Internal Rate of Return

August 22, 2017

Minimum Attractive Rate of Return

Minimum Attractive Rate of Return (MARR) is an interest rate, at which our objective function is economically justified (usually positive).
The MARR is usually a policy issue that resolving following considerations:
The amount of money available for investment, and the source and cost of these funds.
The number of good projects available for investment and their purpose.
The amount of perceived risk associated with investment opportunities available to the firm.
The type of organization involved.

The PW method is based on the concept of equivalent worth of all cash flows relative to some base or beginning point in time called the present.
We write $PW$ as a function of interest rate, i.e. $PW(i)$.
\[ PW(i)=F_0(1+i)^0+F_1(1+i)^{-1}+\dots+F_N(1+i)^{-N}\\=\sum\limits_{k=0}^N F_k(1+i)^{-k}. \]

$i$ - effective interest rate of the project.
$F_k$ - future cash flow at the end of period $k$.
$N$ - number of compounding periods in the planning horizon
When we decide whether to undertake the project, we check the PW decision rule:
\[ PW(i=MARR)\geq 0 \]

A company has issued 10-year bonds, with a face value of $1,000,000 in $1,000 units. Interest at 8% is quarterly. If an investor desires to earn 12% nominal interest (compounded quarterly) on $10,000 worth of these bonds, what would the purchase price have to be?

Internal Rate of Return (IRR) is an interest rate that is found by equalizing the equiavalent worth of an alternative's cash inflows (receipts and savings) to the equivalent worth worth of cash outflows (expenditure, including investment cost).
\[ \sum\limits_{k=0}^N R_k(i)=\sum\limits_{k=0}^N E_k(i) \]

$R_k$ - net revenues or savings for the $k$th year.
$E_k$ - met expenditures, including any investment costs for the $k$th year.
$N$ - project life.
Once $i$ has been calculated the IRR decision rule is to check whether $i\geq MARR$. In this case, the project is economically justified.

A small start-up biotech firm anticipates that it will have cash outflows of $200,000 per year at the end of the next 3 years. Then the firm expects a positive cahs flow of $50,000 at the EOY 4 and positive cash flows of $250,000 at the EOY 5-9. Based on these estimates, would you invest money in this company if your MARR is 15% per year?

We considered decisions rules made in undertaking the projects such as Present Worth Method and Internal Rate of Return methods.
We showed how they relate to the subjective measure of attractiveness to the project, such as Minimum Attractive Rate of Return.