Question

University of California Merced ECON 105- Corporate Finance Instructor: Jesus Sandoval-Hernandez In Class Practice Problems Ch 5. 1. Kristina just won the lottery, and she must choose among three award options. She can elect to receive a lump sum today of $62 million, to receive 10 end-of year payments of $9.5 million, or to receive 30 end-of-year payments of $5,6 million. a. If she thinks she can earn 7% annually, which should she choose? b. If she thinks she can earn 7% annually, which option would you recommend? 2. Jan sold her house on December 31 and took a $10,000 mortgage as part of the payment. The 10-year mortgage has a 10% nominal interest, but it calls for semiannual payments beginning next June 30. Next year Jan must report on schedule B of her IRS Form 4040 the amount of interest that was included in the two payments she received during the year. a. What is the dollar amount of each payment Jan receives? b. How much interest was included in the first payment? How do these values change for the second payment? c. How much interest must Jan report on Schedule B for the first year? Will her interest income be the same next year?

Answer 1

A. Immediate receipt - $62 Million Receive every year $9.5 Milllion for 10 years and can earn 7% interest -9.5*Present value Annuity factor of 7% for 10 years i.e., 9.5*7.024 = $ 66.724 Million Receive every year $5.6 Milllion for 30 years and can earn 7% interest - 9.5*Present value Annuity factor of 7% for 30 years i.e., 5.6*12.41 = $ 69.496 Million Therefore, based on the above calculations, Kristina should the option of receiving $ 5.6 Million every year for 30 years with 7% interest annully Interest @ 10% Annual Intere Interes Total st@ t@ Intere Amount 5%for 5%for st for Receive 1st 2st half the d $ half $ $ year $ 1 10000 500 500 1000 2 9000 4500 450 900 3 8000 400 400 800 Year 2b) Interest payment of 1st year is $1000. The interest for second year is only $900 as there is repayment of PRINCIPAL AMOUNT EVERY YEAR. 2C) Jan must report an interest income of $1000 for the 1st year in Schedule B. The interest WILL NOT BE SAME NEXT YEAR as there is repayment of PRINCIPAL AMOUNT EVERY YEAR. 7000 6000 350 300 700 600 6 5000 7 4000 8 3000 9 2000 10 1000 Answer for 2a 350 300 250 200 150 100 50 50 100