2_2SP04
January 11, 2008
1
Present Value Measurements and “Hicksian” Income
Gaines Ville is considering purchasing a business venture on December 31, Year 0.
If she does
so, she will receive cash (gross) at the end of each year as follows:
Year
Amount
1
$14,000
2
16,000
3
12,000
4
10,000
$52,000
To receive the cash, however, it will be necessary for her to make gross cash payments for assets
and/or services at the end of each year as follows:
Year
Amount
1
$
3,000
2
4,000
3
9,000
4
2,000
$18,000
At the end of the four years this business will have no value. The short duration used here (rather
than a going concern assumption), and the assumption that all payments are made at the end of
the year are solely to simplify computations, i.e., they do not affect the basic idea with which we
are concerned.
After evaluating the risk of this business, Gaines is willing to pay a price that
would secure her a 5% return on investment. This particular business requires no cash on hand
(in general, cash is necessary/desirable because receipts and disbursements do not occur
simultaneously and because of the uncertainty as to the amount and timing of the receipts and
disbursements – however, neither situation exists here).
As a result Gaines withdraws all excess
(net) cash each year, either to consume herself, and/or to invest in another venture.
Upon the purchase of the business, Gaines will be entitled to receive a total of $52,000, but she
will be obligated to pay out $18,000.
The
net
cash flow (NCF) will therefore be a net inflow of a
total of $34,000.
If the price of the business was $34,000, her income over the four years would
be zero--and of course the rate of return on her investment would also be zero. Therefore, the
price (now) has to be lower than $34,000 to yield her the 5% return.