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$1.$ a$.$ Lois Evans has just graduated from Wharton, has obtained a job in New York and wishes to buy an apartment. She plans to do this $7$ years from now at which time she expects the apartment to cost $$275,000.$ She needs to save a down payment equal to $20$ percent of this figure. The rate of interest at the bank she uses is expected to remain constant at $7$ percent per year throughout the next seven years. Three years from now her mother has promised to give $$10,000$ to her which she can put in the bank to help pay for the down payment. How much must she save out of her salary at the end of years $1-5($not $1-7$; i$.$e$.$ she doesn't save out of her salary in years $6$ and $7),$ assuming she saves the same amount for each of the five years, if she wishes to have enough money to pay the down payment seven years from now? b$.$ The Elephant Corporation pays dividends annually. It is just about to pay a dividend of $$8\mathrm{.}30$ per share. Its dividend is expected to grow at a rate of $30$ percent for the next three years $($i$.$e$.$ during years $1,2$ and $3)$ and then at $22$ percent for two years $($i$.$e$.$ during years $4$ and $5).$ After that it is expected to grow at $4$ percent each year forever. The market capitalization rate on similar stocks is $14$ percent. What is the current price of a share of Elephant's stock? $2.$ Consider a world with two points in time, t$0$ and t$1.$ Thomas Wentworth inherits $$4\mathrm{.}0$ million at t$0.$ He has three projects he can invest this inheritance in at t$0.$ Project A costs $$650,000$ at t$0$ and yields $$775,000$ at t$1.$ Project B costs $$850,000$ at t$0$ and yields $$1,160,000$ at t$1.$ Project C costs $$250,000$ at t$0$ and yields $$270,000$ at t$1.$ He can also lend and borrow at a bank at an interest rate of $12$ percent. a$.$ Which projects should Thomas undertake?b$.$ What is the amount Thomas can consume at t$1,$ given he wishes to consume $$2$M at t$0?$ How much does he need to lend or borrow at the bank to achieve this level of consumption?c$.$ How would your answers to $($a$)$ and $($b$)$ be changed if Thomas could lend to the bank at $10$ percent and borrow from the bank at $20$ percent? $3.$ Consider a world with three dates t $=0,1,$ and $2,$ perfect capital markets and no uncertainty. Ms$.$ Innovation has just inherited $$0\mathrm{.}5$ million. She has identified a countrywide market need and therefore; decided to set up a corporation called Bubble.com. This will manufacture and sell kits of liquid soap and wire frames that will allow children and adults to blow soap bubbles. These kits will be marketed over the internet. Suppose initially she can lend and borrow at the bank at $6$ percent per period. Bubble.com has the following projects available. ProjectCost at t $=0$ Revenue at t $=1$ Revenue at t $=2$Large bubble kit $-$$$325,000$$$220,000$ $$260,000$Medium bubble kit $-$$$255,000$$$128,000$ $$140,000$Small bubble kit $-$$$430,000$$$300,000$$$270,000($i$)$ What simple instructions can Ms$.$ Innovation give to ensure that the managers she hires create as much wealth as possible for her? $($ii$)$ Which projects should the managers choose to undertake? $($Use the NPV and the IRR methods to value the projects$)($iii$)$ The managers revised their revenue forecasts for the Small bubble kit project and found that they will be $$250,000$ and $$350,000$ in years $1$ and $2,$ respectively. If Ms$.$ Innovation must EITHER choose the Large or the Small bubble kit project, which one should she take and why? Show your calculations.

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