FIN4320 Exam 2
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%.
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