You are planning to purchase a new house or condominium to use as your primary r
ID: 2710513 • Letter: Y
Question
You are planning to purchase a new house or condominium to use as your primary residence. This assignment will analyze some of the financial aspects of doing so.
The final purchase price is $330,000 and, if you need a mortgage from the bank, your down payment will have to be 20% of the purchase price. The mortgage is a 30-year fixed rate loan with an Annual Percentage Rate (APR) of 4.20%. You will incur a one-time closing cost of $3,000 and you will add this closing cost to the loan borrowed. The mortgage will be amortized over the 30-year period with equal monthly payments. Exactly right after you pay the 60th monthly payment (5 years after the loan starts), you can sell the house for a net proceeds of $455,000 (this is the money you actually received after deducting all sale expenses but BEFORE you pay off your remaining loan principal). Ignore the capital gain tax or property tax in this case.
1. Compute the effective interest rate for this loan.
2. Compute the monthly payment amount of this loan.
3. Compute the remaining principal that will be due on the mortgage when you sell the house. Your last payment is made in month 60, so the remaining principal is the required payment immediately after that monthly payment.
4. Calculate the annual Internal Rate of Return (IRR) for this investment if the above mortgage is involved, assuming 12-monthly payments paid together at the end of each year for this calculation.
5. Calculate the annual Internal Rate of Return (IRR) if an all-cash (no finance) investment is involved; i.e. you pay the full purchase price at the beginning and collect all net sale proceeds at the end. 6. Assuming you can either finance the purchase as (4) or purchase with all-cash as (5) and there is no other differences between the two strategies, conduct an analysis to determine which strategy you should select and provide calculation and explanation for your decision. (Your cost of capital is at 5.00%)
Explanation / Answer
Answer (1)
Effective interest rate = 0.35% per month
Answer (2)
Monthly Payment amount = $ 1,305.68
Answer (3)
Remaining principal after 60 monthly payments = $ 242,266.34
Answer (4)
Internal Rate of Return if a loan is used and property sold after 5 years = 16.09%
Answer (5)
Internal Rate of Return if the purchase is financed from own funds = 10.64%
Answer (6)
Both the IRRs arrived at in answers 4 & 5 are higher than cost of capital 5%
Based on answers 4 & 5 the rate of return is higher if a loan is taken compared to cost of capital, it is better to go for a loan.
Purchase price of House = 330000
Down Payment = 20%
One-time closing cost = 3000
APR = 4.20%
Mortgage Period = 30 years = 30*12 = 360 months
Frequency of payment = monthly
Effective interest rate = 4.20%/12 = 0.35% per month or 0.0035
Loan amount = $ 330000 + $ 3000 - $ 330000 * 0.20 = $ 267,000
Let A be monthly instalment the loan, then
A = P[ r (1+r)^n]/[(1+r)^n -1]
A = 267000 * [0.0035 * (1+0.0035)^360]/[(1+0.0035)^360 -1]
A = 267000 * [0.0035 * 3.517674548]/[3.517674548-1]
A = 267000 * [0.01231186/2.517674548]
A = 267000 * 0.004890172
A = $1,305.6759 or $ 1,305.68 (rounded off)
Loan balance after payment of 60 monthly instalments will be
B = P *[(1+0.0035)^360 –(1+0.0035)^60]/[(1+0.0035)^360 -1]
B = 267000 * [3.517674548 – 1.23322582]/[3.517674548-1]
B = 267000 * (2.284448728/2.517674548)
B = 267000 * 0.90736459
B = $242,266.3449 or $ 242,266.34 (rounded off)
If all the instalments are paid at the end of the year amount paid = $1305.68 * 12
= $15668.16
Net proceeds received after 5 years = $ 455,000
Let r be the internal rate of return to make the net present value of the flows equals zero. That is
-$330,000 - $3000 + $66000 + $15668.16 * [(1-(1/(1+r)^5)/r] + $455000/(1+r)^5 = 0
Let r = 16%, then LHS is equal to
= -267000 + 15668.16 * (1-(1/1.16^5))/0.16 + 455000/1.16^5
= -267000 + 15668.16 * (1-0.476113015)/0.16 + 455000 * 0.476113015
= -267000 + 15668.16 * (0.52886985/0.16) + 216631.40
= -267000 + 15668.16*3.274293654 + 216631.40
= -267000 + 51302.16 + 216631.40
= 933.5789
Let r be equal to 17%. Then LHS is equal to
= -267000 + 15668.16 * (1-(1/1.17^5))/0.17 + 455000/1.17^5
= -267000 + 15668.16 * (1-0.456111152)/0.17 + 455000 * 0.456111152
= -267000 + 15668.16 * (0.543888848/0.17) + 207530.60
= -267000 + 15668.16 * 3.199346163 + 207530.60
= -267000 + 50127.87 + 207530.60
= -9341.56
r = 0.16 + [933.5789 * (0.16-0.17)/(-9341.56-933.5789)
= 0.16 + (9.335789/10275.1389)
= 0.16 + 0.0009085
= 0.1609085 or 16.09%
Instead of taking a loan, if the project involves all cash financing or self financing then the cash flows will be
-330000-3000 + 15668.16 *[(1-(1/(1+r)^5)/r] + $455000/(1+r)^5 = 0
-333000 + 15668.16 *[(1-(1/(1+r)^5)/r] + $455000/(1+r)^5 = 0
Let r = 10%, then LHS will be
= -333000 + 15668.16 *[(1-(1/(1.10)^5)/0.10] + $455000/(1.10)^5
= -333000 + 15688.16 * (1-0.620921323)/0.10 + 455000 * 0.620921323
= -333000 + 15688.16 * (0.379078677/0.10) + 282519.20
= -333000 + 15688.16 * 3.790786769 + 282519.20
=-333000 + 59394.65 + 282519.20
= 8913.856
Let r = 11%, then LHS will be
= -333000 + 15668.16 *[(1-(1/(1.11)^5)/0.11] + $455000/(1.11)^5
= -333000 + 15688.16 * (1-0.593451328)/0.11 + 455000 * 0.593451328
= -333000 + 15688.16 * (0.406548672/0.11) + 270020.40
= -333000 + 15688.16 * 3.695897018 + 270020.40
= -333000+57907.91+270020.40
= -5071.74
r = 0.10 + [((8913.856) * (0.10-0.11))/(-5071.74-8913.856)]
= 0.10 + (89.13856/13985.596)
= 0.10 + 0.0063736
= 0.1063736 or 10.64%
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