#3 Techniques of Capital Budgeting illustrations with solutions pdf capital budgeting solved problems pdf capital budgeting notes with solved illustrations pdf financial management notes with solved illustrations pdf

    Techniques of Capital Budgeting Part 3 solved questions with solutions

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

Year	Project A Cash flow (Rs.)	Project B Cash flow (Rs.)
0	(1,00,000)	(1,00,000)
1	30,000
2	30,000
3	30,000
4	30,000
5	30,000	1,82,500

 

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 × PVAF_{0.1, 5} – Rs.1,00,000

(Since there is equal cash flow, 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 × PVF_{0.1, 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

PVAF_r,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 NPVfor 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 12 % = =( 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:

Year	Project X (Rs.)	Project Y (Rs.)
0	(1,00,000)	(1,00,000)
1	15,000	45,000
2	18,000	45,000
3	30,000	22,000
4	45,000	10,000
5	60,000	10,000

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

Solution

Calculation of NPV & IRR

Year	Project X (Rs.)	Project Y (Rs.)	PVF @ 10 %	PV of X = PVF × cash flow	PV of Y = PVF × cash flow
0	(1,00,000)	(1,00,000)	1	(1,00,000)	(1,00,000)
1	15,000	45,000	0.909	13,635	40,905
2	18,000	45,000	0.826	14,868	37,170
3	30,000	22,000	0.751	22,530	16,522
4	45,000	10,000	0.683	30,735	6,830
5	60,000	10,000	0.621	37,260	6,210
Total of cash inflows	1,68,000
Total of PV of cash inflows				1,19,028	1,07,637
PV of cash outflow				(1,00,000)	(1,00,000)
NPV = Total of PV of cash inflows - PV of cash outflow				19,028	7,637
Profitability index = PV of cash inflows / PV of cash outflow				1.19028	1.07637

 

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 (PVAF_r,5) = Rs. 1,00,000 / Rs.33,600 = 2.976

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).

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% .

Year	Project X (Rs.)	PVF @ 16 %	PVF @ 15 %	PV of cash inflow @ 15 %	PV of cash inflow @ 16 %
0	(1,00,000)	1	1	(1,00,000)	(1,00,000)
1	15,000	0.87	0.862	13050	12930
2	18,000	0.756	0.743	13608	13374
3	30,000	0.658	0.641	19740	19230
4	45,000	0.572	0.552	25740	24840
5	60,000	0.497	0.476	29820	28560
Total of PV of cash inflows				101958	98934
NPV				1,958	(1,066)

 

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 (PVAF_r,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%

Year	Project Y (Rs.)	PVF @ 14 %	PVF @ 15 %	PV of cash inflow @ 14 %	PV of cash inflow @ 15 %
0	(1,00,000)	1	1	(1,00,000)	(1,00,000)
1	45,000	0.877	0.87	39465	39150
2	45,000	0.769	0.756	34605	34020
3	22,000	0.675	0.658	14850	14476
4	10,000	0.592	0.572	5920	5720
5	10,000	0.519	0.497	5190	4970
Total of PV of cash inflows				100030	98336
NPV				30	1,664

 

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-

Year	1	2	3	4	5	6	7	8	9	10
Cash inflow	8000	8000	8000	10000	10000	15000	8000	10000	8000	5000

 

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

6^th year cash inflow = Rs. 15,000

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

NPV calculation

Year	1	2	3	4	5	6	7	8	9	10
Cash inflow	8000	8000	8000	10000	10000	15000	8000	10000	8000	5000
PVF@ 10%	0.909	0.826	0.751	0.683	0.621	0.564	0.513	0.467	0.424	0.386
PV of cash inflow	7272	6608	6008	6830	6210	8460	4104	4670	3392	1930

 

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 (PVAF_r,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).

