SOLUTIONS TO ASSIGNMENT PROBLEMS - …mastermindsindia.com/2.Capital Budgeting2806.pdf · IPCC_33e_F.M_ Capital Budgeting_Assignment Solutions _____1 No.1 for CA/CWA & MEC/CEC MASTER

IPCC_33e_F.M_ Capital Budgeting_Assignment Solutions ________________1

No.1 for CA/CWA & MEC/CEC MASTER MINDS

2. CAPITAL BUDGETING

SOLUTIONS TO ASSIGNMENT PROBLEMS

Problem No.1

Payback reciprocal = %20000,20

100X000,4 =

The above payback reciprocal provides a reasonable approximation of the internal rate of return, i.e. 19%.

Problem No.2 W.N.-1: Calculation of depreciation per annum

Depreciation p.a. =

Life

ValueScrap - Cost

510,00080,000 −= = Rs.14,000 p.a.

W.N.-2: Calculation of PAT p.a.

Year PBDT Depreciation PBT / PAT (PBDT – Dep.)

1 20,000 14,000 6,000

2 40,000 14,000 26,000

3 30,000 14,000 16,000

4 15,000 14,000 1,000

5 5,000 14,000 (9,000) Since Income tax rate is not given in the problem, PBT = PAT.

Calculation of ARR

Step-1: Calculation of Average Profit after Tax

Average Profit after tax=5

000,9000,10000,16000,26000,6 −+++ = Rs. 8,000 p.a

Step-2: Calculation of Average Investment

Average investment = (21

Initial Cost - Salvage Value) + Salvage Value

= (21

80,000 - 10,000) + 10,000 = Rs.45,000

Step-3: Calculation of Accounting Rate of Return (ARR) (Return on Avg. Capital Employed)

ARR = 45,0008,000

x100investmentAverage

AveragePAT = = 17.77%

Step-4: Return on Original Capital employed

Return on Original Capital employed = x100InvestmentOrginal

PATAverage= 100x

000,80000,8

= 10%


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Problem No.3

W.N. 1: Calculation of depreciation per annum

Depreciation p.a. =

Life

ValueScrap - Cost =

50000,80 −

= Rs.16,000 p.a.

Calculation of NPV using Incremental approach Step-1: Calculation of Present Value of Cash Outflows:

Particulars Amount

Investment in new equipment 80,000

Additional working capital 1,50,000

Total 2,30,000

Step-2: Calculation of Present Value of Operating Cash Inflows:

Particulars Amount Rs. Amount Rs.

Incremental net cash in flow Less: additional wages Depreciation(w.n.1) Incremental PBT Less: Tax @ 40 % Incremental PAT Add: depreciation Incremental CFAT p.a

40,000 16,000

1,00,000

56,000 44,000 17,600 26,400 16,000 42,400

Therefore, Present Value of Operating Cash Inflows = 42,000 X PVAF(13%,5)

= 42,400 X 3.517

= 1,49,120 Step 3: Present Value of Terminal Cash Inflows =

Gsp or Nsp on sale of initial equipment = 0

Recovery of additional working capital = 1,50,000 1,50,000

PV there off = 1,50,000 * PVF (13%, 5)

= 1,50,000 X 0.543

= 81,450 Step 4: Calculation of NPV

NPV = PV of cash inflows – PV of cash outflows

= PV of Operating Cash Inflows +PV of Terminal Cash Inflows – PV of cash outflows.

= 1,49,120 + 81,450-2,30,000

= Rs.570 Conclusion: Since NPV is positive it is advisable to accept.

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To MASTER MINDS, Guntur



Problem No.4 W.N – 1: Calculation of depreciation p.a. (Rs. in Lakhs)

Depreciation p.a. =

Life

ValueScrap - Cost=

80140 −

= Rs. 17.5 lakhs p.a.

On supplementary equipment =6

110 − = 1.5 lakhs pa

Calculation of NPV using Incremental approach

Step-1: Calculation of Present Value of Cash Outflows:

Particulars Amount Cost of initial equipment Cost of additional working capital Less: tax free subsidy from government Add: cost of supplementary equipment - 10 Present value there off - 10* pvf ( 12% , 2 ) - 10* 0.797 Present value of cash out flows

