Example - Determine The NPV Of An Opportunity With No Strategic Options

A firm considers investing $296 in a new factory. Cash flows two years from now depend on the economy. At full capacity, those cash flows produce the following pattern. If there are two good years, the cash flow is $834. If one good year is followed by one bad year, the cash flow is $598. If one bad year is followed by a good year, the cash flow is the same. That is the pattern recombines.Finally, if two bad years occur, the cash flow is $83. A market portfolio produces a risk neutral risk probability of 0.6 for upward transitions. In year 1 the firm has no strategic options, and the annual risk free rate is 13% what is the opportunity's net present value in dollars?

$\pi$ = .6

1 - $\pi$ = .4

$r_{f}$ = .06
Investment = 296

Solve using the Two-Period Binomial Valuation

$V_{u}$ = (($\pi$*uu) + ((1 - $\pi$)*ud)) / (1 + $r_{f}$)
$V_{u}$ = ((.4*834) + (.7*598))/(1.06)
$V_{u}$ = 654.51

$V_{d}$ = (($\pi$*du) + ((1 - $\pi$)*dd)) / (1 + $r_{f}$)
$V_{d}$ = ((.3*598) + (.7*83))/1.06
$V_{d}$ = 346.90

$V_{0}$ = (($\pi$*u) + ((1 - $\pi$)*d)) / (1 + $r_{f}$)
$V_{0}$ = ((.3*654.51) + (.7*346.90)/1.06
$V_{0}$ = 489.03

Net Present Value (NPV) = 489.03 - 296 (The initial investment) = 174.33

Two-Period Binomial Tree:
Yr 0………Yr1…….Yr2
…………………………834
…………654.51
489.03……………..598
…………346.90
………………………….83