Annuity Problems Some are original problems from the

Annuity Problems Some are original problems from the class lecture, others are included on the “Basic Valuation Problems” handout

Delayed annuity (#6 of Basic Valuation Problems) What is the value of a 10 -year annuity that pays $300 a year at the end of each year, if the first payment is deferred until 6 years from now, and if the discount rate is 10%? 0 1 2 3 4 5 6 300 7 300 8 9 300 10 • 11 • 12 • 13 14 • • 15 •

Delayed annuity What is the value of a 10 -year annuity that pays $300 a year at the end of each year, if the first payment is deferred until 6 years from now, and if the discount rate is 10%? 0 1 2 3 4 5 6 300 7 300 8 9 300 10 • 11 • 12 • 300 = $1, 144. 59 13 14 • • 15 •

College Planning (from Basic Valuation Problems #7) You have determined that you will need $60, 000 per year four years to send your daughter to college. The first of the four payments will be made 18 years from now and the last will be made 21 years from now. You wish to fund this obligation by making equal annual deposits over the 21 years STARTING ONE YEAR FROM TODAY. You expect to earn r = 8% per year.

College Planning (from Basic Valuation Problems #7) You have determined that you will need $60, 000 per year four years to send your daughter to college. The first of the four payments will be made 18 years from now and the last will be made 21 years from now. You wish to fund this obligation by making equal annual deposits over the 21 years STARTING ONE YEAR FROM TODAY. You expect to earn r = 8% per year. 0 1 2 3 … … 60000 +C +C 18 +C 19 +C 20 +C 21 +C

Example College Planning Step 1 Determine the time 17 value of the obligation: Step 2 2 Determine the equivalent time zero amount:

Step 3 Determine the 21 -year annuity that is equivalent to the time zero amount.

Infrequent annuity – page 110 of book • Ms. Chen receives a annuity payment of $450 every two years over a 20 year period (10 payments). Annual interest rate is 6%. What is the PV of the annuity? 0 1 2 3 4 … 20 450 … 450

Infrequent annuity – page 110 of book • Ms. Chen receives a annuity payment of $450 every two years over a 20 year period (10 payments). Annual interest rate is 6%. What is the PV of the annuity? • [1+(. 06/1)]^2 = 12. 36% -- the effective 2 -yr rate • PV= 450*A 0. 1236, 10= $2, 505. 57

Annuity Due (#3 Additional Valuation Problems) • You won $1 million in the Hoosier Lottery. The prize is paid out in equal semi-annual payments over 50 years with the first payment immediately. A firm in Dallas has offered to buy the ticket for cash today “using an 8% APR to discount the payments. ” How much will they pay? (Ignore taxes) • Remember, payouts start immediately so this is an Annuity Due

Annuity Due • You won $1 million in the Hoosier Lottery. The prize is paid out in equal semi-annual payments over 50 years with the first payment immediately. A firm in Dallas has offered to buy the ticket for cash today “using an 8% APR to discount the payments. ” How much will they pay? (Ignore taxes) Remember, payouts start immediately so this is an Annuity Due $1, 000/100 = $10, 000 every 6 months 0 1000 0 0. 5 1 1. 5 10000 0 . . . 49. 5. . . 10000 • PV=10, 000* A. 04, 100*1. 04 = $254, 852 • Or PV = 10, 000 + A. 04, 99 = $254, 852