Techniques of Capital Budgeting numerical with solutions

Capital Budgeting refers to the expenditure on the capital assets. Spending money on capital assets is a very important decision that a finance manager is required to take. Capital investment expenditure may be on Plant, Machinery Equipment, Land, Building etc. It involves substantially higher amounts than for other routine expenses. The decision is irreversible, i.e. it is not possible to withdraw your steps easily, once you have taken few steps in this regard. It has long term impact on the affairs of a company and it, hence determines the future of a company.

An expenditure made on a capital asset has a long term perspective. We spend today, to gain some advantages in future. This expenditure involves a big cash outflow of funds initially, compensated by small but recurring doses of inflow of funds in future for some time.

The essence of the capital budgeting decision making is to determine, whether the initial expenditure of funds is duly compensated by the inflow of funds occurring in future. If greater values can be assigned to the inflow of funds than the present expenditure, then that capital investment proposal must be accepted because that will add up to the wealth of the company.

Initial Cash Outflow =  Cost of new plan +   Installation expenses  +  Other Capital expenditure  +  Additional working capital  –  [ Salvage value ( Scrap Value)  of old plant  – Tax liability on account  of capital gain on sale of old plant (if any) ]

Subsequent Annual Inflows = Profit after tax (PAT) + Depreciation

Terminal Cash Inflow = Annual cash inflow + Working capital released + [Salvage value (Scrap Value) of new asset – Tax liability on account of capital gain on sale of new asset (if any)]

Capital Gain = Salvage Value of Asset –  Book Value of Asset ( or Written Down Value of asset)

If the value is negative, then it is Capital Loss.

Payback Period

The payback period is the time duration required to recover the initial cash outflows. This method is based on cash flows and not on accounting data.

If the cash inflows are uniform

Payback period  =  Initial cash outflow / Annual cash inflow

If the cash inflows are not uniform then

Payback period = time period in which the cumulative cash flows are equal to initial inflows.

Completed Years + (Cash Flow yet to be recovered / Cash flow for the next year)

Discounted Payback Period

To overcome the limitation of the payback that it does not use time value of money, we may use the discounted cash flows in order to calculate the payback period. Obviously the discounted payback will be longer than the simple payback period.

Accounting Rate of Return (ARR)

Accounting Rate of Return means the average annual yield on the project.

It is calculated by dividing the annual average profits after taxes by the average investment.

ARR = Average PAT / Average Investment

Annual Average profit After Tax  = Total Expected Earning after Depreciation and taxes / Duration of Project

Average Investment =[1/2 (original investment – scrap value)] + working capital + scrap value

Average investment  =   Opening investment + closing investment/ 2

Net Present Value (NPV)

It is net present value of all the cash flows that occur during the entire life span of a project. The outflows will have negative values while the inflows will have positive values. If the present value of inflows is greater than outflows, we get a positive NPV and if the present value of outflows is greater than inflows, we get a negative NPV. The positive NPV means a net gain in value maximization and, therefore, any project which gives a positive NPV is an acceptable project and if it gives a negative NPV, then the project should not be accepted.

NPV = Present value of cash inflows – Present value of cash outflows

Profitability Index

Profitability Index = Present value of cash inflows / Present value of cash outflows

Internal Rate of Return (IRR)

IRR is that rate of discount at which NPV is zero.

Techniques of Capital Budgeting numerical with solutions

1. RBL Ltd. is considering purchasing a machinery to increase its production capacity to meet demand of its products. It is evaluating three machines. The relevant details including estimated yearly expenditure and sales are given below: Corporate Income Tax rate is 30 %.

The economic life of Machine 1 is 4 years, while it is 5 years for the machine II and 6 years for machine III. The scrap values are Rs. 4,00,000, Rs. 5,00,000, and Rs. 6,00,000 respectively. Using Payback method, find out the best alternative out of three machines you will recommend to company.

Solution

Since Machine I has lowest payback, hence company should invest in machine I.

Note: When annual cash inflows are equal

Payback Period = Initial Investment / Annual cash inflow

Depreciation = Initial investment / cost of machine – scrap value / Estimated life

Depreciation on Machinery I = (Rs.30,00,000 – Rs. 4,00,000) / 4 = Rs.6,50,000

Depreciation on Machinery II = (Rs.30,00,000 – Rs. 5,00,000) / 5 = Rs. 5,00,000

Depreciation on Machinery III = (Rs.30,00,000 – Rs. 6,00,000) / 6 = Rs. 4,00,000

2. RBL Academy Ltd. Wants to replace one of its machines in its plant. First option available to company is Installation of equipment “King” having cost of Rs. 7,50,000 with an expectation of cash inflow of Rs. 2,00,000 p.a. for next 6 years. Second is to Install equipment “Queen” having cost of Rs. 5,00,000 which is expected to generate a cash inflow of Rs. 1,80,000 per annum for next 4 years. Which equipment should be preferred under (a) Payback period (b) Internal Rate of Return?