Year	1	2	3	4	5	6	7	8	9	10
Cash inflow	8000	8000	8000	10000	10000	15000	8000	10000	8000	5000
PVFat12%	0.893	0.797	0.712	0.636	0.567	0.507	0.452	0.404	0.361	0.322
PV of cash inflow at 12 %	7144	6376	5696	6360	5670	7605	3616	4040	2888	1610
PVF@13%	0.885	0.783	0.693	0.613	0.543	0.48	0.425	0.376	0.333	0.295
PV of cash inflow at 13%	7080	6264	5544	6130	5430	7200	3400	3760	2664	1475

 

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

Year	1	2	3	4	5	6	7	8	9	10
WDV	400000	300000	225000	168750	126563	94922	71191	53394	40045	30034
Depreciation	100000	75000	56250	42188	31641	23730	17798	13348	10011	7508

 

Calculation of PV of Cash inflow

Year	PBDT	less:Dep	PBT	Less:Tax	PAT	Add:Dep	Cash inflow	PVF @20%	PV of cash inflow
1	180000	100000	80000	24000	56000	100000	156000	0.833	129948
2	200000	75000	125000	37500	87500	75000	162500	0.694	112775
3	200000	56250	143750	43125	100625	56250	156875	0.579	90831
4	200000	42188	157813	47344	110469	42188	152656	0.482	73580
5	100000	31641	68359	20508	47852	31641	79492	0.402	31956
6	100000	23730	76270	22881	53389	23730	77119	0.335	25835
7	100000	17798	82202	24661	57542	17798	75339	0.279	21020
8	100000	13348	86652	25995	60656	13348	74005	0.233	17243
9	100000	10011	89989	26997	62992	10011	73003	0.194	14163
10	100000	7508	92492	27748	64744	7508	72252	0.162	11705
10	Working capital released						80000	0.162	12960
10	Scrap value of plant						50000	0.162	8100
						Total of PV of Cash inflow			550115

 

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(PVF_0.2,1) = 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 vear's 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.

Year	1	2	3	4	5	6	7	8	9	10
EBDT	120000	120000	120000	120000	120000	120000	120000	120000	120000	120000
Less: Dep	40,000	36,000	32,000	28,000	24,000	40,000	32,000	24,000	16,000	8,000
EBT	80,000	84,000	88,000	92,000	96,000	80,000	88,000	96,000	104,000	112,000
Less: Tax	24000	25200	26400	27600	28800	24000	26400	28800	31200	33600
PAT	56,000	58,800	61,600	64,400	67,200	56,000	61,600	67,200	72,800	78,400
Add: Dep	40,000	36,000	32,000	28,000	24,000	40,000	32,000	24,000	16,000	8,000
Cash Inflow	96,000	94,800	93,600	92,400	91,200	96,000	93,600	91,200	88,800	86,400
Terminal cash inflow	Salvage value + current asset= Rs.30,000 +  Rs.50,000 = Rs. 80,000									80000
PVF at22%	0.82	0.672	0.551	0.451	0.37	0.303	0.249	0.204	0.167	0.137
PV of cash inflow	78720	63706	51574	41672	33744	29088	23306	18605	14830	11837
PV of Terminal cash inflow										10,960
Total of PV of cash inflow including Terminal value										3,78,041

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

	A	B
Original Investment (Rs.)	20,000	30,000
Estimated life of the Machine  (Years)	4	6
Estimated Savings in Cost (Rs. )	10,000	10,000
Estimated Savings in Wages (Rs.)	6,000	4,000
Additional Cost of Maintenance (Rs.)	5,000	2,000
Additional Cost of Supervision (Rs.)	3,000	2,000

 

Solution:

	A
Estimated Savings in Cost (Rs. )	10,000	10,000
Estimated Savings in Wages (Rs.)	6,000	4,000
Less: Additional Cost of Maintenance (Rs.)	(5,000)	(2,000)
Less: Additional Cost of Supervision (Rs.)	3,000)	(2,000)
Net cash inflow	8,000	10,000
Payback period	20,000/8,000 = 2.5 years	30,000/10,000= 3 years
Project A should be opted

 

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

	Project A	Project B
Project Cost (Rs.)	6,00,000	8,00,000
Annual Cash Expenses (Rs.)	1,00,000	1,30,000
Life (Years)	10 years	10 years
Salvage Value (Rs.)	1,00,000	1,00,000

 

