The current worth of a future sum of money or stream

The current worth of a future sum of money or stream of cash flows given a
specified rate of return.
•
To compute the PV of money you’ll receive some years from now, a
discount rate is applied
–
PV = FV/(1+r)
n
–
If someone offered you $500 today or $1000 in ten years, and
inflation is
3%, which would you take?
–
What if inflation rate is 1%? Or 8%?
Future cash flows are discounted at the discount rate :
-
Reflects time value of money, risk or uncertainty of future cash flows
-
More uncertainty of cash flows: the higher the discount rate and lower the
PV
of future cash flows

DCF Concept: Future Value
Future Value :
The value of an asset or cash at a specified date in the future that
is equivalent in value to a specified sum today.
•
Most common application of is compounding:
–
The Future Value of money you have today at an interest
rate
–
FV = PV x (1+r)
n
(r = interest rate, n = # periods)
–
Exampl e: $1000 invested today, Interest rate =
10%, Time = 5 years would have a Future Value of
$1,611.00.

FV
PMT
1 2 3 4 … n
0
…
Concept
PV
= $1000
5 years
= $1611
r = 10%

Compounding and Discounting
•
The future value received in a year, from $1 invested
today at 10%, is $1.10.
•
The present value of $1.10 to be paid in a year when the
interest rate is 10% is $1.
•
With compounding, the future value received in 2 years,
from $1 invested today at 10%, is $1.21 = 1 x 1.1 x 1.1.
•
In reverse, the present value of $1.21 to be paid in two
years when the interest rate is 10% is obtained by dividing
the 1.21 by 1.1
2
.

Uses
•
You expect sales will grow so you will need more product.
Is it better to build a plant or “rent” the capacity from
someone else?
•
You want to buy another company and merge it with yours.
Will your increased profitability over time be worth the cost?
What else could you do with the money?
•
We’ve developed a new technology. It will take many
years and a lot of money to bring to market. Will the
expected future sales be worth the investment?
•
Other examples?

Formulas

DCF Steps -> Figures of Merit
Steps:
1. Estimate the relevant cash flows.
2. Calculate the rate of return for the investment.
3. Compare the returns to your acceptance criterion.
But:
4. Step #1 is challenging.
5. Doing it well requires a thorough understanding of the
company ’ s markets, competitive position, and long-run
intentions.
6. Potential estimation difficulties arise with depreciation,
financing costs, working capital investments, shared
resources, excess capacity, contingent opportunities, etc….

Cash Flows for Container-Loading Pier ($M)

Cash Flow Diagram for
Container-Loading Pier

Payback Period & Accounting Rate of
Return, and Related Issues
Concepts:
•
Payback Period : Amount of time the company must wait before
recouping its original investment.
– The pier ’ s payback period is 5 1/3 years ($40M / $7.5M).