Solution

Payback Period Method

Since annual cash inflows are equal;

Payback period for Equipment “King” = Initial investment or cost of equipment ÷ annual cash inflow

= Rs. 7,50,000 / 2,00,000 = 3.75 years.

Payback period for Equipment “Queen” = Initial investment or cost of equipment ÷ annual cash inflow

= Rs. 5,00,000 / 1,80,000 = 2.78 years.

From Payback Period method, equipment “Queen” is better.

Internal Rate of Return method (IRR)

Since cash annual cash inflows are equal for both equipment;

Equipment “King”-

Initial outflow or investment = Rs. 7,50,000

Annual cash inflow = Rs.2,00,000

Calculating PVAF using Payback period method

PVAFr,6  = Rs. 7,50,000 / Rs.2,00,000 = 3.75

Looking at present value annuity factor table, the value nearest to 3.75 in the year 6 in interest rate column is 15 % (3.784) and 16 % (3.685).

Using interpolation formula

= 15 % + [ (3.784 – 3.75) / (3.784 – 3.685)] × (16 % – 15%) = 15.34 %

Equipment “Queen”-

Initial outflow or investment = Rs. 5,00,000

Annual cash inflow = Rs.1,80,000

PVAFr,6  = Rs. 5,00,000 / Rs.1,80,000 = 2.778

Looking at present value annuity factor table, the value nearest to 2.778 in the year 4 in interest rate column is 16 % (2.798) and 17 % (2.743).

Using interpolation formula

= 16 % +[ (2.798 – 2.778) / (2.798 – 2.743)] × (17 % – 16%) = 16.36 %

Since IRR of Equipment “Queen” has higher IRR so equipment “Queen” should be preferred.

3. Machine A costs 1,80,000 payable immediately. Machine B costs Rs. 2,00,000 half payable immediately and half payable in one year’s time. The cash receipts expected are as follows:

At 8 % opportunity cost, which machine should be selected on the basis of NPV?

Solution

NPV = PV of Cash inflow – PV of Cash outflow

NPV of Machine B is higher than Machine A. Hence, Machine B should be selected.

4. A company is considering a new project for which requires a Capital outlay of Rs. 5,00,000 and depreciation is to be allowed at 20 % on SLM basis. Forecasted annual earnings before charging depreciation is as follows:

Evaluate the project using Payback and Accounting Rate of return.

Solution

Payback Period

Payback period = 2 years (Money invested or Capital outlay of Rs. 2,00,000 has been recovered in 2 years.)

Average Rate of return on original investment

Average income = Total net income / no. of years = Rs.3,00,000 / 5 = Rs. 60,000

Rate of return on original investment = (Average income ÷ Average investment) × 100

= (Rs. 60,000 ÷ Rs.2,50,000) × 100 = 24 %.

Average investment = (opening investment + closing investment)/2 = (5,00,000 + 0) / 2 = 2,50,000

5. RBL Academy is considering a project with an initial outflow of Rs. 1,20,000 with following cash inflow:

Comment on the project considering cost of capital to be 7% using internal rate of return method.

Solution

Calculation of Internal rate of return

Cash outflow = Rs.1,20,000

Average cash inflow = Total cash inflow / number of years = Rs. 1,49,000 / 5 = Rs. 29,800

Approximate payback period = Cash outflow / average cash inflow

= Rs. 1,20,000 /Rs.29,800 = 4.0268

In PVAF table, value near to 4.0268 in year 5 is 4.1002 at 7 % and 3.9927 at 8%.

Using interpolation formula

IRR = Lower discount rate + [NPV at lower rate / (NPV at lower rate – NPV at higher rate) × (Difference between two rates)]

= 7% + [2415/2415-(-765.4) × (8% – 7%)]

= 7% + [(2415/3180.4) × 1 %]

7% + 0.7593% = 7.7593 %

Since cost of capital is 7% and IRR is 7.7593%. Hence project should be included.

6. RBL Academy Ltd. is considering two mutually exclusive projects. The after-tax cash flows of these projects are as follows:

Opportunity cost of capital for these projects is 10 %. Calculate

a. NPV and IRR of each project.

b. Is there any conflict in ranking of projects? Which project should be accepted?