140 15

155 20

135

7.97 142.97

Step-2: Calculation of Present Value of Operating Cash Inflows

Selling price per unit = 100

Less: - variable cost @ 40% = 40

Contribution per unit = 60

Particulars Y1 Y2 Y3 to 5 Y6 to 8

a. Sales volume (lakhs of unit) 0.8 1.2 3.0 2.0 b. Total contribution ( a * Rs. 60 per unit) 48 72 180 120 c. Fixed cost 16 16 16 16 d. Advertisement cost 30 15 10 4 e. Depreciation (WN – 1) 17.5 17.5 19(17.5+1.5) 19 f. PBF (b-c-d-e) (loss) (15.5) 23.5 135 81 g. Tax @ 50% (7.75) 11.75 67.5 40.5 h. PAT (f-g) (7.75) 11.75 67.5 40.5 i. CFAT (h+e) 9.75 29.25 86.5 59.5 j. PVF @ 12 % 0.893 0.797 1.915 1.363 k. Present value 8.706 23.31 165.64 278.765

Therefore, Present Value of Operating Cash Inflows = Rs.278.765 Present value factor for years 3 to 5 = PVF (12% , 3) + PVF (12%, 4) + PVF (12%, 5)

= 0.712+0.636+0.567

= 1.915

(or)

PVAF (12%, 5) - PVAF (12%, 2)

= 3.605 - 1.690

= 1.915





Present value factor for years 6 to 8 = PVF ( 12% , 6) + PVF (12%, 7) + PVF (12%, 8)

= 0.507+0.452+0.404

= 1.363

(or)

PVAF(12% , 8) - PVAF (12%, 5)

= 4.968 - 3.605

= 1.363 Step-3: Present Value of Terminal Cash Inflows =

Gsp or Nsp on sale of initial equipment - 0

Gsp or Nsp on sale of supplementary equipment - 1

Recovery of working capital - 15

16 Pv there off = 16 * PVF (12%, 8)

= 16 * 0.404

= 6.464 Step-4: Calculation of NPV



= 278 + 65 – 6.464 = Rs. 142.97 Conclusion: Since NPV is positive it is advisable to accept the project. Note: It is given that the company has other profitable businesses and the loss from one business can be set off against profit of other business. Alternatively it can also be assumed that the loss is carried forward and setoff against future profit.

Problem No.5

Calculation of NPV

a.

Step 1: Calculation of Present Value of Cash Outflows:

Particulars Amount Cost of machinery 4,00,000

Present Value of Cash Outflows 4,00,000

Step 2: Calculation of Present Value of Operating Cash Inflows:

Particulars Amount

a. Sales volume b. Contribution per unit (10-6) c. Total contribution (axb) d. Fixed cost e. CFAT (c-d)

40,000 units Rs.4

1,60,000 20,000

1,40,000 p.a

PV thereof = 1,40,000 X PVAF(15%,6)

= 1,40,000 X 3.784 = 5,29,760





Step-3: Present Value of Terminal Cash Inflows

G.S.P/N.S.P on sale of machinery = 20,000

PV thereof = 20,000 X PVF(15%,6)

= 20,000 X 0.432

= 8,640

Step-4: Calculation of NPV



= 5,29,760+8,640-4,00,000

= 1,38,400

Conclusion: Since NPV is positive it is advisable to accept the project. b. Let, x represents the sale volume required to justify the project. The project is acceptable if NPV is

at least equal to zero Step-1: same as above – 4,00,000. Step-2: present value of operating cash inflows

Particulars Amount (Rs.)

a. Sales volume X unit

b. Contribution per unit (10 – 6) 4

c. Total contribution 4X

d. Fixed cost 20,000

e. CFAT (c-d) 4X-20,000 Present value there of = (4X – 20,000) * PVAF (15%, 6 years)

= (4X – 20,000) *3.784 Step-3: same as above – 8,640 Step-4: Finding the value of X Since NPV is ‘0’ then present value of cash inflows = present value of cash outflows present value of operating cash inflows + present value of terminal cash inflows = present value of cash out flows

(4X – 20,000) * 3.784 + 8,640 = 4,00,000

(4X – 20,000) = 1,03,424

4X = 1,23,424

X = 30,856 units pa

Problem No.6 Given information:

Project Investment NPV A 1,00,000 1,25.000 B 1,50,000 45,000

A&B 2,50,000 2,00,000 C 1,50,000 90,000





a. Selection of the projects if the firm has no budget constraint: Given that all the projects have positive NPV therefore it is beneficial to select all the projects I.e A,B & C.

b. Selection of projects if there is a budget constraint of 2,50,000:

Combination NPV A&B 2,00,000 A&C 2,15,000(1,25,000+90,000)

Since NPV is more in case of projects A&C, it is beneficial to invest in project A&C.

Problem No.7

W.N - 1: Calculation of depreciation per annum

Cost of Machinery 2,50,000 Less: Salvage value 30,000 Depreciable amount 2,20,000

Sum of the years digits = 1 + 2 + 3 + …….. + 10 = 55.

