Internal Rate of Return (IRR) - Capital Budgeting

An alternative to using the Net Present Value (NPV) formula is to use the Internal Rate of Return (IRR) formula. Both of them are closely related because both of them depend on the discounted cash flows that come in from investment projects. For example, consider an investment costing $100 and bringing in cash flows of $110 in 1 year. You then ask, what is the return on this investment? The return on this easy calculation is 10$ which is 10%. Thus, the IRR is 10%.

What makes this a good investment? How do you know if the 10% return you achieved was good? This depends on what YOUR required rate of return is. If you expected your money to grow by 5%, then a 10% return is really good for you. However, if you expected a 15% return, and the investment only brings in a 10% return, this it is not good.

Thus, what's the rule of IRR? An investment project is "acceptable" if the IRR exceeds the required return (your required return). Otherwise, it is NOT acceptable and should be rejected. To illustrate this concept, lets go back to the question we did in the NPV chapter.

Q: XYZ Corporation has $25000 to invest. The following alternative investments and their annual cash flows are presented. The company's required rate of return is 8.3% interest compounded monthly. Which investment would you (as a financial manager) pick? Why?

Notes:

CFO = Initial Investment and is always entered as a negative (since the company is paying out the money). E.g an initial investment of $-10,000 means the company paid out that amount.

CO1 = Cash flow (in) for Year 1
CO2 = Cash flow (in) for Year 2
CO3 = Cash flow (in) for Year 3... etc

	A	B	C	D	E	F
CFO	-10000	-10000	-10000	-25000	-25000	-15000
CO1	800	-50	4000	8000	-500	4000
CO2	800	100	1000	8000	15000	4000
CO3	700	400	500	8000	15000	3000
CO4	700	400	500	1000	10000	3000
CO5	400	700	500	-500		2000
CO6	400	900	3000	-500
CO7	300	900	3000
CO8	200	4000
CO9	100
CO10	-50

In order to perform this calculation, we are going to use the BAII Plus Financial Calculator.

Investment A

In your calculator, type in 2nd -> CF

CFO = -10,000
CO1 = 800
FO1 = 1 (means cash flow for 1 year)
CO2 = 800
FO1 = 1
CO3 = 700
FO1 = 1
CO4 = 700
FO1 = 1
CO5 = 400
FO1 = 1
CO6 = 400
FO1 = 1
CO7 = 300
FO1 = 1
CO8 = 200
FO1 = 1
CO9 = 100
FO1 = 1
CO10 = -50
FO1 = 1

CPT -> IRR

I = 8.3% (this is the company's required rate of return)

IRR -> CPT = -18.37%

Investment B

In your calculator, type in 2nd -> CF

CFO = -10,000
CO1 = -50
FO1 = 1 (means cash flow for 1 year)
CO2 = 100
FO1 = 1
CO3 = 400
FO1 = 1
CO4 = 400
FO1 = 1
CO5 = 700
FO1 = 1
CO6 = 900
FO1 = 1
CO7 = 900
FO1 = 1
CO8 = 4000

CPT -> IRR

I = 8.3% (this is the company's required rate of return)

IRR -> CPT = -4.38%

Can you follow these steps to discount the cash flows for each of the Investments from C to F? If you do, you should get the following answers:

	A	B	C	D	E	F
Initial Investment	10000	10000	10000	25000	25000	15000
IRR	-18.37%	-4.38%	5.89%	-2.08%	17.39%	2.45%

The rules of IRR?

- If the IRR exceeds the required return, go ahead and do the project!
- If the IRR is below the required return, the project should NOT be done.

From the above investments ranging from A to F, which one would you go ahead and invest in?

Solution: Considering the rules of IRR, pick investment E because it is the only one that has an Internal Rate of Return (IRR) of 17.39%, which exceeds the required return of 8.3%. Therefore, reject all the other projects!