Solution

NPV of Project A = PV of cash inflow – PV of cash outflow

= Rs. 30,000 × PVAF0.1, 5 – Rs.1,00,000

(Since there is equal cash inflow, hence PVAF has been taken)

= (Rs. 30,000 × 3.7908) – Rs.1,00,000

= Rs. 1,13,724 – Rs.1,00,000 = Rs.13,724

NPV of Project B = PV of cash inflow – PV of cash outflow

= Rs. 1,90,000 × PVF0.1, 5 – Rs.1,00,000

= (Rs. 1,82,500 × 0.6209) – Rs.1,00,000 = Rs.13,314

Calculation of Internal rate of return

Project A

Initial outflow or investment = Rs. 1,00,000

Annual cash inflow = Rs.30,000

Calculating PVAF using Payback period method

PVAFr,5 = Rs. 1,00,000 / Rs.30,000 = 3.333

Looking at present value annuity factor table, the value nearest to 3.333 in the year 5 in interest rate column is 15 % (3.352) and 16 % (3.274).

We can calculate IRR using both methods

Method 1: Using interpolation formula

IRR = Lower discount rate +  × (Higher discount rate – Lower discount rate)

=   15 % + [ (3.352– 3.333) / (3.352– 3.274)] × (16 % – 15%) = 15.34 % = 15.24

Method 2 : Using NPV for IRR calculation

NPV @ 15 % = PV of cash inflow – PV of cash outflow

= Rs.30,000 × 3.352 – Rs. 1,00,000 = Rs. 560

NPV @ 16% = Rs.30,000 × 3.274 – Rs. 1,00,000 = (Rs.1,780)

IRR = Lower discount rate + [NPV at lower rate / (NPV at lower rate – NPV at higher rate) × (Difference between two rates)]

= 15 % + [(560/560 + 1780) × 1) = 15.24%

Project B:

In this case, there is only one cash inflow in the year 5. We can use Trial and error method. In PVF table, at year 5, we need to find an interest rate whose value when multiplied by cash inflow gives positive return and other which gives negative return and difference between two rates is 1.

Looking into PVF table at year 5, 12 % (0.567) and 13 % (0.543)will be considered.

NPV at 12 % = PV of cash inflow – PV of cash outflow

= (Rs. 1,82,500 × 0.567) – Rs.1,00,000 = Rs. 3,477.5

NPV at 13 % =( Rs. 1,82,500 × 0.543) – Rs.1,00,000  = (Rs. 902.5)

IRR = Lower discount rate + [NPV at lower rate / (NPV at lower rate – NPV at higher rate) × (Difference between two rates)]

= 12 % + [ (3,477.5/ 3,477.5 + 902.5)] × 1 = 12.79 %

According to NPV method and IRR method, Project A is better. There is no difference in ranking A. Difference in ranking of projects arises because of difference in patterns of inflows. However, in this case from both methods, Project A is better than project B, hence, Project A should be opted.

7. A firm whose cost of capital is 10% is considering two mutually exclusive projects X and Y, The after-tax cash flows of these projects are as follows:

Compute the Net Present Value at 10%, Profitability Index, and Internal Rate of Return for the two projects.

Solution

Calculation of NPV & IRR

Calculation of IRR

Project X

Calculating PVAF using Payback period method

Payback value = Initial cash outflow / average cash inflow

Project X average cash inflow = Rs. 1,68,000 / 5 = Rs. 33,600

Payback value (PVAFr,5) = Rs. 1,00,000 / Rs.33,600 = 2.976

The PVAF table indicates that for Project X, the PV Factor closest to 2.976 against 5 years is 2.991 at 20% and In the case of Project X, since Cash inflow in the initial years are considerably smaller than the average cash flows, the IRR is likely to be much smaller than 19%. So, Project X may be tried at 15% and 16% .

IRR = Lower discount rate + [NPV at lower rate / (NPV at lower rate – NPV at higher rate) × (Difference between two rates)]

= 15 % + [ (1,958/ 1,958 + 1,066) × 1] = 15.65%

Project Y

Calculating PVAF using Payback period method

Payback value = Initial cash outflow / average cash inflow

Project Y average cash inflow = Rs.1,32,000/5 = Rs.26,400

Payback value (PVAFr,5) = Rs. 1,00,000 / Rs.26,400 = 3.788

Looking at present value annuity factor table, the value nearest to 3.788 in the year 5 in interest rate column for Project Y, is 3.791 at 10%. In the case of Project Y, Cash inflow in the initial years are considerably larger than the average cash flows, the IRR is likely to be much higher than 10%. Project Y may be tried at 14% and 15%

IRR = Lower discount rate + [NPV at lower rate / (NPV at lower rate – NPV at higher rate) × (Difference between two rates)]

= 14 % + [ (30 / 30 + 1,664) × 1] = 14.02 %

8. A Company requires an initíal investment of Rs. 50,000. The estimated net cash flow are as follows-

Using 10% as the cost of capital (rate of discount), determine (i) Pay-back period (ii) Net Present Value and (iii) Internal Rate of Return.

