FNAN 401 - Homework #1

1)You have two children who will be going to college.The first child will begin 17 years from today, and tuition will be $20,000, $21,000, $22,000 and $23,000 at t=17, 18, 19, and 20.The second will begin college 19 years from today, and tuition will be $22,000, $23,000, $24,000 and $25,000 at t=19, 20, 21, and 22.

a)To fund your children's tuition, you would like to make anequal annual deposit over the next 20 years (first deposit at t=1, last at t=20) in an account earning 4% per year, compounded semi-annually.

What equal amount must you deposit each year?

b)What if (instead of an equal annual deposit) to fund your children's tuition you plan to make deposits over the next 20 years (first deposit at t=1, last at t= 20) that grow each year by 3%.If those deposits earn 4% per year, compounded semi-annually, what is the amount of the first deposit (at t=1)?

c)Good news!Your parents have offered to pay the entire college tuitions of your children.They plan to do this by making a single deposit 5 years from today (at t=5).If invested funds earns4% per year, compounded semi-annually, what single amount should they deposit?

2)A bond issued by Boatholders Corporation has a 6% coupon (paid semiannually), a $1,000 par value, and matures 2 years from today.

a)If the bond's yield to maturityis 4%, at what price should it sell today?

b)What is the current yield of the bond?

c)If the bond's yield to maturity does not change, at what price will the bond sell one month from today (i.e. what is the bond's "dirty" or "invoice" price)?

3)A stock will pay a $3 dividend one year from today (t=1)?The dividend is expected to grow by 14% per year for the subsequent 3 years (t=2,3,4), and then by 4% per year, thereafter.Assume that the required return in 12% per year, compounded annually.

a)At what price should the stock sell today?

b)At what price should the stock sell three years from today (at t=3, the instant before the t=3 dividend is paid)?

c)At what price should the stock sell three years from today (at t=3, the instant after the t=3 dividend is paid)?

4)An investment will provide cash flows of $10,000, every third year, forever!!!The first cash flow will be received one year from today (t=1); the second four years from today (t=4), etc.

a)What is the value today (t=0) of this investment if the required return is 6% per year, compounded annually?(Please use 4 digit accuracy when making your calculations).

b)What is the value today (t=0) of this investment if the required return is 6% per year, compounded semi-annually?(Please use 4 digit accuracy when making your calculations).