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

	Project A	Project B	B over A
Initial Cost	(600000)	(800000)	-200000
Annual Expenses	(100000)	(130000)	(30000)
Depreciation P.a.	(50000)	70000	20000
Annual deductible expenses (Annual Expenses + Depreciation P.a.)	(150000)	(200000)	(50000)
Annual tax saving @40 %	60000	80000	20000
Net outflow (annual deductible Expense - Tax saving  )	(90000)	(120000)	(30000)
Terminal inflow (salvage value)	100000	100000	0
Calculation of NPV
PV of Annual outflows	90000 * 5.65 = (5,08,500)	120000* 5.65 = (6,78,000)	(169500)
Initial Cost /outflow	(600000)	(800000)	(200000)
Total outflows (PV) = PV of Annual outflows +Initial Cost /outflow	(1108500)	(1478000)	(369500)
Less PV of salvage (100000*0.322)	32200	32200	0
NET Present Value	1076300)	(1445800)	(369500)

 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

Year	Units Sold
1	10,000
2	13,000
3	16,000
4	10,000
5	6,000

 

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

Particulars	Year 1	Year 2	Year 3	Year 4	Year 5
Sales (Units)	10,000	13,000	16,000	10,000	6,000
Selling Price /unit )	500	500	500	500	500
Sales	50,00,000	65,00,000	80,00,000	50,00,000	22,80,000
Less: Variable Cost at Rs. 260	(26,00,000)	(33,80,000)	(41,60,000)	(26,00,000)	(15,60,000)
PBDT	24,00,000	31,20,000	38,40,000	24,00,000	7,20,000
Less: Depreciation	(4,24,000)	(4,24,000)	(4,24,000)	(4,24,000)	(4,24,000)
PBT	19,76,000	26,96000	34,16,000	19,76,000	2,96,000
Less: Tax @ 30 %	(5,92800)	(8,08,800)	(10,24,800)	(5,92,800)	(88,800)
PAT	13,73,200	18,87200	23,91,200	13,83,200	2,07200
Add: Depreciation	4,24,000	4,24,000	4,24,000	4,24,000	4,24,000
Operating Cash inflow (1)	17,97,200	23,11,200	28,15,200	18,07,200	6,31200
WC requirement for N+1 year	6,50,000	8,00,000	5,00,000	2,28,000	-----
Change in WC (2)	1,50,000(6,50,000-5,00,000)	1,50,000	(3,00,000)	(2,72,000)	(2,28,000)
Release of WC in year 5 (3)					80,000
Net cash flow (1-2+3)	16,47,200	21,61200	31,15,200	20,79,200	9,39,200
PVF at 15%	.870	.756	.658	.572	.497
PV of cash inflow	14,33,064	16,33,867	20,49,802	11,89,302	4,66,782

 

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

	Year 1	Year 2	Year 3	Year 4	Year 5
Net Profit	10,000	10,000	10,000	10,000	10,000
Add: Residual Value					2,000
Less: Tax @ 40% of preceding year profit		(4,000)	(4,000)	(4,000)	(4,800)
Add: Depreciation	8,000	8,000	8,000	8,000
Add: Working capital recovered					14,000
Cash inflow	18,000	14,000	14,000	16,000	9,200
PVF @ 10%	0.909	.826	.751	.683	.621
PV	16,362	11,564,	10,514	10,928	5,713
Total PV of cash inflow					55,081
Less: Initial cash outflow					(44,180)
NPV					10,901

 

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

	Rs.
Annual benefits (PBDT)	60,000
Less: Incremental Depreciation (Rs.28,000 – Rs.6,000) [Dep on new machine – Dep on old machine]	(22,000)
Incremental Profit before Tax	38,000
Less: Tax @ 40 %	(15,200)
Incremental Profit after Tax	22,800
Add: Incremental Depreciation	22,000
Incremental cash inflows	44,800
Terminal inflow at the end of the year of Project	18,000

 

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

Particulars	Rs.
Decrease in operating cost (PBDT)	30,000
Less: Incremental Depreciation	(13,000)
Incremental PBT	17,000
Less: Tax @ 30%	(5,100)
Incremental PAT	11,900
Add: Incremental Depreciation	13,000
Incremental Annual cash inflow	24,900
Terminal cash inflow (Salvage value )	25,000
PV of Incremental Annual cash inflow = 24,900 ×5.758 (PVAF.1, 9)	1,43,374
PV of terminal cash inflow = 25,000 × 0.424 (PVF0.1, 9)	10,600
Total Present value of inflow = 1,43,374 + 10,600	1,53,974
NPV = Total Present value of inflow - Initial outflow = 1,53,974 – 1,90,000	(36,026)

