FIN4320 Exam 2 Sample Assignment

FIN 4320 - Exam 2

1. A 15 year variable rate mortgage offers a first year teaser rate of 3.11%. After that the rate starts at 5% adjusted based on actual interest rates. If the mortgage is $325,000 compute the monthly payment during the first year

$2262

P/Y = 12

PV = $325,000

I/Y = 3.11

N = 15*12 = 180

FV = 0

PMT = ? = $2,261.69 = $2,262

2. A 30 year variable rate mortgage offers a first year teaser rate of 3%. After that the rate starts at 5.5% adjusted based on actual interest rates. If the mortgage is $325,000 compute the monthly payment during the second year,if the interest rate increases to 5.5%. 

$1831

P/Y = 12

PV = $325,000

I/Y = 3

N = 30*12 = 360

FV = 0

PMT = ? = $1,370.21

2nd AMORT to get loan balance after 1st year

P1 = 1, P2 = 12, down arrow til you get to BAL = $318,214.65

PV = $318,214.65

I/Y = 5.5%

N = 29*12 = 348

FV = 0

PMT = ? = $1,831.46 = $1,831

3. Peter buys a car worth $21,800 by putting a down payment of 10% and taking a loan for the balance amount. The loan carries an interest rate of 3.99% over a period of 5 years and needs to be paid on a monthly basis. What is the total interest Peter is expected to pay over the life of the loan?

Approximately $2,055

PV = $21,800 – 10% = $19,620

I/Y = 3.99%

N = 5*12 = 60

FV = 0

PMT = ? = $361.24

2nd AMORT to get total interest paid on car

P1 = 1, P2 = 60, arrow down to INT = $2,054.62 = $2,055

4. Peter buys a car worth $22,000 by putting a down payment of 30% and taking a loan for the balance amount. The loan carries an interest rate of 5.99% over a period of 3 years and needs to be paid on a monthly basis. What is the total interest Peter is expected to pay over the life of the loan?

Approximately $1,464

PV = $22,000 – 30% = $15,400

I/Y = 5.99%

N = 3*12 = 36

FV = 0

PMT = ? = $468.43

2nd AMORT to get total interest paid on car

P1 = 1, P2 = 36, arrow down to INT = $1,463.41 = $1,464

5. Peter buys a car worth $38,000 by putting a down payment of 15% and taking a loan for the balance amount. The loan carries an interest rate of 4.99% over a period of 5 years and needs to be paid on a monthly basis. What is the total interest Peter is expected to pay over the life of the loan?

Approximately $4,264

PV = $38,000 – 15% = $32,300

I/Y = \4.99%

N = 5*12 = 60

FV = 0

PMT = ? = $609.39

2nd AMORT to get total interest paid on car

P1 = 1, P2 = 36, arrow down to INT = $4,263.57 = $4,264

6. Consider a 15 year fixed rate mortgage for $175,000 at nominal interest rate of 8%. If the borrower wants to pay off the remaining balance on the mortgage after making the 9th payment, what is the remaining balance on the loan? Assume monthly payments.

$170,325

PV = $175,000

I/Y = \8%

N = 15*12 = 180

FV = 0

PMT = ? = $1,672.39

2nd AMORT to get balance after the 9th month

P1 = 1, P2 = 9, arrow down to BAL = $170,325.20 = $170,325

7. Consider a 20 year fixed rate mortgage for $175,000 at nominal interest rate of 8%. If the borrower wants to pay off the remaining balance on the mortgage after making the 12th payment, what is the remaining balance on the loan? Assume monthly payments.

$171,301

PV = $175,000

I/Y = \8%

N = 20*12 = 240

FV = 0

PMT = ? = $1,463.77

2nd AMORT to get balance after the 12th month

P1 = 1, P2 = 12, arrow down to BAL = $171,301.08= $171,301

8. Consider a loan of $175,000 at nominal interest rate of 4.65% for 30 years. How much of the payment during the first year goes towards principal? Assume monthly payments.

$2,749

PV = $175,000

I/Y = \4.65%

N = 30*12 = 360

FV = 0

PMT = ? = $902.36

2nd AMORT to get total principal during the 1st year

P1 = 1, P2 = 12, arrow down to PRN = $2,748.97 = $2,749

9. Consider a 30 year fixed rate mortgage for $175,000 at nominal interest rate of 8%. If the borrower wants to pay off the remaining balance on the mortgage after making the 9th payment, what is the remaining balance on the loan? Assume monthly payments.

