Question $1$: $(15$ marks$)$

$($a$)$ Discuss why corporations typically exhibit separation of ownership and management, as

distinguished from sole proprietorships or partnerships. $.(5$ marks$)$

$($b$)$ Distinguish between a firm's capital budgeting decision and financing decision. Give

examples. $(10$ marks$)$

Question $2$: Application of Time Value of Money $(20$ marks$)$

a$)$ In $30$ years, you plan to set up a fellowship fund for Carleton University that would pay

out $$100,000$ a year in perpetuity with an annually compounded discount rate of $5\%.$ In

order to set up the fund in $30$ years, how much do you need to save each year $($starting this

year$)$ assuming you can get a return of $10\%$ per annum on your savings semi$-$annually

compounded for the next $30$ years? $(4$ marks$)$

b$)$ You are planning to buy a car worth $$40,000.$ Which of the two deals described below

would you choose, both with a $48-$month term? $($NB: estimate the monthly payment of each

offer and compare$).$

i$)$ the dealer offers to take $10\%$ off the price, then lend you the balance at an

annual percentage rate $($APR$)$ of $9\%,$ monthly compounding.

ii$)$ the dealer offers to lend you $$40,000($i$.$e$.,$ no discount$)$ at an APR of $3\%,$

monthly compounding. $(8$ marks$)$

c$)$ You have just joined the investment banking firm of Todd & Co$.$ They have offered you two

different salary arrangements. You can have $$80,000$ per year for the next two years, or you

can have $$70,000$ per year for the next two years, along with a $$20,000$ signing bonus today.

If the interest rate is $12\%$ compounded monthly, which is a better offer? NB: first convert the

annual percentage rate of $12\%$ to EAR and use the EAR as the discount rate. $(8$ marks$).$

Question $3$: Time Value of Money and application $(35$ marks$)$

a$)$ Assume you are $35$ years old today and are considering your retirement needs. You expect

to retire at age $65($in $30$ years$)$ and you plan to live to age $99.$ You want to buy a house

costing $$300,000$ on your $65$th birthday and your living expenses will be $$30,000$ a year

after that $($starting at the end of year $65$ and continuing through the end of year $99,$ i$.$e$.,$ for

$35$ years$).$ Assume an interest rate of $8\%,$ annual compounding:

$($i$)$ How much will you need to have saved by your retirement date to be able to afford this

retirement plan? $(5$ marks$)$

$($ii$)$ Suppose you already have $$50,000$ in savings today. If you can invest money at $8\%$ a

year annual compounding, how much would you need to save at the end of each year for

the next $30$ years to be able to afford this retirement plan? $(5$ marks$)$

b$)$ You have been hired to run a pension fund for Mackay Inc, a small manufacturing firm.

The firm currently has $$5$ million in the fund and expects to have cash inflows $($receipts$)$

of $$2$ million a year for the first $5$ years followed by cash outflows $($payments$)$ of $$3$ million

a year for the next $5$ years. Assume that interest rates are at $8\%.$

$($i$)$ How much money will be left in the fund at the end of the tenth year? $(8$ marks$)$

$($ii$)$ If you were required to pay a perpetuity after the tenth year $($starting in year $11$ and

going through infinity$)$ out of the balance left in the pension fund, how much could you

afford to pay every year? $(2$ marks$)$

$(10$ marks$)$

c$)$ Assume your child has just been born and you are planning for his college education. Based

on your wonderful experience in Finance at Carleton, you decide to send him to Carleton

University. You anticipate the annual tuition at that time to be $$50,000$ per year for the