First Lecture.pdf - 1 1.1 Basic Financial Calculations Overview This chapter aims to give you some finance basics and their Excel implementation If you

First Lecture.pdf - 1 1.1 Basic Financial Calculations...

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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.
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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)
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