Project Valuation II: Less Simple Hotel

Projects $($real options$)$

Spiral Galaxy Hotels is considering two different ways to develop a property they bought for

$$6\mathrm{.}8$million last year. The local hotel market sales are $$250$million annually, and they hope to

get $25\%$of the market if they build a large hotel for $$75$million$.$Alternatively$,$ they could build a

smaller, upscale hotel that would only capture $20\%$of the market for $$40$million$.$The large

hotel would have variable costs that are $30\%$of revenue while the upscale variable costs would

be $35\%$of revenue. The fixed costs are higher for the large hotel at $$8$million$/$year than the

upscale hotel at $$3\mathrm{.}5$million$/$year$.$The large hotel requires additional net working capital of

$$1\mathrm{.}5$million while the upscale hotel requires $$0\mathrm{.}9$million$.$Both hotels will be depreciated to

zero under the rules for nonresidential real property in MACRS, and after $15$years the large

hotel can be sold for $$12\mathrm{.}5$million and the small hotel for $$9\mathrm{.}25$million; the land could be sold

for $$7\mathrm{.}5$million$.$The tax rate is $23\%$for both projects.

In order to finance their investment, Spiral Galaxy Hotels will sell $1\mathrm{.}3$million shares to investors

at $$29\mathrm{.}43/$share$,$and they will borrow any additional funds they need. If they build the large

hotel, creditors will charge $7\mathrm{.}75\%$annually on their debt, but they will only charge $4\mathrm{.}25\%$on

debt for the small hotel. Since the large hotel is a bigger venture that will use more debt, the

firm$$s equity will be considered to be $2\mathrm{.}5$times as risky as investing in publicly traded stocks

$($which we expect to produce $11\%/$year; the risk$-$free rate is $1\mathrm{.}8\%).$The small hotel, on the other

hand, will result in equity that is only $1\mathrm{.}5$times as risky.

For the large hotel, there is a $15\%$chance that the hotel will not do well, and as a result

revenues will be only $50\%$of the expected. There is a $10\%$that the hotel will outperform

expectations and be a huge success, resulting in revenues that are $150\%$of expectations. For

the small hotel, the chance of failure is higher, at $30\%,$but a great success also has a higher

chance of $30\%.$Assume the same changes in revenue for the small hotel.

Determine what the value of each project is and which is preferable.

$($has to be done in excel$)$