1
Basic Financial Calculations
1.1
Overview
This chapter aims to give you some finance basics and their Excel imple-
mentation. If you have had a good introductory course in finance, this
chapter is likely to be at best a refresher.
1
This chapter covers
•
Net present value (NPV)
•
Internal rate of return (IRR)
•
Payment schedules and loan tables
•
Future value
•
Pension and accumulation problems
•
Continuously compounded interest
Almost all financial problems center on finding the
value
today
of a
series of
cash
receipts
over
time
. The cash receipts (or cash flows, as we
will call them) may be certain or uncertain. The
present
value
of a cash
flow
CF
t
anticipated to be received at time
t
is
CF
r
t
t
(
)
1
+
. The numerator
of this expression is usually understood to be the
expected
time-t
cash
flow
, and the discount rate
r
in the denominator is adjusted for the riski-
ness of this expected cash flow—the higher the risk, the higher the dis-
count rate.
The basic concept in present-value calculations is the concept of
opportunity
cost
. Opportunity cost is the return that would be required
of an investment to make it a viable alternative to other, similar, invest-
ments. In the financial literature there are many synonyms for opportu-
nity cost, among them discount rate, cost of capital, and interest rate.
When the opportunity cost is applied to risky cash flows, we will some-
times call it the risk-adjusted discount rate (RADR) or the weighted
average cost of capital (WACC). It goes without saying that this discount
rate should be risk adjusted, and much of the standard finance literature
discusses how to make this adjustment. As illustrated in this chapter,
when we calculate the net present value, we use the investment’s oppor-
tunity cost as a discount rate. When we calculate the internal rate of
1.
In my book
Principles
of
Finance
with
Excel
(Oxford University Press, 2006), I have
discussed many basic Excel/finance topics at greater length.

4
Chapter 1
return, we compare the calculated return to the investment’s opportunity
cost to judge its value.
1.2
Present Value and Net Present Value
Both concepts, present value and net present value, are related to the
value
today
of a set of future anticipated cash flows. As an example,
suppose we are valuing an investment that promises $100 per year at the
end of this and the next four years. We suppose that there is no doubt
that this series of five payments of $100 each will actually be paid. If a
bank pays an annual interest rate of 10 percent on a five-year deposit,
then this 10 percent is the investment’s opportunity cost, the alternative
benchmark return to which we want to compare the investment. We may
calculate the value of the investment by discounting its cash flows using
this opportunity cost as a discount rate:
1
2
3
4
5
6
7
8
9
10
11
12
13
14
A
B
C
D
Discount rate
10%
Year
Cash flow
Present
value
1
100
90.9091 <--
=B5/(1+$B$2)^A5
2
100
82.6446 <--
=B6/(1+$B$2)^A6
3
100
75.1315 <--
=B7/(1+$B$2)^A7
4
100
68.3013 <--
=B8/(1+$B$2)^A8
5
100
62.0921 <--
=B9/(1+$B$2)^A9
Net present value
Summing cells C5:C9
379.08 <--
=SUM(C5:C9)

#### You've reached the end of your free preview.

Want to read all 35 pages?

- Summer '17