Solution

Payback period:

Payback refers to time period in which initial cash outflow is recovered. Cash inflow generated in first 5 year = Rs. 44,000

Remaining cash outlay to be recovered = Rs.50,000 – Rs.44,000 = Rs.6,000

6th year cash inflow = Rs. 15,000

Payback period = 5 years + (6000/15,000) = 5.4 years

NPV calculation

NPV = PV of cash inflow – PV of cash outflow = Rs.55,484 – Rs.50,000 = Rs.5,484

IRR calculation

Calculating PVAF using Payback period method

Payback value = Initial cash outflow / average cash inflow

Average cash inflow = Rs. 90,000 / 10 = Rs. 9,000

Payback value (PVAFr,10) = Rs. 50,000 / Rs.9,000 = 5.556

Looking at present value annuity factor table, the value nearest to 5.556 in the year 10 in interest rate column is 12 % (5.650) and 13 % (5.426).

NPV at 12 % = Rs. 51,005 – Rs. 50,000 = Rs. 1,005

NPV at 13 % = Rs. 48,947 – Rs.50,000 = (Rs.1,053)

IRR = IRR = Lower discount rate + [NPV at lower rate / (NPV at lower rate – NPV at higher rate) × (Difference between two rates)]

= 12% + [ 1005/(1005 + 1,053) × 1] = 12.49%

9. RBL Academy Ltd. is considering the introduction of a new product. It is estimated that profits before depreciation would increase by Rs. 2, 00,000 each year for first four years and Rs. 1,00,000 each for the remaining period. An advertisement cost of Rs. 20,000 is expected to be incurred in the first year, which is not included in the above estimate of profits. The cost will be allowed for tax purpose in the first year. A new plant costing Rs.4,00,000 will be installed for the production of the new product. The salvage value of the plant after its life of 10 years is estimated to be Rs. 50,000. Working capital investment of Rs. 50,000 will be required in the year of installing the plant and a further Rs. 30,000 in the following year. The company’s tax rate is 30% and written down value depreciation at 25%. If the company’s required rate of return is 20%, should the company introduce the new product? Ignore tax effect on Profit/Loss on sale of asset.

Solution

Calculation of Depreciation

Calculation of PV of Cash inflow

Note: PBDT for year 1 has been taken after subtracting advertisement expense.

PV of cash outflow = Initial outflow + working capital in year zero + working capital in year 1

= Rs. 4,00,000 + Rs.50,000 + Rs.24,990  = Rs. 4,74,990

Working capital in year 1 after discounting at 20 % = Rs.30,000 × 0.833(PVF0.2,1) = Rs.24,990

NPV = PV of cash outflow – PV of cash inflow = Rs.5,50,115 – Rs. 4,74,990 = Rs.75,125

Since, NPV is positive, hence project should be accepted.

10. A company is engaged in evaluating an investment project which requires an initial cash outlay of Rs. 2,50,000 on equipment. The project’s economic life is 10 years and its salvage value 30,000. It would require current assets of Rs. 5 0,000. An additional investment of Rs. 60,000 would also be necessary at the end of five years to restore the efficiency of the equipment. This would be written off completely over the last five years. The project is expected to yield annual profit (before tax) of Rs. 1,20,000. The company follows the sum of the years’ digit method of depreciation. Income-tax rate is assumed to be 30%. Should the project be accepted if the minimum required rate of return is 22 %.

Solution

The depreciation of different years have been calculated as per sum of the years’ digit method as follows:

Initial outlay – Salvage value

Rs. 2,50,000 –  Rs.30,000 = Rs. 2,20,000 is to be depreciated over 10 years.

The sum of the years digits for the vears 1-10 is 55.

1+2+3+4+5+6+7+8+9+10 = 55

So, depreciation for year 1 is Rs. 2,20,000 x (10/55) = Rs.40,000

And for the year 2 it is 2,20,000 x (9/55)  = Rs.36,00 and so on.

The total depreciation for first 5 years is Rs. 1,60,000 and so the written down value of the asset at the end of year 5, is Rs. 90,000 (i.e., Rs. 2,50,000 – Rs. 1,60,000).

A capital expenditure of Rs. 60000 is required at that stage. So, the total cost required to be depreciated is Rs.  1,20,000 ( ie, Rs. 90,000- Rs. 60,000 – Rs.30,000) .

As per the sum of the years digit method for 5 years (ie, remaining life), the depreciation for the year 6 is Rs. 1,20,.000 x (5/15) = Rs.40,000

for year 2 is Rs. 1,20,000 x( 4/15) = Rs.32,000 and so on.

Present value of cash outflow = Initial cost + current asset + PV of investment in 5th year

= Rs.2,50,000 + Rs.50,000 + Rs.60,000 × 0.37 = Rs.3,22,200

NPV = Total of PV of cash inflow including Terminal value – Present value of cash outflow

= Rs. 3,78,041 – Rs.3,22,200  = Rs.55,841

Since, NPV is positive, hence project should be accepted.

