Question

Suppose you own a house where you live and a condo for rent. So the rent from the tenant of your condo is your income. The monthly rent is $1,500, but you have to pay taxes, maintenance fees, and insurance premium. They are $500 per month in total. Therefore, the net cash flow from this condo is $1000 per month. Assume the tax is a lump sum, not proportional to the value of a property. Assume there is no depreciation (no wear and tear) and the condo will generate the same cash-flows forever. The first cash flow is one month from now. The discount rate is 0.2% per month, compounded monthly. What is the fair price of the condo?

Answer) $0.5million

P = PV = C/r = 1000/0.002 = 500,000 = $0.5???????

In the above example, assume the net cash-flow C is unknown. If the discount rate changes from 0.2% to 0.1% per month, compounded monthly, what is the net return of the capital gain (or loss) of investment in the condo?

Answer 100%,

P1 = C/0.002, P2=C/0.001,

r = P2/P1-1 = (C/0.001) / (C/0.002) – 1 = 0.002/0.001- 1 = 2-1 =1=100%

Question 1. In the above example, assume the net cash-flow C is unknown. If the discount rate changes from 0.2% to 0.5% per month, compounded monthly, what is the net return of the capital gain (or loss) of investment in the condo? (The answer will be the same regardless of the value of C. So, you can pick whatever number for C and still find the same answer)

1) -10%

2) -30%

3) -50%

4) -60%

5) -80%

Question 2. In the example above Question 1, if the net cash-flow C is doubled and the discount rate r is tripled, what would be the net return of the capital gain (or loss) of investment in the condo? (You can pick any numbers for C and r, and you will still find the same answer).

1) -33.33%

2) -30.15%

3) -25.54%

4) -21.68%

5) -18.96%

Answer 1

Question 1.

Answer: Option 4 (-60%)

P1 = C/0.002, P2=C/0.005,

r = P2/P1-1 = (C/0.005) / (C/0.002) – 1 = 0.002/0.005- 1 = 0.4-1 =1=-60%

Question 2.

Answer: Option 1(-33.33%),

P1 = C/0.002, P2=2*C/0.006,

r = P2/P1-1 = (2*C/0.006) / (C/0.002) – 1 = 0.002/0.003- 1 = 0.6667-1 =1=-33.33%