Rank the projects according to each of the following methods : (i) Pay back (ii) ARR (iii) IRR and (iv) NPV- assuming discount rates of 10% and 30%

Ravi Co Ltd. is considering the following investment projects:

Cash flows (Rs.)

Projects	Year0	Year1	Year2	Year3
A	-10,000	+10,000	-	-
B	-10,000	+7,500	+7,500	-
C	-10,000	+2,000	+4,000	+12,000

D -10,000 +10,000 +3,000 +3,000

a) Rank the projects according to each of the following methods : (i) Pay back (ii) ARR (iii) IRR and

(iv) NPV- assuming discount rates of 10% and 30%

b) Assuming that the projects are independent, which one should be accepted? If the projects are mutually exclusive, which project is the best?

(a) (I) Pay Bank Period = Initial cash out flow

Annual cash Inflow after tax

Project A = 10000 = 1 Year

10000

Project B = 10000 = 1.33 Years

7000

Project C

Year C.I. Cumulative C.I.

1 2000 2000

2 4000 6000

3 12000 22000

2 Years + (10000-6000) = 2.33 Years

12000

Project D

Year C.I. Cumulative C.I.

1 10000 10000

2 3000 13000

3 3000 16000

1 year

(a) (ii) Accounting Rate of Return (APR) = Average Income/Average Investment

Project A = (10000-10000)/10000 = 0

1 2

Project B = (7500+7500-10000)/10000 = .5 or .50%

2 2

Project C = (2000+4000+12000-10000)/10000 = .533 or 53.33%

3 2

Project D = (10000+3000+3000-10000)/10000 = .4 or .40%

3 2

Net Cash Proceed includes recovery of investments also. Therefore net cash earnings are found by deducting initial investment.

(a) (iii) Internal Rate of Return (IRR)

It is the rate of return at which Present Value of cash Inflow is equal to present value of cash outflow.

IRR = Low Rate + NPV at low Rate X (High Rate – Low Rate) NPV at low Rate – NPV at high Rate

Project A

Year PVF @10% PVF@12% C.I. PV @ 10% PV @ 12%

1 .909 .893 10000 9090 8930

Less: PV of outflow

10000 10000

NPV -910 -1070

IRR = 10 + -910 X (12-10) (-910-(-1070)

= 10 + (-1820) = -11.375%

160

Since IRR is negative hence r =0%

Project B

Year PVF @30% PVF@33% C.I. PV @ 30% PV @ 33%

1 .769 .752 7500 5768 5640

2 .592 .565 7500 4440 4238

10208 9878

Less: PV of

Cash Outflow

10000 10000

208 (-) 122

IRR = 30 + 208 X (33-30) (208-(-122))

= 30 + 624 = 31.89 say 32%

330

Project C

Year

PVF @26%

PVF@28%

C.I.

PV @ 26%

PV @ 28%

.794

.761

2000

1588

1522

.630

.610

4000

2520

2440

.500

.477

12000

6000

5724

10108

9686

Less: PV of

Outflow

10000

NPV

108

-314

IRR = 26 + 108 X (28-26)

108-(-314)

= 26 + 216 = 26.51%

422

Project D

Year PVF @37% PVF@38% C.I. PV @ 37% PV @ 38%

1 .730 .725 10000 7300 7250

2 .533 .525 3000 1599 1575

3 .389 .381 3000 1167 1143

PVF of cash

Inflow

Less: PV of

Outflow

10066 9968

10000 10000

NPV 66 -32

IRR = 37 + 66 X(38-37)

66(-(-32)

= 37 + 66 = 37.67%

(a) (iv) Net Present Value NPV = PV of Cash Inflow – PV of Cash outflow

Project A

Year C.I. PV@10% PV@30% PV@10% PV@30%

1 10000 .909 .769 9090 7690

2 -

3 -

Less: PV of

Outflow

9090 7690

10000 10000

NPV -910 -2310

Project B

Year PVF@10% PVF@30% C.I PV@10% PV@30%

1 .909 .769 7500 6818 5768

2 .826 .592 7500 6195 4440

3 .751 .455 - - -

13013 10208

Less: PV of

Outflow

10000 10000

NPV 3013 208

Project C

Year PVF@10% PVF@30% C.I PV@10% PV@30%

1 .908 .769 2000 1818 1538

2 .826 .592 4000 3304 2368

3 .751 .455 12000 9012 5460

14134 9366

Less: PV of

Outflow

10000 10000

NPV 4134 -634

Project D

Year PVF@10% PVF@30% C.I PV@10% PV@30%

1 .909 .769 10000 9090 7690

2 .826 .592 3000 2478 1776

3 .751 .455 3000 2253 1365

13821 10831

Less: PV of

Outflow

10000 10000

NPV 3821 831

Projects are ranked as follow according to the various Method

Methods A B C D

Pay Back Period 1 2 3 1

Accounting Rate of Return 4 2 1 3

Internal Rate of Return 4 2 3 1

Net present Value (@10%) 4 3 1 2

Net present Value (@30%) 4 2 3 1

b) Payback and ARR are unsound method for choosing between the investment Projects. Between the two times adjusted (DCF) investment criteria, NPV and IRR. NPV gives consistent results. If the Projects are independent (and there is no capital rationing) either IRR , NPV can be used since the same set of projects will be accepted by any of the methods.

In the given case, except Project A all the three projects should be accepted if the discount rate is 10%. Only project B & 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 & 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 confirming with the wealth maximization principal. Therefore Project C should be accepted following the NPV rule.

MS-04 Accounting and Finance for Managers

Saturday, June 18, 2011