4320 Finance Exam 3 Sample Assignment

1. Mike currently 35, has $15,000 saved for retirement. He is currently saving $450 at the beginning of every month and his employer matches his total savings contribution on a monthly basis. Mike projects that he could earn 7% on his savings. He plans to retire at 65 and expects to live until age 90. His current expenditure on basic needs at the beginning of every month is $2200 every month which is expected to increase with inflation of 4%.

How much would be Mike’s monthly expenditure once he retires?

N = 65 – 35 = 30 x 12 = 360

I/Y = 4/12 = .33 (inflation)

PV = $2200

PMT = 0

FV = $7,289.70 = $7,290

$7,290

2. Qualified plans are best defined as

Pension structures that comply with established government regulations

3. Amanda is expected to receive full social security retirement benefit of $15500 annually when she turns 65. These benefits can be increased by 40% if she delays taking them till age 70. If her life expectancy is 90 years and expected rate of return is 6%, should Amanda take full benefit at 65 or delay benefit till 70? Assume no other income and taxes during retirement.

Age 65:

N = 90 – 65 = 25

I/Y = 6%

PMT = $15,500

FV = 0

PV = $198,142.02 = $198,142

Age 70:

N = 90 – 70 = 20

I/Y = 6%

PMT = $15,500 x 1.40 = $21,700

FV = 0

PV = $248,897.29

Compare PV of 70 at the age of 65:

N = 70 – 65 = 5

I/Y = 6%

PMT = 0

FV = $248,897.29

PV = $185,990.53 = $185,991

She should start at 65 since present value of benefits is $198,142 as against $185,991 at 70

4. John was considering whether to place $10,000 in a tax-deferred annuity or a tax-free municipal bond. Assume the municipal returned 4% a year and the tax-deferred annuity 5.5%. Calculate approximately how long he would have to hold the annuity so that, if he withdrew the money and paid taxes on it, he would come out ahead. His marginal tax rate is 20%.

1 Year:

Tax deferred annuity:

PV = $10,000

N = 1

I/Y = 5.5%

PMT = 0

FV = $10,550

Post tax amount = $10,550 x (1-.20) = $8,440

Tax free municipal bond:

PV = $10,000

N = 1

I/Y = 4%

PMT = 0

FV = $10,400

There are no taxes in this case

Post tax amount = $10,400

15 Years:

Tax deferred annuity:

PV = $10,000

N = 15

I/Y = 5.5%

PMT = 0

FV = $22,324.76 = $22,325

Post tax amount = $22,325 x (1-.20) = $17,860

Tax free municipal bond:

PV = $10,000

N = 15

I/Y = 4%

PMT = 0

FV = $18,009.44 = $18,009

There are no taxes in this case

Post tax amount = $18,009

16 Years:

Tax deferred annuity:

PV = $10,000

N = 16

I/Y = 5.5%

PMT = 0

FV = $23,552.63 = $23,553

Post tax amount = $23,553 x (1-.20) = $18,842.40

Tax free municipal bond:

PV = $10,000

N = 16

I/Y = 4%

PMT =, 0

FV = $18,729.81 = $18,730

There are no taxes in this case

Post tax amount = $18,730

16 years

5. Susan saved $500 at the end of every month in her retirement account for 10 years (during age 25-35) and then quit saving. However, she did not make any withdrawal until she turned 65 (i.e., 30 years after she stopped saving). Her friend Cathy started saving $650 at the end of every year for 30 years during age 35 - 65. What will be the difference in accumulated balances in their retirement accounts at age 65 if both earned an average return of 9% (compounded monthly) during the entire period?

Cathy:

N = 30 x 12 = 360

I/Y = 9/12

PMT = $650

PV = 0

FV = $1,189,983.26

Susan:

N = 35 – 25 = 10 x 12 = 120

I/Y = 9/12

PMT = $500

PV = 0

FV = $96,757.14

Compute FV of $96,757.14 from 35 to 65 years (30 years). No additional savings so PMT = 0

N = 30 x 12 = 360

I/Y = 9/12

PMT = 0

PV = $96,757.14

FV = $1,425,288.42

$1,425,288.42 - $1,189,983.26 = $235,305.16 = $235,305

$235,305

6. Steve is about to retire and wants to calculate the total worth of his retirement assets. He has a corporate pension paying $2250 at the beginning of every month. He is also entitled for Social Security benefits of $1450 at the beginning of every month. He also has a 401(k) plan with an accumulated balance of $480,000. The regular U.S. government bonds are yielding 5.5% and government inflation indexed bond provides a current return of 3.5% and his remaining life span is 18 years. Compute the combined worth of Steve's retirement assets.

