LECTURE 4: VALUATIONS OF CASH FLOWS  PART 1
Make sure to look at the homework, which is due on the January 30th  11pm
ROADMAP FOR TODAY
The main goal of financial managers is to select investment projects that increase firm value
 However, project payoffs are expected in the future, but investment decisions must be made
today
 How to find the value of future cash flows’ worth today
 Today’s class: How much is a future cash flow worth today?
TIME VALUE OF MONEY
Apparent truism: “A dollar today is worth more than a dollar promised at some time in the future”
 Why is this actually true?
 The discount factor reflects the inflation, risk, and opportunity cost of capital
PRESENT VALUE OF A CASH FLOW
What is the present value of a cash flow of $100, which will be received 1 year ahead?
 Timeline helps visualize cash flows:

 Time on top of each tick
 Cash flows below the ticks
How to solve: draw a timeline, the time (end of year 0  year 1 is exactly one year from now)
 Discount the money by the discount rate  which will reflect compensation for the risk, inflation
(the purchasing power will decrease over time), and opportunity cost (you could have earned
interest from investing the money somewhere else)
PRESENT VALUE FORMULA
PV0 = present value (at time t=0) of cash flow Ct
Present value of a single cash flow:
What goes into the PV formula?
1) amount of cash flow (Ct)  cash flow C at time t in the future
2) number of time periods until this cash flow is received (t)  number of time periods
3) interest rate, also called the discount rate (r) (or the rate that equates the future value of the
money), expressed as a decimal
WHAT IS THE DISCOUNT RATE
 R = discount rate, “exchange rate” between earlier money and later money
 What determines the discount rate?
 Risk of the project (including inflation risk)
 Opportunity cost of capital
 How exactly do we compute the discount rate?  We will address this in detail when we study risk
 For now, we will treat the discount rate as given
 Computer  cost of company's debt, equity and capital structure  we need to have a very rigorous
portfolio assessment
 Drivers of the discount rate
EXAMPLE 1:
The money is only worth 90 today rather than 100 in the future
Excell:

VALUATIONS FORMULAS IN EXCEL
 Recurring regular payment, more than one time  mortga
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