11. Delhi Machinery manufacturing Company wants to replace its manual operations by new machine. There are two alternative models A and B the new machine. Using Payback period, suggest the most profitable investment. Ignore taxation.

Solution:

12. RST is evaluating two mutually exclusive proposals, A and B. Following information is available about these projects:

Other Information: Tax rate 40%, Required Rate of Return 12%; Evaluate the proposals on the basis of incremental Cash flows. (Proposal B over Proposal A).

Solution

Since Project B has negative NPV over A , Proposal A should be preferred.

13. The Eastern Corporation Ltd., a firm in the 30% tax bracket with a 15% required rate of return, is considering a new project. This project involves the introduction of a new product. This project is expected to last five years and then to be terminated. Given the following information, determine the after-tax cash flows associated with the project and then find the project’s net present value and advise the company whether it should invest in the project or not.

Cost of new Plant and Equipment: Rs. 20,90,000

Shipping and Installation Cost Rs. 30,000

Unit sales

Sales Price per unit: Rs. 500/unit in years 1-4 and Rs. 380/unit in year 5

Variable Cost per unit: 260/unit

There will be an initial Working capital requirement of Rs. 80,000 just to get production started. For each year, the total investment in net working capital will be equal to 10% of the rupee value of sales for that year. Thus, the investment in working capital will increase during years 1 through 3, then decrease in year 4. Finally, all working capital is liquidated at the termination of the project at the end of year 5. Use straight-line method for providing depreciation over five years assuming that the plant and equipment will have no salvage value after five years.

Solution

Initial Cash outflow = Cost of machine + Installation cost + Initial Working Capital requirement + Working Capital required for Year 1 in the beginning of the year

= Rs. 20,90,000 + 30,000 + 80,000 + 5,00,000(10 % of sales of first year = 10 % of Rs.50,00,000)

= Rs.27,00,000

Depreciation = (Cost of machine + Installation cost – salvage value) ÷ estimated life

= (Rs. 20,90,000 + Rs.30,000) ÷ 5 = Rs.4,24,000

Change in WC = New WC – Existing WC = Current Year  WC – Previous Year WC

NPV = PV of cash inflow – PV of cash outflow

= Rs.67,72,817 – Rs.27,00,000 = Rs.40,72817

Since NPV is positive, project should be accepted.

14. A particular project has a four years life with yearly projected net profit of Rs. 10,000 after charging yearly depreciation of Rs.8000 but before charging tax in order to write off the capital cost of Rs. 32,000. Out of the capital cost, Rs. 20,000 is payable immediately (year 0) and balance in next year (which will be needed for evaluation). Stock amounting to Rs. 6,000 (to be invested in year 0) will be required throughout the project and for debtors a further sum of 8,000 will have to be invested in year 1. The working capital will be recouped in year 5. It is expected that the machinery will fetch a residual value of Rs. 2,000 at the end of 4th year. Income tax is payable @ 40% and the cost of capital is 10%. Income tax is payable next year. The residual value of the machine, Rs. 2,000 will also bear tax @ 40%. Although the profit is for 4 years, for computation of tax and realization of working capital, the computation will be required up to 5 years. Advise the firm.

Solution

Initial Outflows = capital cost at T0 + capital cost at T1 + Working Capital (Stocks) at T0 + Working Capital (Debtors) at T1

Rs.20,000 + (Rs.12,000 × 0.909) + Rs.6,000 + (Rs.8,000 × 0.909) = Rs.44,180

Subsequent annual Cash inflows

Since NPV is positive, hence project should be accepted.

15. ABC & Co.is considering a proposal to replace one of its plants costing Rs. 60,000 and having a written down value of Rs. 24,000. The remaining economic life of the plant is 4 years after which it will have no salvage value. However, if sold today, it has a salvage of Rs. 20,000. The new machine costing Rs. 1,30,000 is also expected to have a lite of 4 years with a scrap value of Rs. 18,000. The machine, due to its technological superiority, is expected to contribute additional annual benefit (before depreciation tax) of Rs. 60,000. Find out the cash flows associated with the decision given that the tax rate applicable to the firm is 40%. (The capital gain or loss may be taken as not subject to tax).

Solution

Initial cash outflow = cost of machine – Salvage value of existing machine

= Rs.1,30,000  – Rs.20,000 = Rs.1,10,000

Subsequent annual cash inflow

16. A machine purchased six years back for Rs. 1,80,000 has been depreciated to a book value of Rs. 1,08,000. It originally had a projected life of 15 years (Salvage nil). There is a proposal to replace this machine. A new machine will cost Rs. 2,50,000 and result in reduction of operating cost by Rs. 30,000 p.a. for next nine years. The existing machine can now be scrapped away for Rs. 60,000. The new machine will also be depreciated over 9 years period as per straight line method with salvage of 25,000. Find out whether the existing machine be replaced or not given that the tax rate applicable is 30% and cost of capital 10% (profit or loss on sale of assets is to be ignored for tax purposes).