Corporate pension plan:

BGN MODE

N = 18 x 12 = 216

I/Y = 5.5/12

PMT = $2250

FV = 0

PV = $309,497.72

Social Security:

BGN MODE

N = 18 x 12 = 216

I/Y = 3.5/12

PMT = $1450

FV = 0

PV = $232,802.78

$480,000 + $309,497.72 + $232,802.78 = $1,022,300.50 = $1,022,301

$1,022,301

7. Which of the following defines risk management in practical terms?

The process by which we identify risks and control them so that we are able to achieve individual goals

8. Which of the following insurance is intended to provide a limited choice of investments and an insurance component in the event of death?

Universal life

9. When losses are material and there is a strong likelihood that they will occur:

Insurance may not be the appropriate choice

10. Exposure to the risk of loss is:

Peril

11. James bought a $350,000 whole life policy on his own life on July 1 of the current year. The premiums were $275 per month payable of the 1st day of every month. This policy contains a suicide clause for a period of two years. On November 15 of the following year, James committed suicide. What is payable to his beneficiary, assuming the premiums were paid as agreed up to November 1 of the following year. Average interest rate in the economy is 4% per year.

17 x $275 = $4,675

Would have gotten the full $350,00 if he had committed suicide after 2 years.

$4675

12. Consider the following information of a Whole Life policy and a Term Life policy:

Guaranteed Contract Premium

Guaranteed Death Benefit

Projected
Dividend

Projected Cash Value

Term Premium

$2,300

$200,000

0

0

$325

$2,300

0

0

$330

$2,300

0

0

$335

$2,300

0

$3,500

$340

$2,300

$250

$6,000

$355

$2,300

$400

$9,000

$370

$2,300

$600

$15,000

$390

Whole Life

Cash Outflow

Term Life

Cash Outflows

Difference in Cash Outflows

Net Cash Flow

-$2,300

-$325

-$1,975

-$1,975

-$2,300

-$330

-$1,970

-$1,970

-$2,300

-$335

-$1,965

-$1,965

-$2,300

-$340

-$1,960

-$1,960

-$2,050

-$355

-$1,695

-$1,695

-$1,900

-$370

-$1,530

-$1,530

-$1,700

-$390

-$1,310

$11,690

What is the IRR of difference in cash flows between Whole Life and Term Life policies?

CF = 0; CF1 = -1975; CF2 = -1970; CF3 = -1965; CF4 = -1960; CF5 = -1695; CF6 = -1530; CF7 = 11,690

IRR = 1.44%

1.44%

13. Linda is 35 year old but misrepresented her age as 30, while purchasing a life insurance policy for $40,000. For each $1000 of the policy, it costs $45 for age 35, and $35 for age 30. In the event, Linda dies and the insurance company discovers her lie, then what would be the amount which her beneficiary would get?

Total Premium paid = $35/$1000 = .035 x $40,000 = $1,400

$1,400/$45 = $31.11 x $1,000 = $31,111.11 = $31,111

$31,111

14. Marvin had two term policies to compare with costs as shown below. Based on 7% after tax discount rate, which one should he select and why?

Years Policy A Policy B
1 $195 $210
2 $240 $220
3 $250 $235
4 $270 $260
5 $290 $285

Compute NPV at 7%

Policy A:

CF0 = 0; CF1 = $195; CF2 = $240; CF3 = $250; CF4 = $270; CF5 = $290

NPV = $1,008.69

Policy B:

CF0 = 0; CF1 = $210; CF2 = $220; CF3 = $235; CF4 = $260; CF5 = $285

NPV = $981.80

Policy B, since NPV of Policy A is $1009 while NPV of Policy B is $982

15. Charles and Martha (both age 30), each saved $15,000 (pre tax) at the end of every year over their working lives. Both worked till age 65 years. Charles saved his money in a qualified pension plan while Martha saved in her personal account after paying taxes. Martha turned over her portfolio every year and the combination of ordinary income on dividends and interest and capital gains on sale of stock came to a 20% tax rate on investment returns. If both generated a pretax return of 6% per year and were in 25% marginal tax bracket throughout their lives, compute the difference in their net accumulated savings at retirement.

Martha:

$15,000 x 25% = $3,750

$15,000 - $3,750 = $11,250

6% x (1-20%) = 4.8%

N = 65 – 30 = 35

I/Y = 4.8%

PMT = $11,250

PV = 0

FV = ? = $974,986.61

Charles:

N = 35

I/Y = 6%

PMT = $15,000

PV = 0

FV = ? = $1,671,521.70

$1,671,521.70 x (1-25%) = $1,253,641.28

$1,253,641 - $974,987 = $278,654

$278,654

16. Consider the following information of a Whole Life policy and a Term Life policy:

Guaranteed Contract Premium

Guaranteed Death Benefit

Projected Dividend

Projected Cash Value

Term Premium

$2,300

$200,000

0

0

$325

$2,300

0

0

$330

$2,300

0

0

$335

$2,300

0

$3,500

$340

$2,300

$250

$6,000

$355

$2,300

$400

$9,000

$370

$2,300

$600

$13,000

$390

Which policy is better if cash can be invested at 9% return?

