CAPITAL BUDGETING DECISION

INVESTMENT EVALUATION CRITERIA

Three steps are involved in the evaluation of an investment: Estimation of cash flows Estimation of the required rate of return Application of a decision making choice.

Investment Criteria (1) Discounted Cash Flow (DCF) criteria

(i) Net present value (ii) Internal rate of return. (iii) Profitability index or Benefit-cost ratio.

(2) Traditional criteria (i) Payback period (ii) Accounting rate of return

•  NET PRESENT VALUE METHOD

The steps involved in the NPV method are:

•  Cash flows of the investment projects should be forecasted based on realistic assumptions.

•  Appropriate cost of capital should be selected to discount cash flows.

•  The present value of investment proceeds (i.e., cash inflows) and the present value of investment outlay (i.e., cash outflows) should be computed using cost of capital as the discounting rate.

•  The net present value should be found out by subtracting the present value of cash outflow from the present value of cash inflows.

•  The project should be accepted if NPV is positive.

The Equation for the Net Present Value

•  The equation for the net present value, assuming that all cash outflows are made in the initial year (to), will be:

•  NPV= {A1/(1+k) + A2/(1+k)2 + …+ An/(1+k)n} - C

•  = At / (1+k)t - C …….. (1)

•  where A1, A2 ...represent cash inflows, k is the firm's cost of capital, C is the initial outlay of the investment proposal and n is the expected life of the proposal.

∑=

n

t 1

Acceptance Rule

•  Accept if NPV > 0 •  Reject if NPV < 0 •  Marginal project if NPV = 0

ILLUSTRATION 1

•  Calculate the net present value for Project A which initially costs Rs.2,500 and generate year-end cash inflows of Rs.900. Rs.800, Rs.700, Rs.600 and Rs.500 in one through five years. The required rate of return is assumed to be 10 per cent.

Net Present Value of Project A Year Cash inflows

(Rs) Discounting factor at 10% PV of cash inflows

(Rs) 1 2 3 4 5

900 800 700 600 500

.909

.826

.751

.683

.620 Total PV Less: investment outlay Net present value

818 661 526 410 310 2725 2,500 225

EVALUATION OF THE NPV METHOD

•  ADVANTAGE •  Time value: •  It recognizes the time value of money

•  Measure of true profitability

•  Shareholder value

Limitation

•  Cash flow estimation •  Discount rate •  Ranking of projects •  Ranking of investment projects as per the NPV rule is •  not independent of the discount rates.

Consider the following two projects – A and B

Project t0 t1 t2

A B

-Rs50 -Rs50

Rs100 Rs30

Rs25 Rs100

Project NPV at 5% Rank NPV at 10% Rank

A B

67.92 69.27

II I

61.57 59.91

I II

INTERNAL RATE OF RETURN METHOD

•  Assume that you deposit Rs1,000 in a bank and would get back Rs1,100 after one year.

•  What is the rate of return of investment? •  Rate of return = (1,100 -1,000)/1,000 •  =100/1000=0.10 or 10 percent.

INTERNAL RATE OF RETURN METHOD

•  We can develop the formula •  r = (C1-C0 ) /C0 = C1 / C0 - 1 •  Or 1+r = C1 / C0 •  Or C0 = C1 / (1+r) …………(2) •  This implies that the rate of return is the

discount rate which equates the present value of cash inflow to the present value of cash outflow.

INTERNAL RATE OF RETURN METHOD

•  The internal rate of return can be defined as that rate which equates the present value of cash inflows with the present value of cash outflows of an investment.

•  It can be determined by solving the following equation:

•  C= A1/(1+r) + A2 /(1+r)2 + A3 /(1+r)2 +…….+ An /(1+r)n •  •  = A t /(1 + r)t ………….(3) ∑

=

n

t 1

ILLUSTRATION 2

•  A project costs Rs16,000 and is expected to generate cash inflows of Rs8,000, Rs7,000 and , Rs6,000 over its life of three years. You are required to calculate the internal rate of return of the project.

