# Basic Financial Calculations

1.1 Overview

This chapter aims to give you some fi nance basics and their Excel implementation. If you have had a good introductory course in fi nance, 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 fi nancial problems center on fi nding the value today of a series of cash receipts over time. The cash receipts (or cash fl ows, as we will call them) may be certain or uncertain. The present value of a cash fl ow CFt anticipated to be received at time t is

CF

r

t

(1+ )t

. The numerator

of this expression is usually understood to be the expected time-t cash fl ow, and the discount rate r in the denominator is adjusted for the riskiness of this expected cash fl ow—the higher the risk, the higher the discount 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, investments. In the fi nancial literature there are many synonyms for opportunity cost, among them discount rate, cost of capital, and interest rate. When the opportunity cost is applied to risky cash fl ows, we will sometimes 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 fi nance literature discusses how to make this adjustment. As illustrated in this chapter, when we calculate the net present value, we use the investment’s opportunity cost as a discount rate. When we calculate the internal rate of return, we compare the calculated return to the investment’s opportunity cost to judge its value.

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