Whole Life Cash Outflow

Term Life Cash Outflows

Difference in Cash Outflows

Net Cash Flow

-$2,300

-$325

-$1,975

-$1,975

-$2,300

-$330

-$1,970

-$1,970

-$2,300

-$335

-$1,965

-$1,965

-$2,300

-$340

-$1,960

-$1,960

-$2,050

-$355

-$1,695

-$1,695

-$1,900

-$370

-$1,530

-$1,530

-$1,700

-$390

-$1,310

$13,690

CF = 0; CF1 = -1975; CF2 = -1970; CF3 = -1965; CF4 = -1960; CF5 = -1695; CF6 = -1530; CF7 = 13,690

IRR = 5.82%

Term Life Policy since IRR of difference in cash flows is less than 9%

17. Bianca and Mildred had the same starting sum of $115,000. Each made withdrawals of $11,000 at the end of each year. In years 2, 3, and 4, each had returns of 6% percent a year. Bianca had a 30% drop in year 1 and a 40% gain in year 5, while Mildred had a 40% gain in year 1 and a 45 percent drop in year 5. What is the difference in their accounts at the end of year 5.

Bianca:

Year 0: $115,000

Year 1: $115,000 x (1 - .30) - $11,000 = $69,500

Year 2: $69,500 x (1 + .06) - $11,000 = $62,670

Year 3: $62,670 x (1 + .06) - $11,000 = $55,430.20

Year 4: $55,430.20 x (1 + .06) - $11,000 = $47,756.01

Year 5: $47,756 x (1 + .40) - $11,000 = $55,858.40

Mildred:

Year 0: $115,000

Year 1: $115,000 x (1 + .40) - $11,000 = $150,000

Year 2: $150,000 x (1 + .06) - $11,000 = $148,000

Year 3: $148,000 x (1 + .06) - $11,000 = $145,880

Year 4: $145,880 x (1 + .06) - $11,000 = $143,632.80

Year 5: $143,632.80 x (1 - .45) - $11,000 = $67,998.04

$67,998.04 - $55,858.40 = $12,139.64 = $12,140

$12,140

18. Rosa is about to turn 62 and she is in dillema whether to take reduced social security benefits at 62 or wait till 65 to get full benefits. She would be entitled to get $20,250 annually at full retirement age of 65, while she would get 77.5% of this amount if she decides to take social security at 62. Which option she should select if she can earn 6% return and her life expectancy is 85 years?

Alternative 1: Benefits at age 62

77.5% x $20,250 = $15,693.75

PMT = $15,693.75

N = 85 – 62 = 23

I/Y = 6%

FV = 0

PV = ? = $193,086.15 = $193,086

Alternative 2: Benefits at age 65

PMT = $20,250

N = 85 – 65 = 20

I/Y = 6%

FV = 0

PV = ? = $232,265.90

FV = $232,265.90

I/Y = 6

N = 65-62 = 3

PMT = 0

PV = ? = $195,014.93 = $195,015

She should wait till 65 since present value of benefits is $195,015 as against $193,086 at 62

19. Richard has the following three disability policies: (i) Policy A for $12,000 per year has an own occupation definition and was paid for by his employer, (ii) Policy B for $18,000 per year was paid by him and has an own occupation definition, (iii) Policy C for $16,000 annual coverage was purchased by him and has no own definition. Richard is in 28% marginal tax bracket. If Richard suffers an injury at his work and is unable to perform in his existing occupation but can work in some other field; how much post tax dollars would he receive due to these policies?

Policy A: $12,000 x (1 – 28%) = $8,640

Policy B: $18,000

Policy C: $0 (no own occupation definition)

$8,640 + $18,000 = $26,640

$26,640

20. Thomas owns a house which has a replacement cost of $1.2 million. He has an homeowner's policy of $650,000 with a 70% coinsurance clause. There was a major damage in the house which resulted in an outlay of $225,000 to replace it. How much will the insurance company reimburse him for?

Amount of Insurance Required = Coinsurance % x Replacement Cost

70% x $1,200,000 = $840,000

Insurance Reimbursement =

Amount of loss x amount of insurance in force/ amount of insurance required

$225,000 x $650,000/$840,000 = $174,107.14 = $174,107

$174,107