Solution

Initial outflow = Cost of new machine – Salvage value of existing machine

= Rs. 2,50,000 – Rs.60,000 = Rs.1,90,000

Depreciation on new machine = (Cost of machine – Salvage value)/ estimated life = (Rs.2,50,000- Rs.25,000) /9 = Rs.25,000

Depreciation on old machine = Rs.1,80,000/15 or Rs.1,08,000/9 = Rs.12,000

Incremental Depreciation = Depreciation on new machine – Depreciation on old machine

= Rs.25,000 – Rs.12,000 = Rs.13,000

Annual incremental Cash inflow calculation

Since, NPV is negative, hence old machine should be kept and replacement decision should not be opted.

17. RBL Ltd. has a machine having an additional life of 5 years which costs Rs. 10,00,000 and has a book value of Rs. 4,00,000. A new machine costing Rs.20,00,000 is available. Though its capacity is the same as that of the old machine, it will mean a saving inn variable costs to the extent of Rs. 7,00,000 per annum. The life of the machine will be 5 years at the end of which it will have a scrap value of Rs. 2,00,000. The rate of income-tax is 40% and P. Ltd.’s policy is not to make an investment if the yield is less than 12% per annum. The old machine, if sold today, will realize Rs. 1,00,000; it will have no salvage value if sold at the end of 5th year. Advise P. Ltd. whether or not the old machine should be replaced. Capital gain is tax free.. Will it make any difference, if the additional depreciation (on new machine) and loss on sale of old machine is also subject to same tax at the rate of 30%, and the scrap value of the new machine is Rs. 3, 00,000.

Solution

Case I: Ignoring income-tax saving on additional depreciation as well as on loss due to sale of existing machine:

Initial Cash outflow = Cost of new machine – Scrap value of old machine

= Rs.20,00,000 – Rs.1,00,000 = Rs.19,00,000

Annual cash inflow

Case II: if the additional depreciation (on new machine) and loss on sale of old machine is also subject to same tax at the rate of 30%, and the scrap value of the new machine is Rs. 3, 00,000.

Incremental Depreciation = Depreciation on new machine – Depreciation on old machine

= (Rs.20,00,000 – Rs.3,00,000)/5 – Rs.4,00,000/5= Rs. 2,60,000

Cash outflow = Cost of new machine – salvage value of old machine – Tax saving on capital loss on sale of old machine

= Rs.20,00,000 – Rs.1,00,000 – Rs. 90,000 (30 % of Rs.4,00,000 – Rs.1,00,000) = Rs.18,10,000

18. XYZ Ltd. is considering the purchase of a new computer system for its Research and Development Division, which would cost Rs. 35,00,000. The operation and maintenance costs (excluding depreciation) are expected to be Rs. 7 lacs per annum. It is estimated that the useful life of the system would be 6 years, at the end of which the disposal value is expected to be Rs. 1,00,000. The tangible benefits expected from the system in the form of reduction in design and draftsmanship costs would be Rs.12,00,000 per annum. Besides, the disposal of used drawing office equipment and furniture, initially, is anticipated to net Rs. 10,00,000. Capital expenditure in research and development would attract 100 % write-off for tax purposes. The gains arising on disposal of used assets may be considered tax-free. If company’s effective tax rate is 40%. The average cost of capital to the company is 12%. After appropriate analysis of cash flows, please advise the company of the financial viability of the proposal.

Solution

Cash outflow = Cost of new computer – Disposal of used drawing office

= Rs.35,00,000 – Rs.10,00,000 = Rs.25,00,000

Annual cash inflow calculation

Calculation of Present value of annual cash flow and NPV

19. Central Gas Ltd. is considering enhancing its production capacity. The following two mutually exclusive proposals are being considered

Life of the Project is 10 years. Sales promotion expenses of Proposal l are required to be incurred at the end of 2nd year? These expenses have not been considered to find out the Annual earnings (given above). Which proposal be accepted given that the cost of capital of the firm is 10%. Ignore taxation.