To start with, we select a rate of 20 per cent and calculate the present value of cash inflows:

Year Cash inflows (Rs)

Discount factor at 20%

Present value (Rs)

1 2 3

8,000 7,000 6,000

.833

.694

.579

6,664 4,858 3,474 _______ Total PV 14,994 Less: cash outflow 16,000 _______ NPV (-)1,004

The net present value indicates that the chosen rate is a higher rate. Therefore, lower rates should be tried. We try 18 per cent,16 per cent

and 15 per cent and obtain the following results:

Year Cash inflow (Rs)

Discount factor (DF) 18%

PV (Rs)

DF 16% PV (Rs)

DF 15% PV (Rs)

1 8,000 .847 6,776 .862 6,896 .870 6,960

2 7,000 .718 5,026 .769 5,201 .756 5,292

3 6,000 .609 3,646 .641 3,846 .658 3,948

Total PV 15,456 15,943 16,200

Less: cash outlay

16,000 16,000 16,00

NPV (-)544 (-)57 200

•  At 16 percent discount rate the project’s NPV is (-)Rs57, and 15 percent discount rate the NPV is Rs200.

•  Thus the true rate of return should lie between 15 and 16 percent.

•  We can find out a close approximation of the rate of return by the method of linear interpolation as follows;

•  r =15% + (16% -15%) 200/257 •  =15%+ 0.80% = 15.8%

• Acceptance Rule Accept if r>k

Reject if r<k

PROFITABILITY INDEX •  It is the ratio of the present value of future cash benefits to the

initial cash outflow of the investment. •  It may be gross or net, net being simply gross minus one. •  The formula to calculate benefit-cost ratio or profitability index

is as follows: •  PI = PV of Cash Inflows / Initial Cash Outlay

•  = {At/ (1+k)t} / C ……..(4) ∑=

n

t 1

• Acceptance Rule

•  Accept if PI > 1 •  Reject if PI < 1 •  Marginal project if PI = 1

•  ILLUSTRATION 3 •  The initial cash outlay of a project is Rs.

100,000 and it generates cash inflows of Rs.40,000, Rs.30,000, Rs.50,000 and Rs.20,000 in the four years. Calculate the NPV and PI of the project. Assume a 10 per cent rate of discount.

Calculation of NPV and Profitability Index Year Cash inflows

(Rs) Discount factor Present value

(Rs)

1 40,000 0.909 36,300

2 30,000 0.826 24,780

3 50,000 0.751 37,550

4 20,000 0.683 13,660

Total PV Less: outlay

1,12,350 1,00,000

NPV PI

12,350 1,12350/1,00,000 = 1.1235

PAYBACK PERIOD

•  The payback (or payout) period is one of the most popular and widely recognized traditional methods of evaluating investment proposals. It is defined as the number of years required to recover the original cash outlay invested in a project. If the project generates constant annual cash inflows, the payback period can be computed dividing cash outlay by the annual cash inflow. That is:

•  Payback period •  =Cash outlay (investment) / Annual Cash inflow (A)

= C / A …..…(5) • 

ILLUSTRATION 4

•  A project requires an outlay of Rs 50,000 and yields an annual cash inflow of Rs. 12,500 for 7 years. Calculate the payback period.

•  The payback period for the project is: •  Rs 50,000 / Rs12,500 = 4 years

ILLUSTRATION 5

•  Calculate the payback period for a project which requires a cash outlay of Rs.20,000, and generates cash inflows of Rs.8,000; Rs.7,000; Rs.4,000; and Rs.3,000.

•  In case of unequal cash inflows, the payback period can be found out by adding up the cash inflows until the total is equal to the initial cash outlay:

•  When we add up the cash inflows, we find that in the first three years Rs.19,000 of the original outlay is recovered. In the fourth year cash inflow generated is Rs.3,000 and only Rs.1,000 of the original outlay remains to be recovered.

•  Assuming that the cash inflows occur evenly during the year, the time required to recover Rs.1,000 will be (Rs.1,000/Rs.3000) x 12 months =4 months. Thus, the payback period is 3 years and 4 months. .

PAYBACK PERIOD DECISION RULE

1.  Post payback Duration. 2.  Payback should only be used as an initial

screening of projects. 3.  The payback period also offers some indication

of risk. 4.  Liquidity.

•  Acceptance Rule •  Accept if the calculated PB period < the

maximum PB period set up by the management. •  Reject if the calculated PB period > the

maximum PB period set up by the management. •  Marginal project, if the calculated PB period =

the maximum PB period set up by the management.

ILLUSTRATION 6

•  Calculate the payback periods of the following projects each requiring a cash outlay of Rs.10,000. Suggest which ones are acceptable if the standard payback period is 5 years.