Dep. for 1st year = 10x55

000,20,2 = Rs.40,000 2nd year = 9x

55000,20,2

= Rs.36,000

3rd year = 8x55

000,20,2 = Rs. 32,000 4th year = 7x

55000,20,2

= Rs. 8,000

5th year = 6x55

000,20,2 = Rs.24,000

W.D.V at the end of 5th year = Cost – depreciation = 2,50,000 – 1,60,000 = Rs. 90,000

Book value of machine after capital expenditure = 90,000 + 60,000 = Rs. 1,50,000

Depreciable amount from 6th to 10th year = 1,50,000 – 30,000 = Rs. 1,20,000 Sum of the years digits = 1 + 2 + 3 + 4 + 5 = 15

Dep. for 6th year = 5x15

000,20,1 = Rs. 40,000 7th year = 4x

15000,20,1

= Rs. 32,000

8th year = 3x15

000,20,1 = Rs. 24,000 9th year = 2x

15000,20,1

= Rs. 16,000

10th year = 1x15

000,20,1 = Rs. 8,000

Calculation of NPV

Step-1: Calculation of Present Value of Cash Outflows

Particulars Amount

Cost of Machinery Add: Working capital Add: Cost of Additional equipment [60,000 x PVF (20%, 5y)]

2,50,000 50,000 24,120

Present value of Cash Outflows 3,24,120





Step-2: Calculation of Present Value of Operating Cash Inflows. (Rs. in Lakhs)

Particulars Y1 Y2 Y3 Y4 Y5 Y6 Y7 Y8 Y9 Y10

PBDT Less: Dep.(W.N-1)

1.0 0.4

1.0 0.36

1.0 0.32

1.0 0.28

1.0 0.24

1.0 0.40

1.0 0.32

1.0 0.24

1.0 0.16

1.0 0.08

P.B.T Less: Tax @ 40%

0.6 L 0.24 L

0.64 0.256

0.68 0.272

0.72 0.288

0.76 0.304

0.60 0.24

0.68 0.272

0.76 0.304

0.84 0.336

0.92 0.368

P.A.T Add:Depreciation

0.36 0.4

0.384 0.36

0.408 0.32

0.432 0.28

0.456 0.24

0.36 0.40

0.408 0.32

0.456 0.24

0.504 0.16

0.552 0.08

C.F.A.T. X P.V.F (20%, n)

0.76 0.833

0.744 0.694

0.728 0.579

0.712 0.482

0.696 0.402

0.76 0.335

0.728 0.279

0.696 0.233

0.664 0.194

0.632 0.162

P.Value 0.634 0.516 0.422 0.343 0.279 0.255 0.203 0.162 0.128 0.102

Therefore, Present Value of operating cash inflows = Rs.3,04,498

Step-3: Calculation of Present Value of Terminal Cash Inflows (At the end of the project)

Particulars Amount

G.S.P/N.S.P on sale of machinery Add: Recovery of working capital

30,000 50,000

Total of Terminal Cash Inflows 80,000

Present Value thereof = 80,000 X PVF (20%, 10y) = 80,000 X 0.162 = Rs.12,960

Step-4: Calculation of NPV


= PV of Operating Cash Inflows + PV of Terminal Cash Inflows – PV of Cash Outflows

= 3,04,498 + 12,960 – 3,24,120 = - Rs. 6662 Conclusion: Since NPV is negative it is not advisable for the company to accept the project. Assumptions:

• Cash flows are assumed to accrue at the end of each year.

• Interim cash inflows at the end of each year are assumed to be reinvested at the rate of cost of capital.

• Cash flows given in the problem are assumed to be certain.

Problem No.8

Calculation of IRR:

(Single out flow & multiple even cash inflows)

From the given information,

PVA = 36,000 periodic payment = 11,200 term of annuity = 5 years

We know that, PVA = P.P X PVAF (r%, 5 yrs)

36,000 = 11,200 X PVAF

PVAF = 3.214

Trace the PVAF in the PVAF table against 5 years

Therefore IRR = 17% approximately


To MASTER MINDS,



Problem No. 9

(Rs. In Lakhs) Step-1: Calculation of Pay Back Period

Machine – A Machine – B Year

CFAT Accumulated CFAT CFAT Accumulated CFAT

1 2 3 4 5

1.5 2.0 2.5 1.5 1.0

1.5 3.5 6.0 7.5 8.5

0.5 1.5 2.0 3.0 2.0

0.5 2.0 4.0 7.0 9.0

Pay Back Period 2 +

2.53.55.0 −

= 2.6 Years 3 + 3.0

0.45.0 − = 3.33 years

Since Pay Back Period is less for Machine – A, it is beneficial to purchase Machine – A. Step-2: Present Value of Cash Out flows