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 : 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

Net saving in variable cost	7,00,000
Less: Tax at 30%	(2,10,000)
Net benefit / Annual cash inflow	4,90,000
Terminal cash inflow at the end of year 5 (Salvage value of new machine)	2,00,000
PV of cash inflow: Annual cash inflow × PVAF0.12, 5 = 4,90,000 × 3.605 = 17,66,450 Terminal cash inflow × PVF0.12, 5 = 2,00,000 × 0.567 = 1,13,400 Total of PV of Cash Inflow =	18,79,850
Less: PV of cash outflow	(19,00,000)
NPV	(20,150)
Since NPV is negative, there is no need to replace existing machine.

 

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

Net saving in variable cost (PBDT)	7,00,000
Less: Incremental depreciation	(2,60,000)
Incremental PBT	4,40,000
Less: Tax at 30%	(1,32,000)
Incremental PAT	3,08,000
Add: Incremental Depreciation	2,60,000
Incremental annual cash inflow	5,68,000
Terminal cash inflow at the end of year 5 (Salvage value of new machine)	3,00,000
PV of cash inflow: Annual cash inflow × PVAF0.12, 5 = 5,68,000 × 3.605 = 20,47,640 Terminal cash inflow × PVF0.12, 5 = 3,00,000 × 0.567 = 1,70,100 Total of PV of Cash Inflow =	22,17,740
Less: PV of cash outflow	(18,10,000)
NPV	4,07,740
Since NPV is positive, company should replace existing machine

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

Particulars	Rs.
Saving in Design and draftsmanship cost	12,00,000
Less : Operation and maintenance cost	(7,00,000)
PBT	5,00,000
Less: Tax @ 40 %	(2,00,000)
PAT/ Annual cash inflow	3,00,000
Tax saving on purchase of computer system to be available at the end of year 1 =35,00,000 × 0.4	14,00,000
Terminal value (Disposal/salvage value)	1,00,000

 

Calculation of Present value of annual cash flow and NPV

Year	Cash flow	PVF at 12%	PV
0	(25,00,000)	1	(25,00,000)
1	3,00,000 + 14,00,000(Tax saving) = 17,00,000	0.893	15,18,100
2	3,00,000	0.797	2,39,100
3	3,00,000	0.712	2,13,600
4	3,00,000	0.636	1,90,800
5	3,00,000	0.567	1,70,100
6	3,00,000 + 1,00,000 (Terminal value) = 4,00,000	0.507	2,02,800
	NPV		34,500
Since NPV is positive, hence project should be opted.

 

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

	Proposal I	Proposal II
Plant	2,00,000	3,00,000
Building	50,000	1,00,000
Installation cost	10,000	15,000
Working capital required	50,000	65,000
Annual Earnings (before depreciation)	70,000	95,000
Sales Promotion expenses	------------	15,000
Scrap Value of Plant	10,000	15,000
Disposable Value of Building	30,000	60,000

 

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:

	Proposal I	Proposal II
Initial cash outflow: Cost of Plant Add: Installation cost Add: Cost of Building Add: WC required	2,00,000 10,000 50,000 50,000	3,00,000 15,000 1,00,000 65,000
Total Initial cash outflow (I)	3,10,000	4,80,000
Annual cash inflow Profit before Depreciation PVAF0.1, 10 PV (Profit before Depreciation × PVAF0.1, 10) Less: Present value of sales promotion expenses 15,000 ×0.826 (PVF0.1, 2)	70,000 6.145 4,30,150	95,000 6.145 5,83,775 (12,390)
Total of Present value Annual cash inflow (II)	4,30,150	5,71,385
Terminal value Working capital released Sale value of plant Disposable value of building Total Terminal value PVF0.1, 10	50,000 10,000 30,000 90,000 0.386	65,000 15,000 60,000 1,40,000 0.386
Total of Present value of Terminal value (III)	34,740	54,040
NPV = II + III - I	1,54,890	1,45,425
Since NPV of Project I has higher NPV than Project II. Hence Project I should be accepted.

