Introduction to Corporate Finance

Ross et al.: Fundamentals

of Corporate Finance, Sixth

Edition, Alternate Edition

III. Valuation of Future

Cash Flows

6. Discounted Cash Flow
   Valuation

(^198) © The McGraw−Hill
Companies, 2002
Finding the Payment Suppose you wish to start up a new business that specializes in
the latest of health food trends, frozen yak milk. To produce and market your product, the
Yakkee Doodle Dandy, you need to borrow $100,000. Because it strikes you as unlikely
that this particular fad will be long-lived, you propose to pay off the loan quickly by mak-
ing five equal annual payments. If the interest rate is 18 percent, what will the payment be?
168 PART THREE Valuation of Future Cash Flows
SPREADSHEET STRATEGIES
Annuity Present Values
Using a spreadsheet to find annuity present values goes like this:
1 2 3 4 5 6 7 8 9
10
11
12
13
14
15
16
17
ABCDEFG
Whatisthepresentvalueof$500peryearfor 3 yearsifthediscountrateis1 0percent?
Weneedtosolvefortheunknownpresentvalue,soweusetheformulaPV(rate ,nper,pmt,fv).
Paymentamountperperiod: $500
Numberofpayments: 3
Discountrate: 0.1
Annuitypresentvalue: $1,243.43
TheformulaenteredincellB11is=PV(B9,B8,-B7,0);noticethatfviszeroandthat
pmthasanegativesignonit.Alsonoticethatrateisenteredasadecimal,n otapercentage.
Using a spreadsheet to find annuity present values

CALCULATOR HINTS

Annuity Present Values

To find annuity present values with a financial calculator, we need to use the key

(you were probably wondering what it was for). Compared to finding the present value of a

single amount, there are two important differences. First, we enter the annuity cash flow us-

ing the key, and, second, we don’t enter anything for the future value,. So, for ex-

ample, the problem we have been examining is a three-year, $500 annuity. If the discount

rate is 10 percent, we need to do the following (after clearing out the calculator!):

As usual, we get a negative sign on the PV.

N %i PMT PV FV

Enter 3 10 500

Solve for 
1,243.43

PMT FV

PMT