Solution

In this case, the Annual earnings before depreciation are given for the proposals. As the tax is to be ignored, these earning may be considered as cash flows also. (It may be noted that there is no tax benefit of depreciation in this case). The two proposals may be evaluated as follows:

20. ABC Ltd. is in the business of manufacturing coir mattresses. It has a plant on a piece of land measuring two acres which was purchased ten years ago for Rs. 10 lacs. The firm is now planning to set up another plant on the same land. 50% of the existing plot is to be earmarked for this purpose. The accountant has supplied the following information:

Capital Expenditure for setting up new plant (incurred in the beginning of the year):

Year 1:

Cost of land Rs. 5,00,000

Land Development Rs.  17,00,000

Payment for purchase of Machine Rs.18,00,000

Year 2:

Final payment for Land Development Rs. 13,00,000

Final payment to Machine supplier Rs. 67,00,000

The Plant has an estimated useful life of 5 years and company follows SL method of depreciation. The information regarding sales and operational expenses is as follows:

During first year and last year, all sales will be cash sales. In others, 10% of sales will be on credit for a period of one year. If the company’s rate of discount is 15% and the tax rate is 30% should the above proposal be accepted, given that payment for Land Development does not quality for tax rebate.

Solution

Calculation of PV of cash outflows

Change in Working Capital arising out of credit sales:

In First year 100 % cash sales  – So No change in Working capital.

Year 2: 10 % of sales Rs. 30,00,000 is on credit, hence Rs. 3,00,000 has been subtracted

Year 3 : Previous year credit sales received Rs. 3,00,000

Current Year Credit sales = 10 % of Rs. 35,00,000 = Rs. 3,50,000

Hence change in working capital = Rs. 3,00,000 – Rs. 3,50,000 = (Rs.50,000)

Year 4: Previous year credit sales received Rs. 3,50,000

Current Year Credit sales = 10 % of Rs. 40,00,000 = Rs. 4,00,000

Hence change in working capital = Rs. 3,50,000 – Rs. 4,00,000 = (Rs.50,000)

Year 5: Previous year credit sales received Rs. 4,00,000

Current Year 100% sales is on cash, so no credit sales and debtor exist and an extra of Rs.4,00,000 received of previous year. Hence change in working capital = Rs.4,00,000 – Rs.0 = Rs.4,00,000.

Cash Inflow calculation along with NPV

21. The Income Statement of X Ltd. for the current year is as follows

The Plant Manager proposes to replace an existing machine by another machine costing Rs. 2,40,000. The new machine will have 8 years life having no salvage value. It is estimated that new machine will reduce the labour costs by Rs. 50,000 per year. The old machine will realize Rs. 40,000. Income statement does not include the depreciation on old machine (the one that is going to be replaced) as the same had been fully depreciated for tax purposes last year though it will still continue to function, if not replaced, for a few years more. It is believed that there will be no change in other expenses and revenue of the firm due to his replacement. The company requires a “After-Tax Return of 10%. The rate of tax applicable to company’s income is 30%. Should the company buy the new machine, assuming that the company follows straight line method of depreciation?

Solution

Initial Cash Outflow

Cost of new Machine – Salvage value of existing machine + Tax on gain of sale of existing machine

= Rs.2,40,000 – Rs.40,000  + Rs.12,000 = Rs.2,12,000.

Profit on sale of existing Machine = Salvage value – Book value = Rs.40,000 – Re. 0 = Rs.40,000

Tax on gain on sale of existing machine = 30 % of Rs.40,000 = Rs.12,000.

Calculation of Annual incremental Cash inflow

22. Strong Enterprises Ltd. is a manufacturer of high quality running shoes. Mr. RBL, President, is considering the company’s ordering, inventory and billing procedures. He estimates that the annual savings from computerization include a reduction of ten clerical employees with annual salaries of Rs.  15,000 each, Rs. 18,000 from reduced production delays caused by raw materials inventory problems, Rs.12,000 from lost sales due to inventory stock outs and Rs.10,000 associated with timely billing procedures. The purchase price of the System is 2,00,000 and installation costs are Rs.50,000. These outlays will be capitalised (depreciated) on a straight-line basis to a zero book salvage value which is also its market value at the end of five years. Operation of the new system requires two computer specialists with annual salaries of Rs. 40,000 per person. Also annual maintenance and operating (cash) expenses of Rs.12,000 are estimated to be required. The company’s tax rate is 30% and its required rate of return (cost of capital) for this project is 12%. You are required to

(a) Find the project’s different cash flows.

(b) Evaluate the project using NPV method, PI method, and payback period method.

(c) Find the project’s cash flows and NPV assuming that the system can be sold for Rs. 30,000 at the end of five years even though the book salvage value will be zero and that capital gain is subject to tax.

(d) Find the project’s cash flows and NPV assuming that the book salvage value for depreciation purposes is Rs. 20,000 even though the machine is worthless is terms of its resale value, and that such loss of Rs.20,000 (book value) is allowed for tax purposes.

Solution

a. Initial cash outflow = Cost of system + Installation cost = Rs.2,00,000 + Rs.50,000 = Rs.2,50,000.

Depreciation = (Cost of system + Installation cost) ÷ Project life = Rs.2,50,000/5 = Rs.50,000.