$173,914

PV = $175,000

I/Y = \8%

N = 30*12 = 360

FV = 0

PMT = ? = $1,284.09

2nd AMORT to get balance after the 9th month

P1 = 1, P2 = 9, arrow down to BAL = $173,914.58 = $173,914

10. Consider a loan of $220,000 at nominal interest rate of 4.65% for 10 years. How much of the payment during the first year goes towards principal? Assume monthly payments.

$17,696

PV = $220,000

I/Y = 4.65%

N = 10*12 = 120

FV = 0

PMT = ? = $2,295.99

2nd AMORT to get total principal during the 1st year

P1 = 1, P2 = 12, arrow down to PRN = $17,695.81 = $17,696

There is a choice to buy a car worth $28,000 with 100% financing at 4.99% APR for 60 month or lease at $450 per month. The car will need maintenance in the 3rd year worth $525 and $825 in the 4th year. The car will have 35% residual value in the 5th year. Sales tax on new car is 6% and required rate of return is 5%. 

11. Calculate the Ownership Operating Advantage in year 5. 

$8861

Year 0

Year 1

Year 2

Year 3

Year 4

Year 5

Rent

-

$450*12 = $5400

$5400

$5400

$5400

$5400

Year 0

Year 1

Year 2

Year 3

Year 4

Year 5

Residual Value

$28,000*.35 = $9,800

PV = $28,000 N = 5*12 I/Y = 4.99% FV = 0 PMT = ? = $528.27

Year 0

Year 1

Year 2

Year 3

Year 4

Year 5

Sales Tax

$28,000*.06 = $1,680

Maintenance Cost

$525

$825

Annual Payments

$528.27*12 = $6,339

$6,339

$6,339

$6,339

$6,339

Cost of Owning

$1,680

$6,339

$6,339

$6,864

$7,164

$6,339

Year 0

Year 1

Year 2

Year 3

Year 4

Year 5

Rent

-

$5,400

$5,400

$5,400

$5,400

$5,400

+ Residual Value

$9,800

- Cost of Owning

$1,680

$6,339

$6,339

$6,864

$7,164

$6,339

Ownership Operating Advantage

($1,680)

($939)

($939)

($1,464)

($1,764)

$8,861

12. Calculate the cost of Owning this car in year 1.

$6339

PV = $28,000 N = 5*12 I/Y = 4.99% FV = 0 PMT = ? = $528.27

Year 0

Year 1

Year 2

Year 3

Year 4

Year 5

Sales Tax

$28,000*.06 = $1,680

Maintenance Cost

$525

$825

Annual Payments

$528.27*12 = $6,339

$6,339

$6,339

$6,339

$6,339

Cost of Owning

$1,680

$6,339

$6,339

$6,864

$7,164

$6,339

There is a choice to buy a car worth $28,000 with 100% financing at 4.99% APR for 60 month or lease at $450 per month. The car will need maintenance in the 3rd year worth $525 and $825 in the 4th year. The car will have 35% residual value in the 5th year. Sales tax on new car is 6% and required rate of return is 10%. 

13. Which option is better? 

Leasing since IRR is 9.29%

Year 0

Year 1

Year 2

Year 3

Year 4

Year 5

Rent

-

$450*12 = $5400

$5400

$5400

$5400

$5400

Year 0

Year 1

Year 2

Year 3

Year 4

Year 5

Residual Value

$28,000*.35 = $9,800

PV = $28,000 N = 5*12 I/Y = 4.99% FV = 0 PMT = ? = $528.27

Year 0

Year 1

Year 2

Year 3

Year 4

Year 5

Sales Tax

$28,000*.06 = $1,680

Maintenance Cost

$525

$825

Annual Payments

$528.27*12 = $6,339

$6,339

$6,339

$6,339

$6,339

Cost of Owning

$1,680

$6,339

$6,339

$6,864

$7,164

$6,339

Year 0

Year 1

Year 2

Year 3

Year 4

Year 5

Rent

-

$5,400

$5,400

$5,400

$5,400

$5,400

+ Residual Value

$9,800

- Cost of Owning

$1,680

$6,339

$6,339

$6,864

$7,164

$6,339

Ownership Operating Advantage

($1,680)

($939)

($939)

($1,464)

($1,764)

$8,861

CF0= -$1,680 CF1 = -$939 CF2 = -$939 CF3 = -$1,464 CF4 = -$1,764 CF5 = $8,861

IRR = 9.29%

Leasing is the better option because the IRR is less than the required rate of return of 10%.

