### Capital Investment Decisions and the Time Value of Money

```Chapter 21
1
Describe the importance of capital
investments and the capital budgeting process
Use the payback period and rate of return
methods to make capital investment decisions
Use the time value of money to compute the
present and future values of single lump sums
and annuities
Use discounted cash flow models to make
capital investment decisions
2
1
Describe the importance of capital investments
and the capital budgeting process
3
Last chapter
looked at
recurring parallel
options
Took place in
the same time
sequence
Revenues and
expenses
primarily
This chapter we
remove that
timing restriction
Any time you
want
Revenues,
expenses, and
investments
How do we compare return and investment if they
come in different amounts at different times?
4
Should we make the capital investment?
Should we
open another
store or open
an online
store?
Should we
install solar
panels?
5
Should we
start this new
Should we
rebuild?
Simple techniques
The payback method
(Simple) rate of return (ROR)
Techniques using time value of money
Present & future value of a single amount (lump sum)
Present & future value of a payment stream (annuity)
Net present value (NPV)
Profitability index
Internal rate of return (IRR)
What we won’t look at today
Sensitivity analysis
Monte Carlo analysis
Our simple and TVM techniques cover virtually
all of the analysis needs most of us are likely to
ever need.
2
Use the payback and rate of return methods to
make capital investment decisions
9
Measures how quickly managers expect to
recover their investment dollars
The shorter the payback period, the more
attractive the investment
Used to screen capital investment choices
May be the only tool in simple situations
10
If the project provides equal annual returns, then
use this formula:
11
Unequal annual net cash inflows
Total net cash inflows until the amount invested
is recovered
12
Consider the following two investment options for
the My Coffee:
Sell Caffe Rent Caffe
Machines Machines
Initial investment
\$100,000 \$100,000
Year 1 net cash inflows
\$50,000
\$30,000
Year 2 net cash inflows
\$50,000
\$30,000
Year 3 net cash inflows
\$50,000
\$30,000
Year 4 net cash inflows
\$50,000
\$30,000
Years 5-10 net cash inflows
\$0
\$30,000
Based on the payback period.
Which project would you prefer and why?
So much better than nothing
Emphasis on payback, not additional profits
Easy story telling, good for sales
Ignores cash flows after the payback period
An experienced user can do well with it
Requires human thought “seat of the pants”
15
ROR measures the average accounting rate of return
over the asset’s entire life
Focuses on the operating income, from the financials
Maximize reported profitability, not necessarily cash flows
Formula
Average annual operating income
The asset’s total operating income over the course of its
operating life divided by its lifespan
Average amount invested
Net book value at the beginning of the asset’s useful life
plus the net book value at the end of the asset’s useful life
divided by 2
16
Preston, Co. is considering buying a
manufacturing plant for \$1,100,000.
They expect the plan to generate average annual
cash inflows of \$297,000 for 6 years.
They expect to salvage the obsolete factory for
\$550,000 after 6 years.
What is the rate of return of this project?
17
18
3
Use the time value of money to compute the present
and future values of single lump sums and annuities
25
Invested money earns income over time
Timing of capital investments’ net cash inflows
is important
Two methods of capital investment using TVM
The net present value (NPV)
Internal rate of return (IRR)
26
Let’s take a look at what those fancy tables do
on the board!
Watch closely as
I turn \$1 into \$2!
i=15%, N=5
Simple interest
Interest calculated only on the principal amount
Compound interest
Interest is calculated on the principal and on all previously
earned interest
Assumes that all interest earned will remain invested and
earn additional interest at the same interest rate
Capital investments yield compound interest
Assume compounding interest for rest of this chapter
29
The value of an investment at different points in
time
30
Simplify present and future value math
See Appendix B for present and future factor
tables:
Let’s play with the future value table first.
31
Lump sum
Multiply amount by the factor number found in
table
Table based on interest rate and number of periods
\$10,000 invested for 5 periods at 6%
\$10,000 X 1.3382 = \$13,382 Differences due to table decimal places
32
If you invested \$1,000 today into a 6% fixed rate
security, how much would it be worth in 50
years?
Draw a time line indicating knowns and unknowns
Identify table needed and go to it
Look up the factor for the rate and time indicated
Set up the formula and calculate
33
Lump sum
Multiply amount by the factor found in table
Table based on interest rate and number of periods
\$13,383 to be received in 5 periods at 6%
\$13,382 X 0.7473 = \$10,000 Differences due to table decimal places
34
How much would you have to invest today so
that you could buy a \$10,000 car for cash 5
years from today? We earn 3% on our money.
Draw a time line indicating knowns and unknowns
Identify table needed and go to it
Look up the factor for the rate and time indicated
Set up the formula and calculate
35
Annuity: A cash flow that occurs in identical
amounts at repeating intervals.
You could take each and every year and calculate
present/future values for each year…..
OR, you could recognize the annuity and take just
one calculation using the annuity table.
Present
Value
\$100
\$100
\$100
\$100
Future
\$100 Value
\$100
?
?
1
2
3
4
5
6
If we Invest \$2,000 at 6%, at the end of each year for 5
years, how much do we have at the end?
\$2,000
X 5.6371
11,274.20
37
How much do we need to squirrel away today , so we
can pull \$2,000 out to spend at the end of every year for
5 years? Assume 6% interest.
