Practice Your FV and PV Skills
1. You just turned 35 and have been saving for an around-the-world vacation. You want to take
the trip to celebrate your 40th birthday. You have set aside, as of today, $15,000 for such a trip. You
expect the trip will cost $25,000. The financial instruments you have invested the $15,000 in have
been earning, on average, about 8%. (You may ignore income taxes.)
a. Will you have enough money in that vacation account on your 40th birthday to take the trip?
What will be the surplus, or shortfall, in that account when you turn 40? (Hint: Exhibit 1 will be useful
in answering this question.)
b. If you had to, you could further fund the trip by making, starting today, five annual
$500 contributions to the account. If you adhered to such a plan, how much will be in the account on
your 40th birthday? (Hint: Exhibit 3 and the answer to part (a) above will both be useful in answering
this question.)
2. Your company has been offered a contract for the development and delivery of a solar-
powered military troop transport vehicle. The request for proposal provides all the necessary
technical specifications and it also stipulates that two working, economically feasible prototypes must
be delivered in four years, at which time you will receive your only customer payment—a single and
final payment of $50 million. Assume a reinvestment interest rate of 18% for all the monies received
over the next four years. (You may ignore income taxes.)
4 Appendix 2 shows how to adjust the data in Exhibit 4 for cash flows at the beginning (instead of the
end) of the year.
a. What lump-sum dollar amount would you be willing to accept today instead of the
$50 million in four years? (Hint: Exhibit 2 will be useful in answering this question.)
b. Alternatively, what four yearly receipts, starting a year from now, would you be willing to
accept? (Hint: Exhibit 4 and the answer to part (a) above will both be useful in answering this
question.)
3. The aged but centrally located golf course you manage does not have an in-ground automated
water sprinkling system. Instead, to properly water the course, sprinklers and hoses must be
repeatedly set, moved, and put away by some of the grounds crew—a tedious and laborious task. If
over the next 12 years you project annual savings of about
$40,000 from having an automated system, what is the maximum price you would be willing to pay
today for an installed, automated golf course sprinkler system? (Assume an interest rate of 6%, and
you may ignore income taxes.)
a. Redo your calculation using a 10-year time period and $48,000 in annual savings.
b. Redo your initial calculation one more time using $50,000 in annual savings for the first six
years and $30,000 in annual savings for the next six years.
4. The cafeteria you operate has a regular clientele for all three meals, seven days a week. You
want to expand your product line beyond what you are currently able to offer. To do so requires the
purchase of some additional specialty equipment costing $45,000, but you project a resultant increase
in sales (after deducting the cost of sales) of about $8,000 per year for each of the next eight years
with this new equipment. Assuming a required rate of return (i.e., a hurdle rate) of 8%, should you
pursue this opportunity? Why or why not? Do the analysis under two conditions:
a. You are part of an income-tax-exempt enterprise.
b. The enterprise you are part of is subject to a 40% corporate income tax rate, and the straight-
line, depreciable life of the equipment you are contemplating purchasing is five years.
5. You are contemplating the purchase of a one-half interest in a corporate airplane to facilitate
the expansion of your business into two new geographic areas. The acquisition would eliminate about
$220,000 in estimated annual expenditures for commercial flights, mileage reimbursements, rental
cars, and hotels for each of the next 10 years. The total purchase price for the half-share is $6 million,
plus associated annual operating costs of
$100,000. Assume the plane can be fully depreciated on a straight-line basis for tax purposes over 10
years. The company’s weighted average cost of capital (commonly referred to as WACC) is 8%, and its
corporate tax rate is 40%. Does this endeavor present a positive or negative net present value (NPV)?
If positive, how much value is being created for the company through the purchase of this asset? If
negative, what additional annual cash flows would be needed for the NPV to equal zero? To what
phenomena might those additional positive cash flows be ascribable?
6. The final tally is in: This year’s operating costs were down $100,000, a decrease directly
attributable to the $520,000 investment in the automated materials handling system put in
place at the beginning of the year. If this level of annual savings continues for five more years,
resulting in six total years of annual savings, what compounded annual rate of return will that
represent? If these annual savings continue for nine more years, what compounded annual rate of
return will that represent? (You may ignore income taxes.)
