Capital Budgeting Rule

• We still assume that market is ‘perfect’

Definition of Capital Budgeting Rule:

: is a method to decide which projects to take and which to reject.

• accept project iff NPV > 0

What should happen in the real world : if NPV > 0 project was abundant, interest rate will adjust and NPV = 0

Separation theorem

Your needs for cash (or other stuff) will not effect the NPV of a project! Suppose you want ice-cream for $100, and project A will generate 25$ of NPV. Then, you can buy project A, make profit by re - selling it, to generate more cash.

Investment decision and consumption decision can be separated.

Q1 : What is the holding rate of return on a project that costs $13.16 m, and pays $7 m next year, followed by $8 m the year after?

Internal rate of Return (IRR):

To answer previous question, we need a measure that generalized the rate of return.

$! 0 = C_0 + \frac{E(C_1)}{1 + IRR} + \frac{E(C_2)}{(1 + IRR)^2} + \frac{E(C_3)}{(1 + IRR)^3} + ... $!

in the context of bonds, IRR is called Yield - to Maturity.

The concept of IRR:

• The IRR is not a rate of return, because we defined rate of return as “holding rate of return” obtained from investing $$C_0$$ and obtaining $$C_1$$.

• IRR is a characteristic of a project’s cash flows. It maps from summary statistics of many cash flows into one single number.

• Higher IRR means more profitable.

There are some cases where NPV < 0, thus no IRR.

Q2 : If the cash flow were -100, 205, -102, what is the IRR?

There can be multiple IRR for this. This isn’t always the problem, but just be aware that this is the case.

IRR as a Capital Budgeting Rule.

If project begins with money out, and followed by money in, Invest if $$ IRR > r $$

If project begins with money in, and followed by money out, Borrow if $$IRR < r$$

The advantage is: we can talk about the quality of the project with one number, easy to compare.

Also, it does not depend on scale. If cost of capital change, in case of NPV you have to recalculate the whole thing. IRR doesn’t have this issue.

Q3 : There are 2 projects:

A : 1 : -80, 2: 50, 3: 100 B : 1 : -85, 2: 100, 3: 45

Assume that cost of capital is 20%. This makes

$$NPV_A = \$ 31.1 $$

$$NPV_B = \$ 29.58 $$

However, IRR of B is greater! This is problematic. Here, we just use NPV to evaluate. Also, sometimes IRR can’t be used because cost of capital change during time.

Profitability Index

$! PI = \frac{PV(7,8,20\%)}{13.16} = 0.8655 $! PI is PV/cost. Invest if PI > 1, Reject if PI < 1.

Other Investment Rules Payback Period:

It measures how long it takes to get your money back.

It may be useful if managers are trusted to provide good estimates of far our future cash flows.

It is also good if if capital is highly constrained, and if financial markets are not at all perfect.

Do people use these methods?