You are the head of your state's lottery office. Lottery prizes are not paid out immediately, but are parceled out over a 15 year period. You know exactly how much your office needs to pay out in prizes over the next 15 years. You would like to set aside enough money from lottery receipts to invest in secure government bonds to meet this future stream of payments. All remaining lottery receipts will be turned over to the state's treasurer to help fund the education system. You would like to turn over as many of the receipts as possible to the treasurer, so your plan is to purchase a minimal cost mix of bonds that just meets your future cash needs.

Here is the amount of cash you will need (in millions) to make future prize payments:

Year

Needs

0

$10

1

$11

2

$12

3

$14

4

$15

5

$17

6

$19

7

$20

8

$22

9

$24

10

$26

11

$29

12

$31

13

$33

14

$36

There are two bonds currently being offered which you feel are of sufficient quality to guarantee the future stream of prize payments. These bonds are listed in the table below:

Bond

Years to

Maturity

Price ($M)

Coupon ($M)

A

6

.98

.06

B

13

.965

.065

If funds are not invested in bonds, they can be placed into short-term money market funds. You conservatively estimate short-term rates will be about 4% over the 15 year time horizon.

How many of each bond should you buy, and how much additional cash should you allocate to money market funds to minimize your total outlay while still being able to meet all the future prize payments?