A family currently live in an apartment whose monthly rent is $950. They are thinking of buying a house which would cost $220,000. They plan to live in this house for 5 years and sell it at the end of the 5th year. They would put a down payment of $20,000 and finance the balance through a mortgage at 3.5% interest rate. The mortgage is to be repaid in 5 annual installments (which include both principal and interest) at the end of each year for the next 5 years  The house will have the following additional expenses: annual maintenance: $1500; Property taxes:$5500; Insurance: $1200. Assume they are in tax bracket of 25% and the price of home, rent and expenditure increases by 2.5% per year. Their opportunity cost or required rate of return is 5% per year. Note that property taxes are tax deductible and there no tax payable on capital gains. Use annual compounding for amortization schedule of mortgage. 

14. Calculate the expected house price at the end of year 5. 

$248,910

PV = $220,000 N = 5 I/Y = 2.5% PMT = 0 FV = ? = $248,909.81 = $248,910

A family currently live in an apartment whose monthly rent is $950. They are thinking of buying a house which would cost $220,000. They plan to live in this house for 5 years and sell it at the end of the 5th year. They would put a down payment of $20,000 and finance the balance through a mortgage at 3.5% interest rate. The mortgage is to be repaid in 5 annual installments (which include both principal and interest) at the end of each year for the next 5 years  The house will have the following additional expenses: annual maintenance: $1500; Property taxes:$5500; Insurance: $1200. Assume they are in tax bracket of 20% and the price of home, rent and expenditure increases by 2.5% per year. Their opportunity cost or required rate of return is 5% per year. Note that property taxes are tax deductible and there no tax payable on capital gains. Use annual compounding for amortization schedule of mortgage. 

15. Calculate the total cost of owning in year 4. 

$8724

Year 0

Year 1

Year 2

Year 3

Year 4

Year 5

Down Payment

$20,000

Opportunity Cost of Down Payment

$20,000*.05 = $1,000

Maintenance

$1,500

Insurance

$1,200

Property Tax

$5,500(1-.20) = $4,400

Total

$20,000

$8,100

$8,100*1.025 = $8,303

$8,303*1.025 = $8,511

$8,511*1.025 = $8,724

$8,724*1.025 = $8,942

16. Calculate the Post tax Mortgage Cost (principal repayment plus after tax interest cost) for year 1.

$42,896

PV = $200,000 FV = 0 I/Y = 3.5% N = 5 PMT = ? = $

Year 1:            P1 = 1 P2 = 1, arrow down til INT = $7000; PRN = $37,296

Year 2:            P1 = 2 P2 = 2, arrow down til INT = $5695; PRN = $38,602

Year 3:            P1 = 3 P2 = 3, arrow down til INT = $4344; PRN = $39,953

Year 4:            P1 = 4 P2 = 4, arrow down til INT = $2945; PRN = $41,351

Year 5:            P1 = 5 P2 = 5, arrow down til INT = $1498; PRN = $42,798

Year 0

Year 1

Year 2

Year 3

Year 4

Year 5

Interest

-

$7000

$5695

$4344

$2945

$1498

Year 0

Year 1

Year 2

Year 3

Year 4

Year 5

After Tax Interest Cost

-

$7000*(1-.20) = $5600

$5695*(1-.20) = $4556

$4344*(1-.20) = $3475

$2945*(1-.20) = $2356

$1498*(1-.20) = $1198

Principal Repayment

$37,296

$38,602

$39,953

$41,351

$42,798

Post Tax Mortgage Cost

$42,896

$43,158

$43,428

$43,707

$43,996

17. Calculate Ownership Operating Advantage in year 1.

($39,596)

Year 0

Year 1

Year 2

Year 3

Year 4

Year 5

Rent

-

$950*12 = $11,400

$11,400*1.025 = $11,685

$11,685*1.025 = $11,977

$11,977*1.025 = $12,276

$12,276*1.025 = $12,583

Selling Price:

