Ross et al.: Fundamentals
of Corporate Finance, Sixth
Edition, Alternate Edition
III. Valuation of Future
Cash Flows
- Discounted Cash Flow
Valuation
© The McGraw−Hill^229
Companies, 2002
After the child’s sixth birthday, no more payments are made. When the child
reaches age 65, he or she receives $175,000. If the relevant interest rate is
10 percent for the first six years and 6 percent for all subsequent years, is the
policy worth buying?
- Calculating a Balloon Payment You have just arranged for a $300,000 mort-
gage to finance the purchase of a large tract of land. The mortgage has a 9 per-
cent APR, and it calls for monthly payments over the next 15 years. However,
the loan has a five-year balloon payment, meaning that the loan must be paid off
then. How big will the balloon payment be?
- Calculating Interest Rates A financial planning service offers a college sav-
ings program. The plan calls for you to make six annual payments of $5,000
each, with the first payment occurring today, your child’s 12th birthday. Begin-
ning on your child’s 18th birthday, the plan will provide $15,000 per year for
four years. What return is this investment offering?
- Break-Even Investment Returns Your financial planner offers you two dif-
ferent investment plans. Plan X is an $8,000 annual perpetuity. Plan Y is a 10-
year, $20,000 annual annuity. Both plans will make their first payment one year
from today. At what discount rate would you be indifferent between these two
plans?
- Perpetual Cash Flows What is the value of an investment that pays $5,200
every otheryear forever, if the first payment occurs one year from today and the
discount rate is 14 percent compounded daily? What is the value today if the first
payment occurs four years from today?
- Ordinary Annuities and Annuities Due As discussed in the text, an annuity
due is identical to an ordinary annuity except that the periodic payments occur at
the beginning of each period and not at the end of the period (see Question 56).
Show that the relationship between the value of an ordinary annuity and the
value of an otherwise equivalent annuity due is:
Annuity due value Ordinary annuity value (1 r)
Show this for both present and future values.
- Calculating Annuities Due A 10-year annual annuity due with the first pay-
ment occurring at date t7 has a current value of $50,000. If the discount rate
is 13 percent per year, what is the annuity payment amount?
- Calculating EAR A check-cashing store is in the business of making personal
loans to walk-up customers. The store makes only one-week loans at 11 percent
interest per week.
a.What APR must the store report to its customers? What is the EAR that the
customers are actually paying?
b.Now suppose the store makes one-week loans at 11 percent discount interest
per week (see Question 60). What’s the APR now? The EAR?
c. The check-cashing store also makes one-month add-on interest loans at
8 percent discount interest per week. Thus, if you borrow $100 for one month
(four weeks), the interest will be ($100 1.08^4 ) 100 $36.05. Because
this is discount interest, your net loan proceeds today will be $63.95. You
must then repay the store $100 at the end of the month. To help you out,
though, the store lets you pay off this $100 in installments of $25 per week.
What is the APR of this loan? What is the EAR?
CHAPTER 6 Discounted Cash Flow Valuation 199
Challenge
(continued)