Year Project X Project Y Project Z

1 2 3 4 5

Rs 2,500 2,500 2,500 2,500 2,500

Rs 4,000 3,000 2,000 1,000 0

Rs 1,000 2,000 3,000 4,000 0

Payback period:

•  For Project X = Rs 10,000 / Rs 2,500 = 4 yrs •  For Project Y = •  Rs.4,000+ Rs.3,000+ Rs.2,000+Rs.1,000 •  = Rs.10,000 recovered in 4 years •  For Project Z = Rs.1,000+Rs.2,000+Rs.3,000

+Rs.4,000 •  = Rs.10,000 recovered in 4 years

•  The payback period in each case is 4 years, as at the end of fourth year the initial cash outlay of each project is recovered. All projects are acceptable because the standard payback period is higher than the actual payback periods of all projects.

Evaluation

•  Advantages •  Simplicity •  Cost effective •  Risk shield •  Liquidity

Limitation

•  First, it fails to take account of the cash inflows earned after the payback period.

•  Consider the following projects X and Y:

Project C0 C1

C2

C3

Payback NPV at k=.

10

X Y

-4,000 -4,000

0 2,000

4,000 2,000

2,000 0

2 years 2 years

+806 -530

Limitation

•  Second, it fails to consider the pattern of cash inflows, i.e., magnitude and timing of cash inflows.

•  Consider the following projects X and Y:

Project C0 C1

C2

C3

Payback NPV at k=.

10

C D

-5,000 -5,000

3,000 2,000

2,000 3,000

2,000 2,000

2 years 2 years

+881 +798

Limitation

•  Third, there is no rational basis for setting a maximum payback period. It is generally a subjective decision.

•  Fourth, i t is inconsistent wi th shareholder value.

Payback Reciprocal and the Rate of Return

•  Payback is considered theoretically useful in a few situations. One significant argument in favour of payback is that its reciprocal is a good approximation of the rate of return under certain conditions.

•  The payback period is defined as follows: •  Payback •  = Initial investment /Annual cash inflow (annuity) •  = C /A

•  In general terms, the PV of an annuity may be expressed as follows:

•  PVA=

•  C = A/(1+r) + A/(1+r)2+ …..+ A/(1+r)n-1+ A/(1+r)n …(6) •  Where PVA = present value of an annuity which has a

duration of n periods, A= Annuity, r = discount rate.

•  The formula for the PV of an annuity is derived as follows: •  C = A/(1+r)+A/(1+r)2+ ..+ A/(1+r)n-1+ A/(1+r)n ……(6)

•  Multiplying both sides of (6) by (1+r) gives: •  C(1+r) = A + A/(1+r) + A/(1+r)2+ …..+ A/(1+r)n-1 ….(7)

•  Subtracting (6) from (7) yields: •  Cr = A[1- (1+r)-n] …………..(8)

•  Solving for r, we find •  r = A[1- 1/(1+r) n] / C = A/C – A/C [1/(1+r) n] ……(9) •  Where C is the initial investment, A is annual cash inflow,

r is rate of return and n is the life of investment. •  If n is very large or extends to infinity, the second term

becomes insignificant. •  Thus r = A/C = the reciprocal of payback, if the following

two conditions are fulfilled: •  (1) The life of the project is large. •  (2) The project generates equal annual cash inflows.

DISCOUNTED PAYBACK PERIOD

•  One of the serious objections to the payback method is that it does not consider the time value of money.

•  Thus we can discount cash flows and then calculate the payback period.

•  The discounted payback period is the number of periods taken in recovering the investment outlay on the present value basis.

•  The discounted payback period still fails to consider the cash flows occurring after the payback period.

Discounted payback Illustrated for two projects P and Q

C0 C1 C2 C3 C4 Simple PB

Discounted PB

NPV at 10%

P PV of cash flows Q PV of cash flows

-4,000 -4,000 -4,000 -4,000

3,000 2,727 0 0

1,000 826 4,000 3,304

1,000 751 1,000 751

1,000 683 2,000 1,366

2 yrs 2 yrs

- 2.6 yrs - 2.9 yrs

- 987 - 1,421

NET PRFSENT VALUE Vs PROFITABILITY INDEX.

Consider the following illustration where the two methods give different ranking to the projects.

