IFT Notes for Level I CFA^® Program

R28 Uses of Capital

Part 2

3. Investment Decision Criteria

3.1 Net Present Value

Net present value is the present value of the future after tax cash flows minus the investment outlay.

$NPV=CF0\ +\ \left[\frac{CF1}{{\left(1+r\right)}^1}\right]+\ \left[\frac{CF2}{{\left(1+r\right)}^2}\right]+\ \left[\frac{CF3}{{\left(1+\ r\right)}^3}\right]$

Decision rule:

For independent projects:

If NPV > 0, accept.

If NPV < 0, reject.

For mutually exclusive projects:

Accept the project with higher and positive NPV.

Example

Compute NPV for projects A and B given the following data:

Cost of capital = 10%
Expected Net after Tax cash flows
Year	Project A (in $)	Project B (in $)
0	-1,000	-1,000
1	500	100
2	400	300
3	300	400
4	100	600

Solution:

Project A:

NPV = $-1000 + \frac{500}{1.1} + \frac{400}{{1.1}^2} + \frac{300}{{1.1}^3} + \frac{100}{{1.1}^4}$ = 78.82$

On the exam, you can save time by using the calculator to solve for NPV instead of using the above formula. The key strokes are given below:

Key strokes	Display
[CF][2^nd][CLR WORK]	CF0 = 0
1000 [+\|-] [ENTER]	CF0 = -1000
[↓] 500 [ENTER]	C01 = 500
[↓]	F01 = 1
[↓] 400 [ENTER]	C02 = 400
[↓]	F02 = 1
[↓] 300 [ENTER]	C03 = 300
[↓]	F03 = 1
[↓] 100 [ENTER]	C04 = 100
[↓]	F04 = 1
[NPV] 10 [ENTER]	I = 10
[↓] CPT	NPV = 78.82

Project B:

NPV = $-1000 + \frac{100}{1.1} + \frac{300}{{1.1}^2} + \frac{400}{{1.1}^3} + \frac{600}{{1.1}^4}$ =49.18

3.2 Internal Rate of Return (IRR)

IRR is the discount rate that makes the present value of future cash flows equal to the investment outlay. We can also say that IRR is the discount rate which makes NPV equal to 0.

Decision rule:

For independent projects:

If IRR > required rate of return (usually firms cost of capital adjusted for projects riskiness), accept the project.

If IRR < required rate of return, reject the project.

The required rate of return is also called hurdle rate.

For mutually exclusive projects:

Accept the project with higher IRR (as long as IRR > cost of capital).

Example

Compute IRR for projects A and B given the following data.

Cost of Capital = 10%; Expected Net After Tax Cash Flows
Year	Project A (in $)	Project B (in $)
0	-1,000	-1,000
1	500	100
2	400	300
3	300	400
4	100	600

Solution:

Project A:

A very tedious method is to set up the equation below and solve for r using trial and error.

$1000 = \frac{500}{1\ +\ r} + \frac{400}{{\left(1\ +\ r\right)}^2} + \frac{300}{{\left(1\ +\ r\right)}^3}\ + \frac{100}{{\left(1\ +\ r\right)}^4}$ r = 14.49%

A much faster method is to use the calculator:

Key strokes	Display
[CF][2^nd][CLR WORK]	CF0 = 0
1000[+\|-] [ENTER]	CF0 = -1000
[↓] 500 [ENTER]	C01 = 500
[↓]	F01 = 1
[↓] 400 [ENTER]	C02 = 400
[↓]	F02 = 1
[↓] 300 [ENTER]	C03 = 300
[↓]	F03 = 1
[↓] 100 [ENTER]	C04 = 100
[↓]	F04 = 1
[IRR][CPT]	14.49