000 = 0.945 Since PI is less than 1.0, the project is unviable

(iii)Calculation of the Project’s Payback Period (Rs.)

Hence, the payback period is 3 years plus a fraction of the 4th year The fraction of the year can be calculated as under:

64,200= 0.82

78,600

Therefore, the payback period is 3.82 years

20 Five Projects M, N, O, P and Q are available to a company for consideratio The investment required for each project and the cash flows it yields are tabulated below Projects N and Q are mutually exclusive Taking the cost of capital @ 10%, which combination of projects should be taken up for a total capital outlay not exceeding Rs

3 lakhs on the basis on NPV and Benefit-Cost Ratio (BCR)?

(Rs.) Project Investment Cash flow p.a No of years P.V @ 10%

Total Capital outlay < Rs 3.00 lakhs

Solution :

Computation of Net Present Value and Benefit-Cost Ratio for 5 Projects (Rs.)

 Project  Investment Cash flow  No of years  P.V @ 10% P.V  NPV BCR (PV/

M 50,000 18,000 10 6.145 1,10,610 60,160 2.212

 N 1,00,000 50,000 4 3.170 1,58,500 58,500 1.585

O 1,20,000 30,000 8 5.335 1,60,050 40,050 1.334

P 1,50,000 40,000 16 7.824 3,12,960 1,62,960 2.086

Q 2,00,000 30,000 25 9.077 2,72,310 72,310 1.362

Statement showing Feasible Combination of Projects and their NPV, BCR

 Feasible Combination Investment NPV Rank BCR Rank