Gladstone Corporation is an all$-$equity firm whose only asset is the potential to develop a new product. The new product

requires an initial investment of $$100.$ Depending on the success of the new product, the cash flow next year may have one of

two values: $$100$ million, or $$160$ million. These outcomes are all equally likely, the risk is diversifiable, and there will be no cash

flows after one year. The risk$-$free rate is $7\mathrm{.}1\%.$

Gladstone plans to raise $$100$ million by issuing a zero$-$coupon debt. What should be the face value of the debt if debtholders

expect that in the event of default, $12\%$ of the cash flows will be lost due to bankruptcy costs? Ignore all other market

imperfections, such as taxes.

Please write your answer in $million with one digit after the decimal point. For examle, if the answer is $$25\mathrm{.}7$ million, just write

$25\mathrm{.}7)$ Numbers may change in each attempt.