 

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:

Year	1	2	3	4	5
Sales (Rs.)	25 Lakh	30 Lakh	35 Lakh	40 Lakh	45 Lakh
Expenses (Rs.)	5 Lakh	7 Lakh	10 Lakh	12 Lakh	15 Lakh

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

Outflow in the beginning of the year
Land development	17,00,000
Payment for machinery	18,00,000
	35,00,000
Outflow in the beginning of year 2
Final payment for land development	13,00,000
Final Payment for Machine	67,00,000
	80,00,000
PV of outflow in the beginning of year 2 or at the end of year 1 80,00,000 × .870 (PVF0.15, 1) =	69,60,000
Total Cash outflow = 35,00,000 + 69,60,000	1,04,60,000

 

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

Particulars	Year 1	Year 2	Year 3	Year 4	Year 5
Sales	2500000	3000000	3500000	4000000	4500000
Less: Expenses	(500000)	(700000)	(1000000)	(1200000)	(1500000)
Less: Depreciation	(1800000)	(1800000)	(1800000)	(1800000)	(1800000)
PBT	200000	500000	700000	1000000	1200000
Less Tax @ 30 %	(60000)	(150000)	(210000)	(300000)	(360000)
PAT	140000	350000	490000	700000	840000
Add: Depreciation	1800000	1800000	1800000	1800000	1800000
Change in WC		(300000)	(50000)	(50000)	400000
Cash Flow	1940000	1850000	2240000	2450000	3040000
PVF at 15 %	0.87	0.756	0.658	0.572	0.497
PV of cash inflow	1687800	1398600	1473920	1401400	1510880
Total PV of Cash Inflow					74,72,600
Total PV of Cash Outflow					(1,04,60,000)
NPV					(29,87,400)
Since NPV is negative, hence the project should not be opted.

 

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

Particulars	Rs.
Sales	7,00,000
Less: Cost of Material Labour Other operating cost Depreciation	(2,00,000) (2,50,000) (2,50,000) (80,000)
EBIT	1,00,000
Less: Tax @ 30 %	(30,000)
Profit after Tax	70,000

 

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

Particulars	Rs.
Saving in Labour expenses	50,000
Less: Depreciation on new Machine	(30,000)
Incremental PBT	20,000
Less: Tax @ 30 %	(6,000)
PAT	14,000
Add: Depreciation	30,000
Incremental Cash inflow	44,000
PVAF0.1, 8	5.335
PV of incremental cash inflow	2,34,740
Less: PV of cash outflow	(2,12,000)
NPV	22,740
Since NPV is positive, hence replacement of machine should be opted.

 

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

Particulars	Rs.
Saving due to installation of new system
Savings due to Reduction in clerk salaries	1,50,000
Savings due to reduction in production delays	18,000
Savings due to reduction in lost sales	12,000
Gains due to timely billing	10,000
Total savings	1,90,000
Less: additional specialists cost	(70,000)
Less: Maintenance cost	(20,000)
PBDT	1,00,000
Less: Depreciation	(50,000)
PBT	50,000
Less: Tax @ 30 %	(15,000)
PAT	35,000
Add: Depreciation	50,000
Annual Cash inflow	85,000
PVAF.12, 5	3.517
PV of cash inflow	2,98,945
PV of cash outflow	(2,50,000)
B. NPV = PV of cash inflow - PV of cash outflow	48,945
Profitability Index = PV of cash inflow / PV of cash outflow	1.2
Payback period = PV of cash outflow / Annual cash inflow = 2,50,000 /85,000	2.94 years
Since NPV is positive and PI is greater than 1, hence project should be accepted.

 

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 (PVF_{0.12, 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.

Particulars	Rs.
Saving due to installation of new system	1,50,000
Savings due to Reduction in clerk salaries	18,000
Savings due to reduction in production delays	12,000
Savings due to reduction in lost sales	10,000
Total savings	1,90,000
Less: additional specialists cost	(70,000)
Less: Maintenance cost	(20,000)
PBDT	1,00,000
Less: Depreciation	(46,000)
PBT	54,000
Less: Tax @ 30 %	(16,200)
PAT	37,800
Add: Depreciation	50,000
Annual Cash inflow	87,800
PVAF.12, 5	3.517
PV of cash inflow	3,08,792
Terminal value arising due to tax saving on loss of asset as it will not realize any value though salvage is 20,000 = 30 % of Rs.20,000	6,000
PV of terminal value = (PVF0.12, 5) 0.567 × 6,000	3,402
Total PV of cash inflow = PV of terminal value + PV of cash inflow	3,12,194
PV of cash outflow	(2,50,000)
NPV = PV of cash inflow - PV of cash outflow	62,194

