Question

Mr. Conrad Willig liked the idea of hotels made of ice more than anything else. While he was pretty sure that the initial investment of one ice hotel would cost $12 million, there was some uncertainty concerning annual cash flows. He believed that there was a 75 percent probability that the idea would be successful with an annual cash flows of $3 million and a 25 percent probability that the idea will fail with an annual cash flows of only $1 million. However, if the idea turned out to be successful, Mr. Willig would want to expand, and therefore build 10 hotels in total instead of only one. He felt that 20 percent was an appropriate discount rate, given the risk of this new venture. And he believed that the cash flows would be perpetual.

Please compute the value of the option to expand.
(Hint: You need to compute the value of the project without expanding option as well as the value with expanding option. The difference of these two values will be the value of the option.)

Answer 1

Intac umvestment Te miceion Successfue Prob Annua Cauh m feow 75 YearD Baie) rvicoessfee Annuoe Cf Prob 1-75 m 10 Gpron) Value of usyocthot exhondin oltion NeY NPY (Aucceadu)t NPY unaccduofu) fotsle uCol ony one Le 9 Present Value dCaoh ow tcc Cash Roow Desccunt vate tualuy dNPV (ucesofee) 1 m 3 X.75 mcCion NPYnauccasfeul). 75 - 12 m t X5-

Date Value of foryet wdhout conding 5 mt (-115) m m annuiaC cah he ehoulc the meeon then ficst ahand NPv (if exterd um ab NPYus +re X lo X15 25 X X - 12 + 2.5 mt I15) m 2o 15 = m option Value (NPv)expond NPY thooxend Vue 75 m 5 m 20.5 m Nate rwob CF = Cauh low