•  ILLUSTR.4TION 8

Project C (Rs)

Project D (Rs)

PV of Cash inflows 1,00,000 50,000

Initial cash outflow 50,000 20,000

NPV 50,000 30,000

PI 1,00,000/50,000 = 2.0

50,000/20,000 = 2.5

•  Project C should be accepted if we use the NPV

method, but Project D is preferable according to the PI. The question, therefore, to be answered is: which method is better?

•  The NPV method should be preferred, except under capital rationing, because the net present value represents the net increase in the firm's wealth.

Project C will also be acceptable if we calculate the

incremental profitability index. This is shown as follows:

Project C (Rs)

Project D (Rs)

Incremental flow (Rs)

PV of Cash inflows

1,00,000 50,000 50,000

Initial cash outflow

50,000 20,000 30,000

NPV 50,000 30,000 20,000

PI 1,00,000 /50,000 =2

50,000/20,000 = 2.5

50,000/30,000 =1.7

Consider a different situation Project A (Rs)

Project B (Rs)

PV of Cash inflows 3,00,000 2,00,000

Initial cash outflow 2,00,000 1,00,000

NPV 1,00,000 1,00,000

PI 3,00,000/2,00,000 = 1.5

2,00,000/1,00,000 = 2

NET PRESENT VALUE Vs INTERNAL RATE OF RETURN

•  Equivalence: Conventional investment •  We know that

•  NPV = {At / (1+k)t} – C ………(11)

•  and IRR is defined to be that rate r which satisfies the following equation:

•  0 = {At / (1+r)t} – C ………(12)

•  Subtracting Eq. (12) from (11), we get

•  NPV = [ {At / (1+k)t} – {At / (1+r)t}] …….(13)

•  As we know that At , k, r, and t are positive, •  NPV >0, if r>k. •  NPV = 0, if r=k, and •  NPV <0, it r<k.

∑=

n

t 1

∑=

n

t 1

∑=

n

t 1

The following figure substantiates this above arguments

•  NPV •  a2

•  a1

•  0 r1 r2 r3 •  a3

•  If the discount rate (say r1) is lower than r2, the NPV is positive. Thus the project will be accepted under both the methods

•  If the discount rate is r2 which is also IRR, the NPV is zero •  If the discount rate (r3) higher than r2, the NPV is negative. Thus the project

will be rejected under both the methods.

Difference: Case of Ranking Dependent Projects

•  The conflicting ranking by the two methods occurs under the following conditions:

1.  The cash flow pattern of the projects may differ. That is, the cash flows of one project may increase over time, while those of the other decrease.

2.  The projects have different expected lives. 3.  The cash outlay of one project is larger than

that of the other.

Timing of cash flows •  A commonly found condition for the conflict between the

two methods is the timing of the cash flows. Let us consider the following illustration.

•  Which project should we accept?

Project C0 C1 C2 C3 NPV at 9%

IRR

M N

-1680 -1680

1,400 140

700 840

140 1,510

301 321

23% 17%

NPV Profiles of Projects M and N

Discount rate (%) Project M Project N

0 5 10 15 20 25 30

560 409 276 159 54 -40 -125

810 520 276 70 -106 -257 -388

NPV versus IRR •  NPV •  1000

•  800 Project N Project M •  •  600

•  400 •  •  200

•  0 •  0% 5% 10% 15% 20% 25% 30% •  -200

•  -400

•  The internal rates of the two projects are 23 percent and 17 per cent respectively.

•  At 10 per cent required rate both methods are equally profitable if we use the NPV method.

•  It is also noticeable that if the required rate of return is less than 10 percent (the rate at which NPVs of both the projects are equal), project N has the higher NPV but lower IRR, 17 per cent.

•  On the other hand, if the required rate of return is greater than 10 per cent, project M has both higher NPV as well as higher IRR, 23 per cent.

Which project should we choose between Projects M and N?

•  Both projects generate positive NPV at 9% cost of capital. Therefore, both are profitable.

•  But Project N is better since it has higher NPV. •  The IRR rule, however, indicates that we should choose Project M

as it has a higher IRR. •  If we choose Project N, following the NPV rule, we shall be richer by

an additional value of Rs20. •  Should we have the satisfaction of earning a higher rate of return, or

should we like to be richer? •  The NPV rule is consistent with the objective of maximising wealth.

