MIRR Formula

MIRR Formula

IRR use the same rate for reinvestment of fund, which is not practical. Therefore MIRR concept has been introduced, which uses the cost of capital as reinvestment.

MIRR = n√A/B

n= life of project

A= Recovery phase Cash flows

B= Investment phase Cash flow

Example

Year               Cash Flows

0                          (100,000)

1                            (20,000)

2                             50,000

3                             50,000

4                             40,000

5                            (20,000)

IRR is 12% and discount Rate is 8%, Calculate MIRR?

Solution

Investment Phase discounting

Year       Cash Flows      Discount              PV

0               (100,000)          1                      (100,000)

1                (20,000)          (1.08)^-1                   (18,518)

Total                                                           118,518

Recovery Phase flows

Year     Cash Flows       Discount         PV

2                  50,000          (1.08)³           62986

3                  50,000          (1.08)²           58320

4                  40,000           (1.08)¹          43200

5                  (20,000)          1                (20000)

                                                               144,506

MIRR = n√A/B -1

= 5√144,506/118518

=4.04%

IRR Formula

IRR Formula

IRR can be calculated with the help of following formula. It is important that IRR is an estimated calculation only. IRR tell us about the rate, where NPV will become zero. IRR is return of the project, if such return is greater than expected return, then project is to be selected, otherwise rejected.

R_L+ {  NPV_L          } x (R_H-R_L)

         NPV_L-NPV_H

R_L= Lower rate of Return

R_H= Higher Rate of Return

NPV_L = NPV with Lower rate of Return

NPV_H= NPV at higher rate of return

Example

Year

0     100,000

1      30,000

2      30,000

3      35,000

4      15,000

Calculate IRR?

Solution

We assume that IRR falls between 10% & 15%.

Year                  Discount           PV @10%     Discount           PV @ 15%

0     100,000         1                   (100,000)                           (100,000)

1      30,000       (1+10%)^-1          27,272        (1+15%)^-1        26,086  

2      30,000       (1+10%)^-2          24,793       (1+15%)^-2        22,684   

3      35,000       (1+10%)^-3          26,296       (1+15%)^-3         23,013   

4      32,000       (1+10%)^-4          21,856        (1+15%)^-4        18,296

NPV                                             217                                (9,921)            

R_L+ {  NPV_L          } x (R_H-R_L)

         NPV_L-NPV_H

= 10% + [ 217/(217- (-9921)]x [ 15%-10%)

=10%+ [217/10,138] x [5%]

=10.10%

Negative NPV Formula

Negative NPV Formula

NPV negative mean when present value of cost exceeds the benefit. In simple word when cost is more than benefit at present date. It is logical that a project with negative NPV would be rejected.

Negative NPV = PV of Benefits < PV of Cost

Example

Investment required for a project = 500,000

First & Second Year income =     300,000 & 280,000

Weighted Cost of capital= 12%

Solution

 Years                  Year 0                Years 1                   Year 2

Initial investment      500,000

Income                                                           300,000

Income                                                                                                    280,000

Discount Factor        (1+.12)^-0                                      (1+.12)^-1                                   (1+.12)^-2

PV                               (500,000)                      267857                         223,214

NPV = 267,857+223,214-500,000

=(8,929)

Positive NPV Formula

Positive NPV Formula

NPV is positive, when present value of benefit is greater than present value of costs. It means that if all thing happening today, benefits are greater, and therefore project is to be selected. It is important that NPV does not take into account relevant risk associated with project.

Positive NPV = PV of Benefits > PV of Cost

Example

Initial investment for a proposed = 300,000

First Year income from project =     180,000

Second Year Income from Project= 180,000

Cost of capital= 12%

Solution

                                Year 0            Years 1         Year 2

Initial investment            300,000

Income First Year                                           180,000

Income  2^nd Year                                                                        180,000

Discount Factor                (1+.12)^-0                       (1+.12)^-1                    (1+.12)^-2

PV                                      (300,000)              160,714             143,495

NPV = 160,714+143,495-300,000

=4,209

NPV Formula

NPV Formula

Net present value shortly known is NPV is calculated by deducting present value of cost from the present value of benefit. It is important to remember that benefits are cash inflows , where cost are cash outflows. The NPV formula can be mathematically expressed as under

NPV = PV Inflows- PV of Outflow

Example

Project cost = 50,000

Project income = 30,000

Calculate NPV?

Solution

PV of Cost = 50,000 x (1+12%) ⁰

= 50,000 x 1

= 50,000

PV of Benefit

  Years                                     1                               2               Total

Cash Flows                                   30,000                      30,000

Discount                                      (1+12%)^-1                          (1+12%)^-2

PV                                                  26,786                      23,916           50,702

NPV = 50,702-50,000

= 702