 

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

	Machine A	Machine B
Cost	10,00,000	8,00,000
Estimated life	3 years	2 years
PV of annual cost	Rs.5,00,000 × PVAF0.09, 3 = Rs.5,00,000 ×2.531 = Rs.12,65,500	Rs.3,00,000 × PVAF0.09, 2 = Rs.3,00,000 × 1.759 = Rs.5,27,700
	Rs.22,65,500	Rs.13,27,700
PVAF0.09, n	2.531	1.759
Equivalent Annuity value (EAV)	Rs.22,65,500/2.531 = Rs.8,95,100	Rs.13,27,700/1.759 = 7,54,804

 

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

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

	Project X	Project Y
Outlay	35,000	55,000
Annual net inflow	14,000	15,000
Life	4 years	7 years
Scrap value	5,000	3,000

 

Evaluate the proposals if the discount rate is 12%.

Solution

Calculation of NPV for Project X & Y

Particulars	X	Y
Annual Cash inflow	14,000	15,000
PVAF0.12, 4 PVAF0.12,, 7	3.037	4.564
PV of cash inflow X = (Annual Cash inflow × PVAF0.12, 4) Y =(Annual Cash inflow × PVAF0.12, 7)	42,518	68,460
Terminal value (Salvage value)	5,000	3,000
PVF0.12, 4 PVF0.12, 4	0.636	0.452
PV of Terminal value X = (Annual Cash inflow × PVF0.12, 4) Y =(Annual Cash inflow × PVF0.12, 7)	3,180	1,356
Total PV of cash inflow = PV of cash inflow + PV of Terminal value	45,698	69,816
PV of cash outflow	(35,000)	(55,000)
NPV	10,698	14,816

 

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 :

	Machine X		Machine Y
Year	Cash flow	Certainty equivalent	Cash flow	Certainty equivalent
0	(30,000)	1.00	(40,000)	1.00
1	15,000	.95	25,000	.9
2	15,000	.85	20,000	.8
3	10,000	.70	15,000	.7
4	10,000	.65	10,000	.6

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

Solution

Yr	Machine X					Machine Y
	Cash flow (A)	Certainty equivalent (B)	Certain cash flow (A ×B)	PVF@6%	PV	Cash flow (A)	Certainty equivalent (B)	Certain cash flow (A×B)	PV = PVF@6% × Certain cash flow
0	(30,000)	1.00	(30,000)	1	(30,000)	(40,000)	1.00	(40,000)	(40,000)
1	15,000	.95	14,250	.943	13,438	25,000	.9	22,500	21,218
2	15,000	.85	12,750	.890	11,348	20,000	.8	16,000	14,240
3	10,000	.70	7,000	.840	5,880	15,000	.7	10,500	8,820
4	10,000	.65	6,500	.792	5,148	10,000	.6	6,000	4,752
NPV =Total of  PV of cash inflow- PV of Cash outflow					5,724				9,030
Since NPV of Machine Y is more than Machine X. Hence Machine Y should be accepted

 

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

	A	B	C
Net cash outlay	(1,10,000)	(1,30,000)	(2,20,000)
Project Life	5 years	5 years	5 years
Annual cash inflow	32,000	43,000	71,000
Coefficient of Variation	0.4	0.8	1.2

 

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

Coefficient of variation	Risk adjusted rate of discount	Payment value factor 1 to 5 years at Risk adjusted rate of discount
0.0	10%	3.791
0.4	12%	3.605
0.8	14%	3.433
1.2	16%	3.274
1.6	18%	3.127
2.0	22%	2.864
More than 2.0	25%	2.689

 

