Ross et al.: Fundamentals
of Corporate Finance, Sixth
Edition, Alternate EditionIII. Valuation of Future
Cash Flows- Discounted Cash Flow
Valuation
(^200) © The McGraw−Hill
Companies, 2002
Finding the Rate The last question we might want to ask concerns the interest rate im-
plicit in an annuity. For example, an insurance company offers to pay you $1,000 per year
for 10 years if you will pay $6,710 up front. What rate is implicit in this 10-year annuity?
In this case, we know the present value ($6,710), we know the cash flows ($1,000 per
year), and we know the life of the investment (10 years). What we don’t know is the dis-
count rate:
170 PART THREE Valuation of Future Cash Flows
Finding the Number of Payments
You ran a little short on your spring break vacation, so you put $1,000 on your credit card. You
can only afford to make the minimum payment of $20 per month. The interest rate on the
credit card is 1.5 percent per month. How long will you need to pay off the $1,000?
What we have here is an annuity of $20 per month at 1.5 percent per month for some un-
known length of time. The present value is $1,000 (the amount you owe today). We need to do
a little algebra (or else use a financial calculator):
$1000 $20 [(1 Present value factor)/.015]
($1,000/20) .015 1 Present value factor
Present value factor .25 1/(1 r)t
1.015t1/.25 4
At this point, the problem boils down to asking the question, How long does it take for your
money to quadruple at 1.5 percent per month? Based on our previous chapter, the answer is
about 93 months:
1.015^93 3.99 4
It will take you about 93/12 7.75 years to pay off the $1,000 at this rate. If you use a fi-
nancial calculator for problems like this one, you should be aware that some automatically
round up to the next whole period.
EXAMPLE 6.6
CALCULATOR HINTS
Finding the Number of Payments
To solve this one on a financial calculator, do the following:Notice that we put a negative sign on the payment you must make, and we have solved for
the number of months. You still have to divide by 12 to get our answer. Also, some financial
calculators won’t report a fractional value for N; they automatically (without telling you) round
up to the next whole period (not to the nearest value). With a spreadsheet, use the function
NPER(rate,pmt,pv,fv); be sure to put in a zero for fv and to enter 20 as the payment.N %i PMT PV FV1.5 20 1,000
93.11
EnterSolve for