Particulars Amount

5,00,000 Cost of Machinery Present Value of Cash Outflows 5,00,000

Step-3: Present Value of Operating Cash Inflows

Machine – A Machine – B Year

Y1 Y2 Y3 Y4 Y5 Y1 Y2 Y3 Y4 Y5

CFAT PVF @ 10% PV

1.5 0.909 1.3635

2.0 0.826 1.652

2.5 0.751 1.8775

1.5 0.683 1.0245

1.0 0.621 0.621

0.5 0.909 0.4545

1.5 0.826 1.239

2.0 0.751 1.502

3.0 0.683 2.049

2.0 0.621 1.242

Present Value there of for Machine – A= 6.5385 Present Value there of for Machine – B= 6.4865

Step-4: Present Value of Terminal Cash Inflows - Nil Step-5: Calculation of NPV and Profitability Index

Particulars Machine A Machine B

6.5385 (5.0)

6.4865 (5.0)

Present Value of cash inflows Present Value of cash outflows NPV @ 10% Profitability Index (P.V of Cash Inflows / Cash Outflows)

1.5385 1.31

1.4865 1.30

Since NPV and P.I. are higher for Machine – A, it is beneficial to purchase Machine – A. Step-6: Calculation of I.R.R for Machine – A

NPV @ 20% NPV @ 24% Year Cash flow

PVF P V PVF P V

0 1 2

5.0 1.5 2.0

1.0 0.833 0.694

(5.0) 1.25 1.39

1.0 0.806 0.650

(5.0) 1.21 1.30



3 4 5

2.5 1.5 1.0

0.579 0.482 0.402

1.45 0.72 0.40

0.524 0.423 0.341

1.31 0.63 0.34

NPV 0.21 (0.21) Using Interpolation

IRR = Ll + 2L NPV@1L NPV@

1L NPV@

−(L2 – L1) = 20 + ( )4

21.00.210.21

+ = 22%.

Step-7: Calculation of IRR for Machine – B

NPV @ 18% NPV @ 20% Year Cash flow

PVF P V PVF P V

0 1 2 3 4 5

5.0 0.5 1.5 2.0 3.0 2.0

1.0 0.847 0.718 0.609 0.516 0.437

(5.0) 0.42 1.08 1.22 1.55 0.87

1.0 0.833 0.694 0.579 0.482 0.402

(5.0) 0.42 1.04 1.16 1.45 0.80

0.14 (0.13)

Using Interpolation

IRR = Ll + 2L NPV@1L NPV@

1L NPV@

− (L2 – L1)

= 18 + 0.13 0.14

0.14+

× 2 = 18 + 1.012 = 19.04%

= 19.04% Since IRR is high for Machine – A, it is beneficial to purchase Machine – A. Step-8: Calculation of Average Rate of Return

Particulars Machine– A Machine – B

1. Depreciation

−Life

ScrapCost 1,00,000 1,00,000

2. Average Investment =

( ) Add.W/capScrapScrapInvestmentInitial2

1++− 2,50,000 2,50,000

3. Average PAT. p.a. (Avg CFAT – Depreciation)

70,000

−

++++1

5

11.52.521.5

80,000

−

++++1

5

2321.50.5

4. Average Rate of Return (3) / (2) 0.28 (70,000/2,50,000) 0.32 (80,000/2,50,000)

Since machines are mutually exclusive and A.R.R. is high for Machine – B, it is beneficial to purchase Machine – B. Conclusion: In all the above cases except in the case of A.R.R - purchase of Machine - A is beneficial.


To MASTER MINDS,



Assumptions: 1. For Pay back period: Cash flows are assumed to accrue evenly throughout the year. 2. For NPV


• Interim cash inflows at the end of each year are assumed to be reinvested at the rate of cost of capital.

• Cash flows given in the problem are assumed to be certain. 3. For IRR


• Interim cash inflows at the end of each year are assumed to be reinvested at the rate of IRR.

• Cash flows given in the problem are assumed to be certain.

Problem No. 10

Step-1: Calculation of CFAT p. a

Particulars Machine X Machine Y

Estimated savings in cost Estimated savings in Wages

500 6,000

800 8,000

Less: Additional cost of maintenance Additional cost of supervision

800 1,200

1,000 1,800

CFAT p.a 4,500 6,000 Step-2: Calculation of Pay back period


Payback period = CFAT

InvestmentInitial

4500

9000 = 2yrs.

