**HP Prime: Combined Internal Rate of Return**

**Introduction**

An investor has several projects, each with their own initial
investments and discount rate. The net
present value is calculated (NPV) for each project. If the investor combined all the projects
into one set of cash flows, what is the effective internal rate of return
(IRR)? The program COMBIRR tackles this
question.

For example, an investor has the following projects, each
lasting five years:

Project A: NPV: -$3,500, discount rate: 10%

Project B: NPV: $18,000, discount rate: 12%

Project C: NPV: $20,000, discount rate: 9%

If the investor combines all three projects, what would be
the combined internal rate of return? I use
the following steps:

1. Calculate the NUS (net utility stream) of each project. Since we are only given the net present value
in this case, will need to determine a payment flow. The NUS calculates the cash flow of each
year, assuming they are equal.
Setup: N = number of years, I/YR
= discount rate, PV = -NPV, FV = 0, P/Y = 1.

2. Combine the
present values from each project, along with net utility streams calculated
from each project. Calculate IRR. Setup:
CF0 = -ΣNPV, Cash Flows = ΣNUS, frequency length of project

This procedure, like the program COMBIRR, assumes that each
project has the same length. With some
adjustments, you can calculate combined IRR using projects of the same length.

Going back to our example:

Project A: NPV: -$3,500, discount rate: 10%, NUS: -$569.61

Project B: NPV: $18,000, discount rate: 12%, NUS: $3,185.71

Project C: NPV: $20,000, discount rate: 9%, NUS: $3,116.40

ΣNPV: $34,500, ΣNUS: $5,732.50

Calculate IRR with CF0 = -34500.00, Cash Flows: 5,732.50 with a frequency of 5

Result: 10.49 (Combined IRR: 10.49%)

**How to Run COMBIRR:**

1. Enter the length of each of the projects. COMBIRR assumes each project has the same
length.

2. Enter the NPV and
discount RATE for the first project.
Each time the program will ask you “ENTRY?”. Select YES for additional entries, NO to stop
entering amounts.

3. The combined IRR
is calculated.

**HP Prime Program: COMBIRR**

sub1(); // data subroutine

EXPORT COMBIRR()

BEGIN

// EWS 2018-05-10

// Combined IRR using

// same length projects

// initialize

LOCAL L1,U,T,L,C;

LOCAL h,N,I;

// input

INPUT(L,"Number of
Periods",

"LEN: ");

// entry routine

REPEAT

L1:=sub1(); N:=L1(1); I:=L1(2);

T:=T-N;

U:=U+Finance.TvmPMT(L,I,−N,0,1);

CHOOSE(h,"ENTRY?","YES","NO");

UNTIL h==2;

// calculate combined IRR

C:=Finance.CashFlowIRR(

{T,{U,L}},1);

RETURN C;

END;

// data entry subroutine

sub1()

BEGIN

LOCAL x1,x2;

INPUT({x1,x2},"Data
Entry",

{"NPV: ","RATE:
"});

RETURN {x1,x2};

END;

Eddie

All original
content copyright, © 2011-2018. Edward
Shore. Unauthorized use and/or
unauthorized distribution for commercial purposes without express and written
permission from the author is strictly prohibited. This blog entry may be distributed for
noncommercial purposes, provided that full credit is given to the author. Please contact the author if you have
questions.

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