Incremental approach

•  If we prefer Project N to Project M, there should be incremental benefits in doing so. To see this let us calculate the incremental flows of Project N over Project M. We obtain the following cash flows:

Project C0 C1 C2 C3 NPV at 9%

IRR

(N-M) 0 -1,260 140 1370 20 10%

2.The projects have different expected lives.

Project t0 t1 t5 NPV (k=10%)

IRR

X -10,000 12,000 909 20%

Y -10,000 20,120 2,493 15%

Incremental Approach

Project t0 t1 t5 NPV (k=10%)

IRR

Y-X 0 -12,000 20,120 1,584 13.8%

•  NPV = PV of inflow – PV of outflow •  = 20,120 / (1.1)5 - 12,000/(1.1) •  =12493 – 10909 = 1,584

•  IRR is calculated as follows: •  12,000 / (1+r) = 20120 / (1+r)5

•  (1+r)4 = 20,120 / 12,000 = 1.67 = (1.138)4 = (1+.138)4

•  r = 0.138 = 13.8%

3. Scale of Investment

Project t0 t1 NPV (k=10%)

IRR

M -1,000 1,500 363.50 50%

N -100,000 120,000 9080 20%

Incremental Approach

Project t0 t1 NPV at 10% IRR

(N-M) -99,000 118,500 8,727 19.75

Non-conventional Investments : Problem of Multiple IRRs

•  Let us consider the following project I:

•  We can use the IRR formula to solve the internal rate of return of this project

•  4000 / (1+r) - 3750 / (1+r)2 =1,000

Project C0 C1 C2

I -1000 4,000 -3750

•  Assuming 1/(1+r) = x, we obtain •  -3750 x2 + 4000x – 1000 =0 •  This is the quadratic equation of the form: ax2 + bx +c =0, and we

can solve it by using the following formula: •  x = [-b (b2-4ac)1/2 ] / 2a •  Substituting values in the above equation, we obtain •  x= [-4000 {40002-4(-3750)(-1000)}1/2 ] / 2(-3750) •  = [-4000 1,000]/ (-7500) = 2/5, 2/3 •  Since x= 1/(1+r) , therefore •  1/(1+r) = 2/5, 1/(1+r) = 2/3 •  r = 3/2 or 150%, r=1/2 or 50%

±

±±

•  Assuming 1/(1+r) = x, we obtain •  -3750 x2 + 4000x – 1000 =0 •  This is the quadratic equation of the form: ax2 + bx +c =0, and we

can solve it by using the following formula: •  x = [-b (b2-4ac)1/2 ] / 2a •  Substituting values in the above equation, we obtain •  x= [-4000 {40002-4(-3750)(-1000)}1/2 ] / 2(-3750) •  = [-4000 1,000]/ (-7500) = 2/5, 2/3 •  Since x= 1/(1+r) , therefore •  1/(1+r) = 2/5, 1/(1+r) = 2/3 •  r = 3/2 or 150%, r=1/2 or 50%

±

±±

Dual Rates of Return

•  NPV

•  250

•  0 •  50% 100% 150% 200% discount rate •  -250

•  -500

•  -750

NPV, IRR, REINVESTMENT ASSUMPTION and MIRR

•  Consider two projects A and B both of which have initial cash outlay of Rs1000,000. Cash inflows of both the projects are as follows:

C1 C2 C3 C4 C5

Project A Project B

400,000 100,000

400,000 100,000

400,000 100,000

400,000 1000,000

400,000 1000,000

NPV of Project A using 10% cost of capital

Year Cash flow PV factor at 10% PV 1 2 3 4 5

400,000 400,000 400,000 400,000 400,000

0.90909 0.82644 0.75131 0.68301 0.62092

363,636 330,579 300,526 273,206 248,369 ________ PV of inflows 1516,315 PV of outflows 1000,000 __________ NPV 516,315

NPV of Project B using 10% cost of capital

Year Cash flow PV factor at 10% PV 1 2 3 4 5

100,000 100,000 100,000 1000,000 1000,000

0.90909 0.82644 0.75131 0.68301 0.62092

90,909 82,645 75,131 683,013 620,921 ________ PV of inflows 1552,620 PV of outflows 1000,000 __________ NPV 552,620