6000

18000= 3 yrs.

Assumption: The two machines are mutually exclusive. Conclusion: It is beneficial to select the machine with least pay back period i.e. Machine X.

Problem No.11

(a)

(i) Payback Period

Project A: 10,000/10,00 = 1 year

Project B: 10,000/7,500 = 1 1/3 years.

Project C: 2 years + 31

2000,12

000,6000,10 =− years

Project D: 1 year.

(ii) ARR

Project A: 02/1)000,10(

2/1)000,10000,10( =−


To MASTER MINDS,





Project B: %50000,5500,2

2/1)000,10(2/1)000,10000,15( ==−

Project C: %53000,5667,2

2/1)000,10(3/1)000,10000,18( ==−

Project D: %40000,5000,2

2/1)000,10(3/1)000,10000,16( ==−

Note: This net cash proceed includes recovery of investment also. Therefore, net cash earnings are found by deducting initial investment.

(iii) IRR

Project A: The net cash proceeds in year 1 are just equal to investment. Therefore, r = 0%

Project B: This project produces an annuity of Rs.7,500 for two years. Therefore, the required PVAF is: 10,000/7,500 = 1.33. This factor is found under 32% column. Therefore, r = 32%

Project C: Since cash flows are uneven, the trail and error method will be followed. Using 20% rate of discount the NPV is + Rs.1,389. At 30% rate of discount, the NPV is –Rs.633. The true rate of return should be less than 30%. At 27% rate of discount it is found that the NPV is –Rs.86 and at 26% + Rs.105. Through interpolation, we find r = 26.5%

Project D: In this case also by using the trail and error method, it is found that at 37.6% rate of discount NPV becomes almost zero.

Therefore, r = 37.6%

(iv) NPV

Project A: at 10% -10,000+10,000x0.909 = -910 at 30% -10,000+10,000x0.769 = -2,310

Project B: at 10% -10,000+7,500(0.909+0.826) = 3,013 at 30% -10,000+7,500(0.769+0.592) = +208

Project C: at 10% -10,000+2,000x0.909+4,000x0.826+12,000x0.751 = +4,134 at 30% -10,000+2,000x0.769+4,000x0.592+12,000x0.455 = -633

Project D: at 10% -10,000+10,000x0.909+3,000x(0.826+0.751) = +3,821 at 30% -10,000+10,000x0.769+3,000x(0.592+0.4555) = +831 The Project are ranked as follows according to the various methods:

Ranks Projects PB ARR IRR NPV (10%) NPV (30%

A 1 4 4 4 4 B 2 2 2 3 2 C 3 1 3 1 3 D 1 3 1 2 1





(b) Payback and ARR are theoretically unsound method for choosing between the investment projects. Between the two time-adjusted (DCF) investment criteria, NPV and IRR, NPV gives consistent results. If the projects are independent (and there is no capital rationing), either IRR or NPV can be used since the same set of projects will be accepted by any of the methods. In the present case, except Project A all the three projects should be accepted if the discount rate is 10%. Only Projects B and D should be undertaken if the discount rate is 30%. If it is assumed that the projects are mutually exclusive, then under the assumption of 30% discount rate, the choice is between B and D (A and C are unprofitable). Both criteria IRR and NPV give the same results – D is the best. Under the assumption of 10% discount rate, ranking according to IRR and NPV conflict (except for Project A). If the IRR rule is followed, Project D should be accepted. But the NPV rule tells that Project C is the best. The NPV rule generally gives consistent results in conformity with the wealth maximization principle. Therefore, Project C should be accepted following the NPV rule.

Problem No.12

(a)

Payback Period Method:

A = 5 + (500/900) = 5.5 years

B = 5 + (500/1200) = 5.4 years

C = 2 + (1000/2000) = 2.5 years Net Present Value:

ANPV = (- 5000) + (900 - 6.145) = (5000) + 5530.5 = Rs.530.5

BNPV is calculated as follows:

Year Cash flow (Rs.) 10% discount factor Present value (Rs.)

0 (5,000) 1.000 (5,000)

1 700 0.909 636

2 800 0.826 661

3 900 0.751 676

4 1,000 0.683 683

5 1,100 0.621 683

6 1,200 0.564 677

7 1,300 0.513 667

8 1,400 0.467 654

9 1,500 0.424 636

10 1,600 0.386 618

1591 NPVC = (-5000) + (2000×2.487) + (1000×0.683) = Rs.657

Internal Rate of Return

If ANPV = 0, present value factor of IRR over 10 years = 5000/900 = 5.556

From tables, AIRR = 12 per cent.





IRRB

Year Cash flow (Rs.)

