Question $2(13$ marks$)$Working as a senior manager at a fast$-$growing technology company, Gold Standard Ltd $($GST$),$you hold $5,000$ shares of Gold Standard stock $($via employee stock holding scheme$)$ that iscurrently trading at $$100$ per share. You also have $$750,000$ invested in another $($defensive$)$ stock,Natural Gas Ltd$.($NGL$),$ to balance the risk of your portfolio.The market information on the two stocks are as follows: Stock Gold Standard: Expected rate of return $=12\%,$ Standard Deviation $=9\mathrm{.}11\%$ Stock Natural Gas: Expected rate of return $=6\%,$ Standard Deviation $=3\mathrm{.}00\%$ Correlation Coefficient of Stock Gold Standard with Stock Natural Gas $=0\mathrm{.}70$The probabilities and rate of returns for GTS under different states of the economy are as follows:State of theEconomyProbability Expected rate of return ofStock Gold Standard undervarious states of the economyBoom $0\mathrm{.}2540\%$Normal $0\mathrm{.}5012\%$Bust $0\mathrm{.}25?($a$)$ Given that the expected rate of return of GST is $12\%,$ calculate its expected return when thestate of the economy is Bust. $(4$ marks$)($b$)$ What is the expected return of your portfolio? $[$Hints: Calculate the weight of GST and NGLas your first step.$](5$ marks$)($c$)$ What is the standard deviation of your portfolio? $(4$ marks$)$Question $3(12$ marks$)$Kempinski Ltd$.$ has just paid a cash dividend of $$2$ per share. The market forecasts that thedividend payments of the company will grow at $20\%$ per year for the next three years, $15\%$ forthe following year and then settle down to $10\%$ per year afterwards.Given the risk$-$free rate is $4\%,$ the market risk premium is $10\%$ and Kempinskis stock has abeta of $1\mathrm{.}2.($a$)$ What is the required return for Kempinski based on CAPM? $(2$ marks$)($b$)$ Calculate the $($intrinsic$)$ value of Kempinski stock at time $0.(6$ marks$)($c$)$ Given the expected dividend growth path $($as forecasted above$),$ is Kempinskis share over$-$valued or under$-$valued if it is selling at $$100$ three years from now? What is the tradingsignal it implies? $(4$ marks$)4$Question $4(8$ marks$)$Halcyon Lines Inc. is considering purchasing a new ship for $$8$ million now. The forecasted cashinflows for the project are $$1$ million a year for $15$ years. A major refit costing $$2$ million will berequired at the end of Year $5$ and Year $10.$ After $15$ years, the ship is expected to be sold at $$1\mathrm{.}5$million, ignore any depreciation and tax considerations.What is the NPV of the project if the relevant discount rate is $8\%$ per year? Should you go aheadwith the project? $[$Hint: Just set up the NPV formula that includes all the relevant cash inflowsand outflows.$]$