Parsons

Core Finance

Homework 1

___________________________________________________________________________ Question 1

You are head of a Family Endowment for the Arts. You have decided to fund a music school in San Diego in perpetuity. You will give the school $1 million immediately, and subsequent annual $1 million dollar payments growing at the rate of inflation, which you estimate to be 3% per year (i.e., you will contribute $1,000,000 plus inflation next year (one year from today), the year after, the year after, etc.,). If the interest rate is 8% per year, what is the present value of your gift?

Question 2

Your friend has a business she wants you to value. The business will not generate any money for the next three years, but in the fourth year it will start turning a profit and will make a payment (the first payment) of $150,000 to the owners at the end of the fourth year. Your friend expects to be able to grow the business, and the payments made to the owners, by 4% per year forever, and the owners will receive their payments at year end. If the appropriate discount rate is 14%, what is the value of the business today? Question 3

Pauli found a book on Finance in a garbage can. After reading it, he tells Silvio that if Silvio will give him $10,000/year for five years with the first payment at the end of this year, then he will give Silvio $10,000/year forever with the first payment occurring at the end of year 6. Silvio’s next-best alternative (i.e., what he would do with his money if he didn’t take Pauli’s offer) is to loan the money to Christopher at 12%

a. What NPV does Silvio get if he takes Pauli’s offer?

b. Should Silvio take Pauli’s offer?

c. Why or why not?

Question 4

Congratulations! You have won the Powerball! The Lottery Commission informs you that Chris Parsons page 2

you have won a million dollars, and that your million dollar prize will be paid to you in 20 equal installments of $50,000 to arrive every year, with the first payment coming today, and subsequent payments each year at the end of the years.

a. What is the present value of your lottery winnings? Did you really win a million dollars? Your first calculation didn’t make you feel great, but you still feel pretty rich. But now someone reminds you that the lottery winnings are taxable, and that you’re going to have to pay 35% in taxes on the date you receive the payments.

b. What is the present value of your after-tax lottery winnings? c. Given the payoff scheme of the lottery where you receive 20 equal annual payments with the first payment received today, what face amount must you win to be a true present-value after-tax millionaire (use the same 35% tax rate as above)? Use a discount rate of 8% in all PV calculations.

Question 5

You are thinking of purchasing a home. The house costs $400,000. You have $40,000 in cash for a down payment on the home, but you need to borrow the rest of the purchase price. Since your down payment is less than 20 percent of the purchase price, you need to take out two mortgages. The first mortgage on $320,000 has a fixed interest rate of 7% APR and a maturity of 30 years (360 months). The second mortgage on $40,000 has a fixed interest rate of 8% APR and a maturity of 15 years (180 months). You will have to make equal monthly payments on each mortgage until the maturity (i.e., the monthly principal payment plus the interest payment on each mortgage remains constant over the life of the mortgage). What will be your monthly mortgage payment for your mortgages? (hint: mortgages are quoted as annual APR rates, but they compound monthly)

Question 6

You have two children. One will start college in 13 years and the other in 10 years. You expect to pay $25,000 per year per child for college. You feel it’s your parental responsibility to pay for four years of college, but no more. You plan on saving an equal amount every year (first investment to be made one year from today). The first tuition...