Solution

	Project A	Project B	Project C
Net cash outflow	(1,10,000)	(1,30,000)	(2,20,000)
Coefficient of Variation (COV)	0.4	0.8	1.2
Risk adjusted discounted rate as per COV	12%	14%	16%
PVAF r, 5 as per Risk adjusted discounted rate	3.605	3.433	3.274
Annual Cash Inflow	32,000	43,000	71,000
PV of cash inflow = Annual Cash Inflow × PVAF r, 5 as per Risk adjusted discounted rate	1,15,360	1,47,619	2,32,454
NPV = PV of cash inflow - Net cash outflow	5,360	17,619	12,454

 

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:

Year	Project A		Project B
	Cash inflow	Certainty equivalent	Cash inflows	Certainty equivalent
1	95,000	.8	95,000	.9
2	1,10,000	.7	95,000	.8
3	1,10,000	.5	1,10,000	.6

 

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

Yr	Project A					Project B
	Cash flow (A)	Certainty equivalent (B)	Certain cash flow (A ×B)	PVF@6%	PV	Cash flow (A)	Certainty equivalent (B)	Certain cash flow (A×B)	PV = PVF@6% × Certain cash flow
0	(1,80,00)	1.00	(1,80,000)	1	(1,80,000)	(1,65,000)	1.00	(1,65,000)	(1,65,000)
1	95,000	.8	76,000	.943	71,668	95,000	.9	85,500	80,627
2	1,10,000	.7	77,000	.890	68,530	95,000	.8	76,000	84,550
3	1,10,000	.5	55,000	.840	46,200	1,10,000	.6	66,000	55,440
NPV =Total of  PV of cash inflow- PV of Cash outflow					6,398				20,617
Since NPV of Project B is more than Project A. Hence Project B should be accepted. Project A is riskier because its certainty equivalent is lower. Project A being more risky, it would be analyzed with higher discount rate.

 

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

	Year 1	Year 2	Year 3	Year 4	Year 5
Refabricated units (25,000 – 20 % of 25,000)	20,000	20,000	20,000	20,000	20,000
Sales after refabrication at Rs.1500/unit × 20,000	3,00,00,000	3,00,00,000	3,00,00,000	3,00,00,000	3,00,00,000
Less: Loss of Sales before refabrication (25,000 ×1,000)	(2,50,00,000)	(2,50,00,000)	(2,50,00,000)	(2,50,00,000)	(2,50,00,000)
Incremental Sales	50,00,000	50,00,000	50,00,000	50,00,000	50,00,000
Less: Refabrication cost(25,000 × 100)	(25,00,000)	(25,00,000)	(25,00,000)	(25,00,000)	(25,00,000)
Incremental PBDT	25,00,000	25,00,000	25,00,000	25,00,000	25,00,000
Less: Depreciation at 25% WDV	(20,00,000)	(15,00,000)	(11,25,000)	(8,43,750)	________
Incremental Profit before Tax	5,00,000	10,00,000	13,75,000	16,56,250	25,00,000
Less: Tax at 30%	(1,50,000)	(3,00,000)	(4,12,500)	(4,96,875)	(7,50,000)
Incremental PAT	3,50,000	7,00,000	9,62,500	11,59,375	17,50,000
Add: Depreciation	20,00,000	15,00,000	11,25,000	8,43,750
Incremental Cash inflow	23,50,000	22,00,000	20,87,500	20,03,125	17,50,000
Terminal cash inflow					24,59,375
PVF at 12 %	0.893	0.797	0.712	0.636	0.567
PV of cash inflow	20,98,550	17,53,400	14,86,300	12,73,988	23,86,715
Total PV of cash inflow					89,98,953
PV of cash outflow					90,00,000
NPV					1,047
Since NPV is negative, hence project should not be accepted.
As there is no other asset in the same block of assets, no depreciation will be charged in the last year.

 

Terminal Cash inflow calculation

Tax shield on short term capital loss
WDV of asset	25,31,250
Less: Salvage value	(10,00,000)
	15,31,250
Tax saving at 30 % = 0.3 × 15,31,250 (a)	4,59,375
Salvage value (b)	10,00,000
Release of working capital (c)	10,00,000
Total Terminal Value (a+b+c)	24,59,375

 

Calculation of Depreciation and WDV in the year 5

	Year 1	Year 2	Year 3	Year 4	Year 5
Book Value	80,00,000	60,00,000	45,00,000	33,75,000	25,31,250
Depreciation	20,00,000	15,00,000	11,25,000	8,43,750