10% discount factor

Present value (Rs.)

20% discount

factor

Present value (Rs.)

0 (5,000) 1.000 (5,000) 1.000 (5,000) 1 700 0.909 636 0.833 583 2 800 0.826 661 0.694 555 3 900 0.751 676 0.579 521 4 1,000 0.683 683 0.482 482 5 1,100 0.621 683 0.402 442 6 1,200 0.564 677 0.335 402 7 1,300 0.513 667 0.279 363 8 1,400 0.467 654 0.233 326 9 1,500 0.424 636 0.194 291 10 1,600 0.386 618 0.162 259 1,591 (776)

Interpolating: IRRB = )776591,1(

10x591,110

++ = 10+6.72 = 16.72 per cent

IRRC

Year Cash flow (Rs.)

15% discount

factor

Present value (Rs.)

18% discount

factor

Present value (Rs.)

0 (5,000) 1.000 (5,000) 1.000 (5,000)

1 2,000 0.870 1,740 0.847 1,694

2 2,000 0.756 1,512 0.718 1,436

3 2,000 0.658 1,316 0.609 1,218

4 1,000 0.572 572 0.516 516

140 136

Interpolating: IRRC = 52.115)136140(

3x14015 +=

++ = 16.52 per cent

Accounting Rate of Return

ARRA: Average capital employed = 2000,5

= Rs.2,500

Average accounting profit = 10

)000,5000,9( − = Rs.400

ARRA = 500,2

)100x400( = 16 per cent

ARRB: Average accounting profit = 10

)000,5500,11( − = Rs.650

ARRB = 500,2

)100x650( = 26 per cent

ARRC = Average accounting profit = 4

)000,5000,7( − = Rs.500

ARRC = 500,2

)100x500( = 20 per cent



(b) Summary of Results

Project A B C

Payback (years) 5.5 5.4 2.5 ARR (%) 16 26 20 IRR (%) 12.4 16.7 16.5 NPV (Rs.) 530.5 1,591 657

Comparison of Rankings

Method Payback ARR IRR NPV

1 C B B B 2 B C C C 3 A A A A

Problem No.13

Calculation of NPV & IRR:

Using interpolation,

IRR = )ll(l@NPVl@NPV

l@NPVl 12

21

11 −

−+

=12% + %)12%13(500,88000,74 −

= 12.836%

Since NPV is positive, it is beneficial for the company to accept the proposal. Since IRR is > cost of capital, it is beneficial for the company to accept the proposal.

Problem No.14

1. Computation of Net Present Values of Projects:

Discounting Discounted Cash flows

Factor @ 16% Cash flow Year Project A

Rs. (1) Project B

Rs. (2)

(3) Project A

Rs. (3) x (1) Project B

Rs. (3) x (2) 0 1,35,000 2,40,000 1.000 1,35,000 2,40,000 1 - 60,000 0.862 - 51,720 2 30,000 84,000 0.743 22,290 62,412

NPV at the rate of 12% NPV at the rate of 13% Year Cash flow

PVF @12% PV PVF @13% PV

0 (35,00,000) 1 (35,00,000) 1 (35,00,000)

1-4 10,00,000 3.037 30,37,000 2.974 29,74,000

5 5,00,000 0.567 2,83,500 0.543 2,71,500

6 5,00,000 0.507 2,53,500 0.48 2,40,000

NPV 74,000 (14,500)





3 1,32,000 96,000 0.641 84,612 61,536 4 84,000 1,02,000 0.552 46,368 56,304 5 84,000 90,000 0.476 39,984 42,840

Net present value 58,254 34,812 2. Computation of Cumulative Present Values of Projects Cash inflows:

Project A Project B PV of Cumulative Year PV of cash

inflows Cumulative

PV cash inflows PV Rs. Rs. Rs. Rs. 1 - - 51,720 51,720 2 22,290 22,290 62,412 1,14,132 3 84,612 1,06,902 61,536 1,75,668 4 46,368 1,53,270 56,304 2,31,972 5 39,984 1,93,254 42,840 2,74,812

(i) Discounted payback period: (Refer to Working note 2)

Cost of Project A = Rs.1,35,000

Cost of Project B = Rs.2,40,000

Cumulative PV of cash inflows of Project A after 4 years = Rs.1,53,270

Cumulative PV of cash inflows of Project B after 5 years = Rs.2,74,812

A comparison of projects cost with their cumulative PV clearly shows that the project A’s cost will be recovered in less than 4 years and that of project B in less than 5 years. The exact duration of discounted pay back period can be computed as follows:

