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Supplement
F Financial Analysis
1. Time Value of Money
Underlying concept:
1. Future value of an investment
a. Compounding interest
b. Future value of an investment
c. Formula
F = P(1+r)n
where
F =
P =
r =
n =
d. Application F.1: Future Value of an Investment
An investment of $500 will earn interest of 6%, compounded annually for 5 years. The
future value is:
F = P(1+r)n
where
P =
r =
n =
F =
2. Present value of an investment
a. Present value of a future amount
b. Discounting
c. The general formula is:
( )
1n
F
Pr
=+
3. Present value factors (pf)
• To find the present value of a future amount, write the above formula as:
( )
1
1n
PF r
=
+
• Multiply F by the present value factor (pf).
b. Application F.2: Present Value of a Future Amount
An investment will be worth $500 in 5 years. The interest rate is 6%. The present value
is:
( )
1n
F
Pr
=+
F =
r =
n =
P =
Solving instead using present value factor (pf) from the table:
P = F (pf)
pf =
P =
4. Annuities
a. Definition:
b. Present value of an annuity can be found using the present value factors of an annuity
table. Multiply the amount received each year (A) by the present value factor (af):
P = A (af)
c. Application F.3: Annuities
You wish to investment and amount that will allow you to withdraw $500 per year for 5
years. The interest rate is 6%. The present value of your investment is:
P = A (af)
A =
af =
P =
2. Methods of Financial Analysis
• Three basic financial analysis techniques
o Net present value method
o Internal rate of return method
o Payback method
1. Depreciation and taxes
a. Depreciation
b. Straight-line depreciation
D = (I
−
S) / n
c. Accelerated depreciation: The Modified Accelerated Cost Recovery System (MACRS)
• 3-year class
• 5-year class
• 7-year class
• 10-year class
d. Income-tax
2. Analysis of cash flows: Four steps
a. Step 1: Subtract the new expenses attributed to the project from new revenues.
Alternatively, use cost savings if revenues are not affected.
b. Step 2: Subtract the depreciation to get pre-tax income.
c. Step 3: Subtract taxes to get net operating income (NOI).
d. Step 4: Compute the total after-tax cash flow by adding back depreciation.
3. Net present value method (NPV)
a. NPV = the original investment – the present values of all after-tax cash flows.
b. Hurdle rate
c. Application F.4: Net Present Value from Project
A project under study involves the purchase of new equipment and has an initial cash
outflow of $1,550. After-tax cash inflow for the next 3 years is estimated to be:
The discount rate is 12%.
Present value of investment (Year 0)
= $
Present value of Year 1 cash flow
=
Present value of Year 2 cash flow
=
Present value of Year 3 cash flow
=
Project’s NPV
=
$
4. Internal rate of return (IRR) method
a. The discount rate that makes the NPV of a project zero.
b. Can be found by trial and error.
c. Application F.5: IRR for Project
Compute the internal rate of return for this project:
Discount
Rate
NPV
10%
$500 ( ) + $650 ( ) + $900 ( ) =
$
12%
$500 ( ) + $650 ( ) + $900 ( ) =
$
14%
$500 ( ) + $650 ( ) + $900 ( ) =
$
Conclusion:
5. Payback method
a. How long before the total after-tax cash flows will “pay back” initial investment?
b. Application F.6: Payback for Project
What is the payback period for this same project?
Payback for year 1
= $
Payback for years 1 and 2
= $
Proportion of year 3
= $
Payback periods for project
= years
6. Computer support
Example F.1
3. Using Judgment with Financial Analysis
• The danger is in a preference for short-term results.
• This can be the result of the precision and detachment that come from using the NPV, IRR, or
Payback methods and from the reality that projects with the greatest strategic impact may
have qualitative benefits that are difficult to quantify.
• Financial analysis should augment, not replace, the insight and judgment that comes from
experience.
