Principles of Managerial Finance

168 PART 2 Important Financial Concepts

In Practice

For almost 3,000 car dealers,

December 2000 marked the end of

a 103-year era. General Motorsan-

nounced that it would phase out

the unprofitable Oldsmobile brand

with the production of the 2004

model year—or sooner if demand

dropped too low. GM entered into

a major negotiation with owners of

Oldsmobile dealerships to deter-

mine the value of the brand’s deal-

erships and how to compensate

franchise owners for their invest-

ment. Closing out the Oldsmobile

name over the 4-year period could

cost GM $2 billion or more, de-

pending on real estate values, the

future value of lost profits, and

leasehold improvements.

As they waited to see what

would happen, many Olds dealers

voiced concern about recent

expenditures to upgrade their

facilities to comply with GM stan-

dards. They also wondered about

the franchise’s viability during the

phase-out. After all, how many

customers will want to buy

Oldsmobiles, knowing the brand is

being discontinued?

In a letter to dealers, William

J. Lovejoy, GM’s North American

group sales vice president, says

GM will repurchase all unsold

Olds vehicles regardless of model

year, as well as unused and un-

damaged parts; will remove and

buy back all signage; and will

buy back essential tools but let

dealers retain tools exclusively

designed for Olds products. By

mid-2001, GM had offered Olds

dealers cash to surrender fran-

chises, up to about $2,900 per Olds

sold during the best year between

1998 and 2000.

Cal Woodward, a CPA with

expertise in dealership account-

ing, worked with the negotiating

team to develop an appropriate list

of requests. He recommended that

they include reimbursement for the

present value of future profits they

will lose as a result of the closing

of their Oldsmobile franchises and

for reduced profits or losses in the

interim period. Mr. Woodward

suggested that they use a 9 per-

cent interest factor to calculate

the present value of 10 years of in-

cremental franchise profits.

Sources: Adapted from James R. Healey and

Earle Eldridge, “Good Olds Days Are

Numbered,”USA Today (September 10,

2001), p. 6B; Maynard M. Gordon, “What’s an

Olds Franchise Worth?” Ward’s Dealer

Business (February 1, 2001), p. 40; Al

Rothenberg, “No More Merry Oldsmobile,”

Ward’s Auto World (March 1, 2001), p. 86.

FOCUS ONPRACTICE Farewell to the Good “Olds” Days

Finding the Future Value of an Annuity Due

We now turn our attention to annuities due. Remember that the cash flows of an

annuity due occur at the start of the period.A simple conversion is applied to use

the future value interest factors for an ordinary annuity (in Table A–3) with

annuities due. Equation 4.17 presents this conversion:

FVIFAi,n(annuity due)FVIFAi,n(1i) (4.17)

This equation says that the future value interest factor for an annuity due can

be found merely by multiplying the future value interest factor for an ordinary

annuity at the same percent and number of periods by (1i). Why is this adjust-

ment necessary? Because each cash flow of an annuity due earns interest for one

year more than an ordinary annuity (from the start to the end of the year). Multi-

plying FVIFAi,nby (1i) simply adds an additional year’s interest to eachannu-

ity cash flow. The following example demonstrates how to find the future value

of an annuity due.

EXAMPLE Remember from an earlier example that Fran Abrams wanted to choose

between an ordinary annuity and an annuity due, both offering similar terms

except for the timing of cash flows. We calculated the future value of the ordi-

nary annuity in the example on page 164. We now will calculate the future value

of the annuity due, using the cash flows represented by annuity B in Table 4.1

(page 163).