\$8,424
\$2,000
X 4.212
\$8.424
38
Draw a time line indicating knowns and unknowns
Identify table needed and go to it
Look up the factor for the rate and time indicated
Set up the formula and calculate
How much do you need?
Annual expenditure expectations
Solve for balance at the beginning of retirement
How are you going to get it there?
Lump sum deposit now
Annual retirement contributions
39
4
Use discounted cash flow models to make
capital investment decisions
40
Payback and ROR do not recognize time value
of money
Net present value (NPV) and internal rate of
return (IRR) do recognize time value of money
Both compare amount of investment with its
expected net cash inflows
Cash outflow for investment usually occurs now
Cash inflows usually occur in the future
Companies use present value to make the
investment comparison, not future value
41
NPV—the net difference between the present
value of the investment’s net cash inflows and
the investment’s cost (cash outflows)
Discount rate—the interest rate that discounts or
reduces future amounts to their lesser value in the
present (today).
Discount rate uses the firms desired rate of return
Based on cost of capital
If present value of the investment’s net cash
inflows exceeds the initial cost of the investment,
then it is a good investment
42
for cash.
Cost \$10,000
Lease the welder
for \$1,500/year
for 10 years
Assume:
Discount rate 10%
Zero salvage
Average welder life in our
hands is 10 years.
Investment required: \$250,000
Annual earnings of \$50,000
You will own it for 20 years.
You will then sell it for \$1,000,000.
Your cost of capital is 10%
What is the NET present value of this project?
Harley Davidson
Purchase cost
\$25,000
Salvage value
\$17,000
Annual costs \$500
more than
Kawasaki.
Kawasaki
Purchase cost
\$12,000
Salvage value
\$1,000
Assume you win the lottery
Option #1: \$1,000,000 now
Option #2: \$150,000 the end of each year for next ten years
Option #3: \$2,000,000 ten years from now
Which option is the best?
Use PV factors for single sum and annuities to find out
Option #1 is \$1,000,000 in your hand today
Option #2 is an annuity, 10 payments
Using PV annuity tables, assuming 8%
\$150,000 x 6.7101 = \$1,006,515
10 payments yield a present value of
\$1,006,515 and more than \$1,000,000
46
Assume you win the lottery
Option #1: \$1,000,000 now
Option #2: \$150,000 the end of each year for next ten years
Option #3: \$2,000,000 ten years from now
Use PV factors for single sum to find out what option
#3 is worth today
Option #3 \$2,000,000 x .4632 = \$ 926,400
Option #1 = \$1,000,000
Option #2 = \$1,006,515
Option #3 = \$ 926,400
Option #2 is the highest of the three
47
Computes the number of dollars returned for
every dollar invested
Profitability index =
55
Present value of net cash inflows
Investment
Another discounted cash flow model for capital
budgeting
Rate of return a company can expect to earn by
investing in the project
The interest rate that will cause the present value
to equal zero
Present value of the investment’s net cash inflows
– Investment’s cost (Present value of cash outflows)
\$0
58
The internal rate of return measures the real rate
of return provided by the project.
Higher return better
Lower return worse
59
Year(s)
Flow
Type
Present
Cash
Discount Value of
Flow
Rate &
Cash
Amount Factor
Flow
12%
0
Lump
-18600
1
-18600
6
Annuity
5000
4.111
20555
6
Lump
9125
0.507
4626
Net Present Value
6581
NPV is easier to use.
NPV Provides \$\$ results to
compare: \$\$ pay the bills!
IRR provides a
comparable % return vs.
strict dollar value. This
can facilitate better
evaluation of different
scale/size/cost projects.
Too much voodoo math?
Capital budgeting is planning to invest in long-term
assets in a way that returns the greatest profitability to
the company. Capital rationing occurs when the
company has limited assets available to invest in longterm assets. The four most popular capital budgeting
techniques used are payback period, rate of return
(ROR), net present value (NPV), and internal rate of
return (IRR).
72
The payback period focuses on the time it takes for
the company to recoup its cash investment, but
ignores all cash flows occurring after the payback
period. Because it ignores any additional cash flows
(including any residual value), the method does not
consider the profitability of the project. The ROR,
however, measures the profitability of the asset over
its entire life using accrual accounting figures. It is the
only method that uses accrual accounting rather than
net cash inflows in its computations. The payback
period and ROR methods are simple and quick to
compute, so managers often use them to screen out
undesirable investments. However, both methods
ignore the time value of money.
73
Invested money earns income over time. This is called
the time value of money, and it explains why we
would prefer to receive cash sooner rather than later.
The time value of money means that the timing of
capital investments’ net cash inflows is important. The
cash inflows and outflows are either single amounts or
annuities. An annuity is equal cash flows over equal
time periods at the same interest rate. Time value of
money tables in Appendix B help us to adjust the cash
flows to the same time period (i.e., today or the
present value, or a future date or the future value).
74
The NPV is the net difference between the present
value of the investment’s net cash inflows and the
investment’s cost (cash outflows), discounted at the
company’s required rate of return (hurdle) rate. The
investment must meet or exceed the hurdle rate to be
acceptable. The IRR is the interest rate that makes the
cost of the investment equal to the present value of the
investment’s net cash inflows. Capital investment
(budgeting) methods that consider the time value of
money (like NPV and IRR) are best for decision
making.
75