Payback period refers to the time it takes(i.e. n) to recover
the initial investment cost (i.e. P) of an investment.
General equation is: 0 = -P  A(P/A,i,n)  F(P/F,i,n)
( frequently requires trial and error solution)
Business persons sometimes use simple payback (ignoring interest).
Such a procedure,while ‘simple’, obviously yields a lower n value
than the correct one.
Example: A racing team purchased a transporter for $175,000.They will be able
to sell the truck at any time within the next 5 years for $90,000, after which it will
sell for $70,000. If they expect to win an average of $25,000 more per year because
of the truck (i.e. being able to go to more races), how long will it take to recover
their investment at (a) i = 0%, and (b) i = 12% per year?
Solution:
(a) 0 = -175,000 + 25,000(n) + 90,000
n = 3.4 ,or 4 years
(b) 0 =- 175,000 +25,000(P/A,12%,n) + 90,000(P/F,12%,n)
for n≤5
0 =- 175,000 +25,000(P/A,12%,n) + 70,000(P/F,12%,n)
for n>5
By trial and error, n =12.6 , or 13 years