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

© The McGraw−Hill^199

Companies, 2002

CHAPTER 6 Discounted Cash Flow Valuation 169

In this case, we know the present value is $100,000. The interest rate is 18 percent,
and there are five years. The payments are all equal, so we need to find the relevant an-
nuity factor and solve for the unknown cash flow:

Annuity present value $100,000 C[(1 
Present value factor)/r]

C{[1 
(1/1.18^5 )]/.18}

C[(1 
.4371)/.18]

C3.1272

C$100,000/3.1272 $31,977

Therefore, you’ll make five payments of just under $32,000 each.

CALCULATOR HINTS

Annuity Payments

Finding annuity payments is easy with a financial calculator. In our example just

above, the PV is $100,000, the interest rate is 18 percent, and there are five years. We

find the payment as follows:

Here we get a negative sign on the payment because the payment is an outflow for us.

N %i PMT PV FV

Enter 5 18 100,000

Solve for 
31,978

SPREADSHEET STRATEGIES

Annuity Payments

Using a spreadsheet to work the same problem goes like this:

1 2 3 4 5 6 7 8 9

10

11

12

13

14

15

16

ABCDEFG

Whatistheannuitypaymentifthepresentvalueis$100,000,theinterestr ateis 18 percent,and

thereare 5 periods?Weneedtosolvefortheunknownpaymentinanannuity,s oweusethe

formulaPMT(rate,nper,pv,fv).

Annuitypresentvalue: $100,000

Numberofpayments: 5

Discountrate: 0.18

Annuitypayment: $31,977.78

TheformulaenteredincellB12is=PMT(B10,B9,-B8,0);noticethatfvisze roandthatthepayment

hasanegativesignbecauseitisanoutflowtous.

Using a spreadsheet to find annuity payments