Calculation of subsequent cash inflow

C. Calculation of cash flows in case system can be sold for Rs.30,000 at the end of fifth year

Since, book value of system at the end of fifth year will be nil. Salvage value of Rs.30,000 will be considered as capital gain and tax on capital gain at the rate of 30 % will be deducted from salvage value. Present value of after tax salvage value will be added to current NPV

Salvage value after charging 30 % tax = Rs.30,000 – (Rs.30,000 × 0.3) = Rs.21,000

PV of Post tax salvage value = Rs.21,000 × 0.567 (PVF0.12, 5) = Rs.11,907

New NPV = Rs.48,945 + Rs.11,907 = Rs.60,852.

Since NPV is positive, project should be accepted.

D. Project’s cash flows and NPV assuming that the book salvage value for depreciation purposes is Rs. 20,000 even though the machine is worthless is terms of its resale value, and that such loss of Rs.20,000 (book value) is allowed for tax purposes:

Depreciation = (Cost of system + Installation cost – salvage value) ÷ Project life

= (Rs.2,50,000-Rs.20,000)/5 = Rs.46,000.

23. A company has to make a choice between two identical machines A and B, which have been designed differently but do exactly the same job. Machine A costs Rs. 10,00,000 and will last for 3 years. It will cost Rs. 5,00,000 per year to run. Machine B is an economy model costing only Rs. 8,00,000. But it will last only 2 years. Its running charges are Rs. 3,00,000 per year. Ignore taxes. If the opportunity cost of capital is 9%, which machine the company should buy?

Solution

Since EAv of Machine B is less , hence Machine B should be preferred.

24. ABC Ltd. is evaluating the following two mutually exclusive proposals.

Evaluate the proposals if the discount rate is 12%.

Solution

Calculation of NPV for Project X & Y

In this case, the Project X is giving NPV of Rs.10,698  after 4 years and the Project Y is giving NPV of Rs.14,816 after 7 years. They can be made comparable by finding out the value of equivalent annuity as follows:

Equivalent Annuity amount = NPV/ PVAF r, n

Equivalent Annuity amount of Project X = Rs.10,698 / 3.037 = Rs.3,522

Equivalent Annuity amount of Project Y = Rs.14,816 / 4.564 = Rs.3,246

Company should opt Project X as Equivalent Annuity amount of Project X is more than Project Y.

25. ABC and Co. is considering two mutually exclusive machines X and Y. The company uses a Certainty Equivalent approach to evaluate the proposals. The estimated cash flow and certainty equivalents for both machines are as follows:

Which machine should be accepted, if the risk free discount rate is 5 %.

Solution

26. Determine the Risk Adjusted Net Present Value of the following projects:

The company selects the risk adjusted rate of discount on the basis of coefficient of variation:

Solution

27. Delta Corporation is considering an investment in one of the two mutually exclusive proposals-

Project A: It requires initial outlay of Rs. 1,80,000.

Project B: It requires initial outlay of Rs. 2,00,000.

The Certainty-Equivalent approach is employed in evaluating risky investments. The current yield on treasury bills is 6 % and the company uses this as riskless rate. Expected values of net cash inflows with their respective certainty-equivalents are:

Which project should be accepted? Which project is riskier? If the company was to use the Risk Adjusted Discount rate method, which project would be analyzed with higher rate?

Solution

28. Alpha Engineering company is generating Rs. 1,00,000 units of waste material per annum. The waste material can be processed further and sold at Rs. 1000 per unit and the variable cost of processing comes to 70% of selling price.

Out of the processed waste material, 25% can be refabricated at a cost of Rs. 10 per unit and the refabricated product can be sold at a price of Rs. 1,500 per unit and there is a waste of 20% of processed material at the time of refabrication.

The refabrication procedure requires a capital expenditure of Rs.80,00,000 with a life of  5 years.(Depreciation is chargeable at 25% WDV) and additional working capital of Rs.10,00,000. Evaluate the proposal to refabricate the processed waste material given that:

(i) Required rate of return is 15%.

(ii) Tax rate applicable to company is 30%.

(iii) Expected salvage value of the plant is Rs. 10,00,000.

(iv) There is no other asset in the same block of assets.

Solution

Out the total waste material that is 1,00,000 units, only 25 % i.e. 25,000 units can be processed and refabricated.

Cash outflow = Capital expenditure + additional working capital

= Rs.80,00,000  + Rs.10,00,000 =  Rs.90,00,000

Calculation of subsequent cash inflow

Terminal Cash inflow calculation

Calculation of Depreciation and WDV in the year 5

29. Fin man Construction Company is interested in the computerization of its office work. For this purpose two models have been shortlisted, for which the relevant information is as follows:

Find out which model is better given that

(i) Tax rate is 35%.

(ii) Required rate of return is 13%.

(ii) There is no other asset in the same block of assets.

Solution

Initial cash outflow

Calculation of initial cash inflow