Time Value 2
1. GronkRobkowski has asked your help in deciding between two contract offers made by the Patriots. The first is a four year contract with a $10 M signing bonus today, and salaries starting next year for $12.5 M, followed by $13M, $14M and $15 M in the following years. Total cash flows from the contract are $64.5 M.
For salary cap purposes, the Partiots have also proposed a contract with a $5 M signing bonus today and annual salaries of $10M, $10M, $10M, and 15M. The club will also fund an annuity starting at age 34 and ending at age 60 of $2M per year.
Total cash flows from the second contract amount to $104 M. Both contracts are guaranteed and the appropriate returns on contracts is 10%. Which contract should Gronk choose?
2. Suppose you start working at age 21 and work until age 6 and your job pays $59,000. Assume you get paid once a year at the end of the year and assume your annual salary increases by 3% per year. Each year, you intend to invest a constant proportion of your salary in an investment account paying 6% annual interest.
You withdraw your 1st retirement check at age 68 and intend to live for 15 years. You want your first retirement check to be 70% of what you made at age 67, and you want your retirement benefit to increase by 3% per year. What proportion of your salary do you need to invest per year to meet your retirement needs?
3. Friday night's Megamillions drawing will offer to prizes - a lump sum of $235 Million or $405 Million paid out in 30 equal installments of $13.5 Million, with the first payment being made Friday. Ignoring taxes, at what interest rate are you indifferent between the two prizes?
4. Suppose you start working full time at age 21. From ages 21-30, starting on your birthday, you save $200 per month toward retirement. From age 31-40, you save $300 per month, from 41-50, $400 per month, from 51-60, $500 per month, and 61-66, $600 per month.
Assume your savings earn 6% annually (but compounded monthly). How much do you have on your 67th birthday, one month after your last deposit If your life expectancy is 15 years (180 months) after you retire, how much can you collect per month?
5. Consider a project with the following cash flows after tax. Assume a cost of capital of 12%.
|
Year
|
CFAT
|
|
0
|
$ (1,250,000.00)
|
|
1
|
$ 340,000.00
|
|
2
|
$ 460,000.00
|
|
3
|
$ 350,000.00
|
|
4
|
$ 240,000.00
|
|
5
|
$ 261,000.00
|
Calculate the project's NPV and IRR. Graph NPV vs discount rates for rates from 0 to 15% by whole percents.
6. Suppose I deposit and withdraw finds in the following sequences:
|
Sequence A
|
|
Sequence B
|
|
Sequence C
|
|
Year
|
Deposit/ Withdrawal
|
Year
|
Deposit/ Withdrawal
|
Year
|
Deposit/ Withdrawal
|
|
1
|
$ 1,000.00
|
|
1
|
$ 10,000.00
|
|
1
|
$ 10,000.00
|
|
2
|
$ 2,000.00
|
|
2
|
$ 9,000.00
|
|
2
|
$(10,000.00)
|
|
3
|
$ 3,000.00
|
|
3
|
$ 8,000.00
|
|
3
|
$ 9,000.00
|
|
4
|
$ 4,000.00
|
|
4
|
$ 7,000.00
|
|
4
|
$ (9,000.00)
|
|
5
|
$ 5,000.00
|
|
5
|
$ 6,000.00
|
|
5
|
$ 8,000.00
|
|
6
|
$ 6,000.00
|
|
6
|
$ 5,000.00
|
|
6
|
$ (8,000.00)
|
|
7
|
$ 7,000.00
|
|
7
|
$ 4,000.00
|
|
7
|
$ 7,000.00
|
|
8
|
$ 8,000.00
|
|
8
|
$ 3,000.00
|
|
8
|
$ (7,000.00)
|
|
9
|
$ 9,000.00
|
|
9
|
$ 2,000.00
|
|
9
|
$ 6,000.00
|
|
10
|
$ 10,000.00
|
|
10
|
$ 1,000.00
|
|
10
|
$ (6,000.00)
|
|
11
|
$(10,000.00)
|
|
11
|
$ (1,000.00)
|
|
11
|
$ 5,000.00
|
|
12
|
$ (9,000.00)
|
|
12
|
$ (2,000.00)
|
|
12
|
$ (5,000.00)
|
|
13
|
$ (8,000.00)
|
|
13
|
$ (3,000.00)
|
|
13
|
$ 4,000.00
|
|
14
|
$ (7,000.00)
|
|
14
|
$ (4,000.00)
|
|
14
|
$ (4,000.00)
|
|
15
|
$ (6,000.00)
|
|
15
|
$ (5,000.00)
|
|
15
|
$ 3,000.00
|
|
16
|
$ (5,000.00)
|
|
16
|
$ (6,000.00)
|
|
16
|
$ (3,000.00)
|
|
17
|
$ (4,000.00)
|
|
17
|
$ (7,000.00)
|
|
17
|
$ 2,000.00
|
|
18
|
$ (3,000.00)
|
|
18
|
$ (8,000.00)
|
|
18
|
$ (2,000.00)
|
|
19
|
$ (2,000.00)
|
|
19
|
$ (9,000.00)
|
|
19
|
$ 1,000.00
|
|
20
|
$ (1,000.00)
|
|
20
|
$(10,000.00)
|
|
20
|
$ (1,000.00)
|
Assuming your investments earn 6%, how much is left in each account immediately after the last withdrawal in year 20?
3. Suppose you start working at age 21 and work until age 67. Assume you get paid once a year at the end of the year and assume your annual salary increases by 3% per year. Each year, you intend to invest a constant proportion of your salary in an investment account paying 6% annual interest. You withdraw your 1st retirement check at age 68 and intend to live for 15 years. You want your first retirement check to be 70% of what you made at age 67, and you want your retirement benefit to increase by 3% per year. What proportion of your salary do you need to invest per year to meet your retirement needs?
4. Friday night's Megamillions drawing will offer to prizes - a lump sum of $235 Million or $405 Million paid out in 30 equal installments of $13.5 Million, with the first payment being made Friday. Ignoring taxes, at what interest rate are you indifferent between the two prizes?
5. Suppose you start working full time at age 21. From ages 21-30, starting on your birthday, you save $200 per month toward retirement. From age 31-40, you save $300 per month, from 41-50, $400 per month, from 51-60, $500 per month, and 61-66, $600 per month. Assume your savings earn 6% annually (but compounded monthly). How much do you have on your 67th birthday, one month after your last deposit If your life expectancy is 15 years (180 months) after you retire, how much can you collect per month?
6. Consider a project with the following cash flows after tax. Assume a cost of capital of 12%.
|
Year
|
CFAT
|
|
0
|
$ (1,250,000.00)
|
|
1
|
$ 340,000.00
|
|
2
|
$ 460,000.00
|
|
3
|
$ 350,000.00
|
|
4
|
$ 240,000.00
|
|
5
|
$ 261,000.00
|
Calculate the project's NPV and IRR. Graph NPV vs discount rates for rates from 0 to 15% by whole percents.