$5.$ BTC Corporation is in big trouble. It recently sold off its tangible assets because it could not operate its business profitably. BTC$$s only remaining asset is $$2$ million in cash. Unfortunately, BTC previously issued bonds with a face value of $$3$ million.

$($a$)$ If BTC were to be liquidated immediately, what would be the amounts paid to the bond holders and to the stockholders, respectively?

$($b$)$ BTC$$s managers $($who are also the stockholders$)$ are considering using the $$2$ million in cash to fund a risky investment. In exchange for investing the $$2$ million, BTC would immediately receive either $$3\mathrm{.}8$ million or $$0,$ with equal probability. What is the NPV of this proposed investment? $($Use a zero discount rate$).$

$($c$)$ Assume that BTC commits to making this investment, but that the outcome is not yet known. BTC would be liquidated as soon as the outcome was known. What is the market value now of BTC$$s stock and of its bonds? $($Continue to use a zero discount rate$).$

$($d$)$ Explain the principle illustrated here.