Project A Project B

Excess PV of cash inflows over the

18,270 34,812

Project cost (Rs.) (Rs.1,53,270 – Rs.1,35,000) (Rs.1,53,270 – Rs.1,35,000)

Computation of period required

0.39 year 0.81 years

To recover excess amount of cumulative PV over project cost

(Rs.18,270 / Rs.46,368) (Rs.34,812 / Rs.42,840)

(Refer to Working note2)

Discounted payback period 3.61 year 4.19 years

(4 – 0.39 years (5 – 0.81) years

(ii) Profitability Index : =houtlayinitiancas

lowsinfuntcashSumofdisco

Profitability Index (for Project A) = 000,35,1.Rs254,93,1.Rs

= 1.43

Profitability Index (for Project B) = 000,40,2.Rs812,74,2.Rs

= 1.15

(iii) Net present value (for Project A) = Rs.58,254 (Refer to Working note 1) Net present value (for Project B) = Rs.34,812



Problem No.15

Advise to the Hospital Management:

Determination of Cash inflows Amount

Sales Revenue Less: Operating Cost Less: Depreciation (80,000 – 6,000)/8 Net Income Tax @ 30% Earnings after Tax (EAT) Add: Depreciation Cash inflow after tax per annum Less: Loss of Commission Income Net Cash inflow after tax per annum In 8th Year : New Cash inflow after tax Add: Salvage Value of Machine Net Cash inflow in year 8

40,000 7,500

32,500 9,250

23,250 6,975

16,275 9,250

25,525 12,000 13,525

13,525 6,000

19,525 Calculation of Net Present Value (NPV):

Year CFAT PV Factor @10% Present Value of Cash inflows

1 to 7 8 Less: Cash Outflows

13,525 19,525

NPV

4.867 0.467

65,826.18 9,118.18

74,944.36 80,000.00 (5,055.64)

outflows cash of value Presentinflows cash discounted of Sum

Indexity Profitabil =000,80

36.944,74= =0.937

Advise: Since the net present value is negative and profitability index is also less than 1, therefore, the hospital should not purchase the diagnostic machine. Note: Since the tax rate is not mentioned in the question, therefore, it is assumed to be 30 percent in the given solution.

Problem No.16

(i) Payback Period of Projects

Particulars C0 C1 C2 C3

A (10,000) 6,000 2,000 2,000 3 years

B (10,000) 2,500 2,500 5,000 3 years

C (3,500) 1,500 2,500 1 year and 9.6 months

D (3,000) 0 0 3,000 3 years

i.e. 000,2x500,212

(ii) If standard payback period is 2 years, Project C is the only acceptable project. But if standard payback period is 3 years, all the four projects are acceptable.



(iii) Discounted Payback Period (Cash flows discounted at 10%)

A 10,000 + 5,454.6 + 1,652.8 + 1,502.6 + 8,196

390,1x

196,812

years3 + = 3 years and 2 months

B 10,000 + 2,272.75 + 2,066 + 3,756.5 + 5,122.50

75.904,1x

55.122,512

years3 + = 3 years and 4.6 months

C 3,500 + 1,363.65 + 2,066 + 375.65 + 3,415

35.70x65.375

12years2 + =2 years and 2.25 months

D 3,000 + 0 + 0 + 2,253.9 + 4,098

10.746x098,412

years3 + =3 years and 2.18 months

If standard discounted payback period is 2 years, no project is acceptable on discounted payback period criterion. If standard discounted payback period is 3 years, Project ‘C’ is acceptable on discounted payback period criterion.

Problem No.17

Recommendations regarding Two Alternative Proposals: (i) Net Present Value Method:

Computation of Present Value

Project A = Rs.4,00,000 x 3.791 = Rs.15,16,400

Project B = Rs.5,80,000 x 3.791 = Rs.21,98,780

Computation of Net Present Value:

Project A = Rs.15,16,400 – 12,00,000 = Rs.3,16,400

Project B = Rs.21,98,780 – 18,00,000 = Rs.3,98,780

Advise: Since the net present value of Project B is higher than that of Project A, therefore, Project B should be selected.

(ii) Present Value Index Method:

Present Value Index = estmentInitialInv

lowinfofCashesentValuePr

Project A = 000,00,12

400,16,15 = 1.264

Project B = 000,00,18780,98,21

= 1.222

Advise: Since the present value index of Project A is higher than that of Project B, therefore, Project A should be selected.