Calculation of IRR

•  Calculation of IRR of project A •  Let IRR be r, then •  1000,000 = 400,000/(1+r) + 400,000/(1+r)2 + 400,000/(1+r)3 + •  400,000/(1+r)4 + 400,000/(1+r)5 •  Solving this equation we get IRR for project A is 28.65%

•  Calculation of IRR of project B •  Let IRR be r, then •  1000,000 = 100,000/(1+r) + 100,000/(1+r)2 + 100,000/(1+r)3 + •  1000,000/(1+r)4 + 400,000/(1+r)4 •  Solving this equation we get IRR for project B is 22.8%

Mutually Exclusive Projects

•  We have got the following results

•  If the projects A and B are mutually exclusive, which project should we select?

Project NPV IRR A B

Rs516,315 Rs552,620

28.65% 22.8%

•  If for both A and B the cost of capital were different, say 25%, we would calculate different NPVs and come to a different conclusion. In this case:

•  Project A still has a positive NPV, since its IRR > 25%, but B has a negative NPV, since its IRR<25%.

Project NPV IRR

A B

Rs75,712 -Rs67,520

28.65% 22.8%

Reinvestment assumption

•  When evaluating mutually exclusive projects, the one with the highest IRR may not be the one with the best NPV. The IRR may give a different decision than NPV when evaluating mutually exclusive projects because of the reinvestment assumption:

•  NPV assumes cash flows are reinvested at the cost of capital. •  IRR assumes cash flows are reinvested at the internal rate of return

NPV assumes cash flows are reinvested at the cost of capital.

•  Assume cash flows of a project are –Rs100 , Rs10 and Rs110 for the year t = 0,1,and 2.

•  If the cost of capital is k=9%, NPV of the project is

•  NPV = 10/(1.09) + 110/(1.09)2 - 100 •  =9.1743+92.5847 – 100 = 1.759

NPV assumes cash flows are reinvested at the cost of capital.

•  If the cash inflow of Rs10 received at the end of year 1 is reinvested @9%, it would be Rs10(1+.09) = Rs10.90 at the end of year 2.

•  Thus the total inflow at the end of year 2 is Rs(110+10.9) = Rs120.9.

•  Using cost of capital of k=9%, NPV is again the same amount

•  NPV = 120.90/(1.09)2 - 100 = 101.759 – 100 = 1.759

IRR assumes cash flows are reinvested at the internal rate of return •  Assume cash flows of a project are –Rs100 ,

Rs10 and Rs110 for the year t = 0,1,and 2. Find the IRR of the project.

•  Assuming IRR =r, we get •  100 = 10/(1+r) + 110/(1+r)2

•  Solving this equation we get r=10%.

IRR assumes cash flows are reinvested at the internal rate of return •  If the cash inflow of Rs10 received at the end of year 1 is

reinvested @10%, it would be Rs10(1+.1) = Rs11 at the end of year 2.

•  Thus the total inflow at the end of year 2 is Rs(110+11) = Rs121.

•  Assuming IRR =r, we get •  100 = 121/(1+r)2 or (1+r)2 = 121/100 = 1.21 =(1+0.1)2 •  Thus we get r=10%.

What do you do with the cash inflows when you get them?

•  We generally assume that if you receive cash inflows,

you’ll reinvest those cash flows in other assets. •  Suppose we can reasonably expect to earn only the cost

of capital on our investments. Then for projects with an IRR above the cost of capital, we would be overstating the return on the investment using the IRR.

•  Consider project A once again. If the best you can do is reinvest each of the Rs400,000 cash flows at 10%, these cash flows are worth Rs2442,040:

•  Future value of project A’s cash inflows each invested at 10% •  = Rs400,000 (FVAF10%, 5) •  =Rs400,000 (6.2051) = Rs2442,040

•  Investing Rs1000,000 at the beginning of the year 1 produces a value of Rs2442,040 at the end of year 5 (cash flows plus the earnings on these cash flows at 10%).

•  This means that if the best you can do is reinvest cash flows at 10%, then you earn not the IRR of 28.65%, but rather 19.55%:

•  FV = PV (1+i)n •  Rs2442,040 = Rs1000,000 (1+i)n •  i = 19.55%

•  Consider projects A and B and their MIRRs with reinvestment at the cost of capital:

Project MIRR IRR NPV

A B

19.55% 20.12%

28.65 22.79%

Rs516,315 Rs552,619