PV = $220,000 N = 5 I/Y = 2.5% PMT = 0 FV = ? = $248,909.81 = $248,910

Year 0

Year 1

Year 2

Year 3

Year 4

Year 5

After Tax Interest Cost

-

$7000*(1-.20) = $5600

$5695*(1-.20) = $4556

$4344*(1-.20) = $3475

$2945*(1-.20) = $2356

$1498*(1-.20) = $1198

Principal Repayment

$37,296

$38,602

$39,953

$41,351

$42,798

Post Tax Mortgage Cost

$42,896

$43,158

$43,428

$43,707

$43,996

Year 0

Year 1

Year 2

Year 3

Year 4

Year 5

Down Payment

$20,000

Opportunity Cost of Down Payment

$20,000*.05 = $1,000

Maintenance

$1,500

Insurance

$1,200

Property Tax

$5,500(1-.20) = $4,400

Total

$20,000

$8,100

$8,100*1.025 = $8,303

$8,303*1.025 = $8,511

$8,511*1.025 = $8,724

$8,724*1.025 = $8,942

Year 0

Year 1

Year 2

Year 3

Year 4

Year 5

Rent

-

$11,400

$11,685

$11,977

$12,276

$12,583

+Selling Price

$248,910

- Mortgage Cost

$42,896

$43,158

$43,428

$43,707

$43,996

- Cost of Owning

$20,000

$8,100

$8,303

$8,511

$8,724

$8,942

Total

($20,000)

($39,596)

($39,776)

($39,962)

($40,155)

$208,555

18. Calculate Ownership Operating Advantage in year 4.

($40,155)

Year 0

Year 1

Year 2

Year 3

Year 4

Year 5

Rent

-

$11,400

$11,685

$11,977

$12,276

$12,583

+Selling Price

$248,910

- Mortgage Cost

$42,896

$43,158

$43,428

$43,707

$43,996

- Cost of Owning

$20,000

$8,100

$8,303

$8,511

$8,724

$8,942

Total

($20,000)

($39,596)

($39,776)

($39,962)

($40,155)

$208,555

19. Calculate the rent saved during year 2. 

$11,685

Year 0

Year 1

Year 2

Year 3

Year 4

Year 5

Rent

-

$950*12 = $11,400

$11,400*1.025 = $11,685

$11,685*1.025 = $11,977

$11,977*1.025 = $12,276

$12,276*1.025 = $12,583

20. Should they buy this house or continue to rent? 

Buy since IRR is 5.47%

Year 0

Year 1

Year 2

Year 3

Year 4

Year 5

Rent

-

$950*12 = $11,400

$11,400*1.025 = $11,685

$11,685*1.025 = $11,977

$11,977*1.025 = $12,276

$12,276*1.025 = $12,583

Selling Price:

PV = $220,000 N = 5 I/Y = 2.5% PMT = 0 FV = ? = $248,909.81 = $248,910

Year 0

Year 1

Year 2

Year 3

Year 4

Year 5

After Tax Interest Cost

-

$7000*(1-.20) = $5600

$5695*(1-.20) = $4556

$4344*(1-.20) = $3475

$2945*(1-.20) = $2356

$1498*(1-.20) = $1198

Principal Repayment

$37,296

$38,602

$39,953

$41,351

$42,798

Post Tax Mortgage Cost

$42,896

$43,158

$43,428

$43,707

$43,996

Year 0

Year 1

Year 2

Year 3

Year 4

Year 5

Down Payment

$20,000

Opportunity Cost of Down Payment

$20,000*.05 = $1,000

Maintenance

$1,500

Insurance

$1,200

Property Tax

$5,500(1-.20) = $4,400

Total

$20,000

$8,100

$8,100*1.025 = $8,303

$8,303*1.025 = $8,511

$8,511*1.025 = $8,724

$8,724*1.025 = $8,942

Year 0

Year 1

Year 2

Year 3

Year 4

Year 5

Rent

-

$11,400

$11,685

$11,977

$12,276

$12,583

+Selling Price

$248,910

- Mortgage Cost

$42,896

$43,158

$43,428

$43,707

$43,996

- Cost of Owning

$20,000

$8,100

$8,303

$8,511

$8,724

$8,942

Total

($20,000)

($39,596)

($39,776)

($39,962)

($40,155)

$208,555

CF0 = -$20,000 CF1 = -$39,596 CF2 = -$39,776 CF3 = -$39,962 CF4 = -$40,155 CF5 = $208,555

IRR = 5.47%

Buy since the IRR is greater than the required rate of return of 5%.