(iii) Internal Rate of Return (IRR): Project A:

P.V. Factor = 000,00,4000,00,12

InflowAnnualCashestmentInitialInv = = 3

PV factor falls between 18% and 20%

Present Value of cash inflow at 18% and 20% will be:

Present Value at 18% = 3.127 x 4,00,000 = 12,50,800 Present Value at 20% = 2.991 x 4,00,000 = 11,96,400

IRR = 18 + )1820(x400,96,11800,50,12000,00,12800,50,12 −

−−

= 18 + 2x400,54800,50

= 18 + 1.8676 = 19.868% Project B:

P.V. Factor = 103.3000,80,5000,00,18 =

Present Value of cash inflow at 18% and 20% will be:

Present Value at 18% = 3.127 x 5,80,000 = 18,13,660 Present Value at 20% = 2.991 x 5,80,000 = 17,34,780

IRR = 18 + )1820(x780,34,17660,13,18000,00,18660,13,18 −

−−

= 18 + 2x880,78660,13

= 18 + 0.3463 = 18.346% Advise: Since the internal rate of return of Project A is higher than that of Project B, therefore, Project A should be selected.

Problem No.18

Working notes:

Depreciation on machine. X =

Life

ValueScrap - Cost =

5

000,50,1= Rs.30,000

Depreciation on machine. Y =

Life

ValueScrap - Cost =

6

000,40,2= Rs.40,000


Annual savings: Wages Scrap Total savings(A)

90,000 10,000

1,00,000

1,20,000 15,000

1,35,000

Annual estimated cash cost: Indirect material Supervision Maintenance Total cash cost(B)

6,000 12,000 7,000 25,000

8,000 16,000 11,000 35,000





75,000 30,000

1,00,000 40,000

45,000 13,500

60,000 18,000

31,500 30,000

42,000 40,000

Annual cash savings(A-B) Less: depreciation Annual savings before tax Less: tax @ 30 % Annual profit after tax Add: depreciation Annual cash in flows

61,500 82,000

Evaluation of alternatives: (i) ARR = average annual net savings

Average investment

Machine X = 100x000,75500,31

= 42%

Machine Y = 100x000,20,1000,42

= 35%

Decision: Machine X is better. [Note: ARR can be computed alternatively taking initial investment as the basis forcomputation (ARR = Average Annual Net Income/Initial Investment). The value ofARR for Machines X and Y would then change accordingly as 21% and 17.5%respectively] (ii) Present Value Index Method

Present Value of Cash Inflow = Annual Cash Inflow x P.V. Factor @ 10%

Machine X = 61,500 x 3.79

= Rs.2,33,085

Machine Y = 82,000 x 4.354

= Rs.3,57,028

P.V index = present value of cash inflow

Investment

Machine X = 5539.1000,50,1085,33,2 =

Machine Y = 4876.1000,40,2028,57,3 =

Decision: Machine X is better.

Problem No.19

PART – A

Project Present Value of Cash Inflows Initial cash

outlay NPV P.I

Ranking as per NPV

Ranking as per

P.I A 1,87,600 x PVAF (12%, 2y ) = 317044 3,00,000 17,044 1.057 IV V B 66,000 x PVAF (12%, 5y ) = 2,37,930 2,00,000 37,930 1.19 III III C 1,00,000 x PVAF (12%, 3y) = 2,40,200 2,00,000 40,200 1.201 II II D 20,000 x PVAF (12%, 9y) = 1,06,560 1,00,000 6,560 1.066 V IV E 66,000 x PVAF (12%, 10y) = 3,72,900 3,00,000 72,900 1.243 I I





PART – B All the projects have positive NPV. So, we can accept all the projects subject to availability of funds. It is also given that the company is having limited funds of Rs.4,00,000 and we need Rs.11,00,000 to invest in all the projects. So, it is required to do capital rationing.

Capital Rationing, assuming that the projects are divisible

Project Cash Outflow NPV Surplus funds

E 3,00,000 72,900 1,00,000

C 1,00,000 20,100

000,00,1x

000,00,2200,40

-

Total 93,000 -

PART - C All the projects have positive NPV. To accept all the projects we need initial investment of Rs.11,00,000. But the available funds are just Rs.5,00,000. Therefore, it is necessary to do capital rationing.

Capital Rationing, assuming that the projects are divisible

Project Cash outlay NPV Surplus funds

E 3,00,000 72,900 2,00,000 C 2,00,000 40,200 ---

Total 1,13,100 Assumptions:

• Perfect linear relationship is assumed to exist between inflows and outflows. In other words, NPV changes proportionately to changes in investment.

• It is assumed that there is scarcity of funds in the current year only. In other words, there is no scarcity of funds in subsequent years.

• The given projects are mutually independent.

• A project can be accepted only once.

• A project can either be accepted now or rejected. In other words, there is no question of postponement.

THE END

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