Question

You are considering buying a beach house as an investment property. The price today for the
beach house is $240,000. You can fully depreciate the house on a straight-line basis over a
thirty year period (and deduct this depreciation expense from your income taxes). The rent
you will charge on an annual basis will be $10,000. You will face maintenance costs of
$2,000 every year (also tax deductible). You intend to sell the property in ten years, and you
expect that during the next ten years the market value of the property will appreciate at an
annual rate of 5%. Assume that the tax rate for income on the property is 40%, and the tax
rate for capital gains on the property is 20%. Also, assume that the appropriate discount rate
for your calculations is 12%.

a) What is the NPV of the purchase of the property?
b) What is the IRR of the purchase of the property? Could you predict whether the IRR was
higher or lower than 12% without calculating it? If so, how?

Answer 1

Given,

Price of the house = $240,000

Depreciation per annum = $240,000/30 = $8000

Rent for the house = $10,000

maintenance cost = $2,000

Question (a)

Computation of annual cash flows from the property

Rent received = $10,000

less: maintenance cost = $2000

less: depreciation = $8000

Profit = $0

Tax on profit = $0

Add: Depreciation = $8000

Cash flows after tax = $8000

PvAF(12%,10y) = 5.65

Present value of annual cash inflows for 10 years = $45,200

Computation of cashflows on sale of property

Sale value of property = $240,000 + ($240,000 5% 10) = $360,000

WDV of the property = $240000 - (8000 10) = $160,000

Profit on sale of property = $200,000

Tax on capital gain = $200,000 40% = $80,000

Cash flows after tax = $280,000

Present value of terminal cash inflows = $280,000 0.322 = $90160

Computation of NPV

Present value of annual cash inflows + present value of terminal cash inflows - Present value of cash-outflows

$45200 + $90160 - $240,000 = -$104640

Question (b)

Computation of IRR

Discount cashflows at 4%

Present value of annual cash inflows = $8000 8.111 = $ 64,888

Present value of terminal cash inflows = $280,000 0.676 = $ 189280

NPV at 4% = $189280 + $64888 - $240,000 = $254168 - $240,000 = $14168

Discount cashflows at 5%

Present value of annual cash inflows = $8000 7.722 = $ 61,776

Present value of terminal cash inflows = $280,000 0.614 = $ 171920

NPV at 4% = $233696 - $240,000 = -$6304

IRR = 4% + [$14168(14168 + $6304)] = 4.69%

Yes we could predict that IRR would be lower than 12% because NPV is negative at 12%.

NPV would be positive if IRR is higher than 12%.