Question

32 Assume your $200,000 home appreciates in value at a rate of 5% per year. Assume you take out an 80% mortgage (loan to original value) at 6% interest rate for 30 years. Therefore, you provide 20% or $40,000 equity in the home at the outset of the mortgage. What is the amount of equity (the then current value of home (current market value) less mortgage outstanding) at the end of the 60th payment? 33 Step 1: Value of home after 5th yr (using annual rate for depreciation) Value of home after 5th year Step 2: Balance of Mortgage after 60th Payment Original Balance / rate / term Monthly Payment Current Term Remaining on Loan PV of Remaining Payments Step 3: Equity = Current Market Value less Current Loan Balance 36 If an asset pays you the following, what is the value to you at a 10% interest rate? $40 every 6 months for the next 10 years. $1,000 at the end of 10 years. NOTE: these cash flows are really a 'bond' What would be the price you would pay for the asset in #6 if you require a 6% interest rate? 37 An apartment complex has an after-tax cash flow of $100,000 per month. What is the value of the complex using a 12% yeild (assume 20 year horizon)?

Answer 1

33)

Value of the home after 5th year = $ 200,000 x ( 1 + 0.05)⁵

Value of the home after 5th year = $ 255,256.31

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34)

Monthly payment on the loan is calculated as follows

Present value of the loan 1-(1 + interest rate) -nt interest rate

$160,000 PMT = - 1-(1 +100 0.06 -360 0.06

Monthly payment = $ 959.28

Balance of mortgage after 60th payment = $ 959.28 x 360 months -  $ 959.28 x 60 months

Current loan balance = $287,784.25

Original balance = $ 959.28 x 360 months ( $345,341.10 )

Current term remaining on loan = 300 months

PV of remaining payment = $ 959.28 x PVIFA_{0.5%, n = 300 months}

PV of remaining payment = $148,886.97

Equity = Current market value - Current loan balance

Equity =  $ 255,256.31 -  $287,784.25

Equity =  - $ 32,527.94

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36) The value of the asset is calculated as follows

Price = $ 40 x PVIFA_{r=5%, n = 20 years} + $ 1000 x PVIF_{r=5% , n = 20 years}

Price = $ 875.38

Price if the required rate is 6%

Price = $ 40 x PVIFA_{r=3%, n = 20 years} + $ 1000 x PVIF_{r=3% , n = 20 years}

Price = $ 1148.77

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37)

Al (1+r)-1] Future value annuity =

$100,000 (1 + 9:22) * - 1 Future value annuity = 0.12 12

Value of the complex = $98,925,536.54