Question

Assume that the price of real estate is determined by P=PV(all cash flows generated by the real estate).

After you have graduated you work for some years and can save some money. You decide to invest in a house which you want to rent out for a rate of SEK 8,000 per month. Assume that the rental rate will increase with 1.2% per year (which is 0.1% per month). (For the sake of simplicity, also assume that there are no further costs involved e.g. renovating or repair).

a) As the market risk of renting out the house is low, you think that a discount rate of 3.5% (APR with monthly compounding) would be appropriate. What is the price of the house under the assumption that the cash flows from rent will last forever?

Answer: the price of the house under these assumptions is SEK  million. (round to two decimals)

b) If discount rate is 1% lower than 3.5% what is the price of the house?

Answer: the price of the house is SEK million. (round to two decimals)

c) You want to make the valuation of the house more realistic by assuming that the time horizon for the valuation should be 50 years. Again, you assume that the house will generate SEK 8,000 rental income per month for the next 50 years, and the rental income is assumed to grow by 1.2% per year (or 0.1% per month). What is the value of the house with a discount rate of 3.5% APR with monthly compounding?

Answer: the price of the house is SEK million. (round to two decimals)

d) Make the same assumptions as in (c) but assume a 1% lower discount rate. What is the price of the house?

Answer: the price of the house is SEK million. (round to two decimals)

Answer 1

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Answer:

a. This is an example of a growing perpetuity Which is given by C/(r-g) C = 8000 r = 3.5 per annum = 0.2916% per month =0.002916 g = 1.2% per annum = 0.1% per month =0.001 PV of cash flow = 8000/(0.002916-0.001) - 4,175,365 b. If discount rate = 2.5% per annum. The monthly rate = 2.5/12 = 0.20833% = 0.00208333 PV of cash flow = 8000/(0.00208333-0.001) = 7,384,638.11 SEK c. Now it becomes a growing annuity and the formula is given by P/(r-g) *(1 - (1+g/1+r)^n) where P =8000 r = 3.5/12 = 0.0029167 g = 0.001 n = 50*12 = 600 PV = 8000/(0.0029167 -0.001)*(1-(1.001/1.0029167)^600) = 2,849,302.12 SEK d. When r = 2.5% per annum = 0.2083% per month = 0.0020833 PV = 8000/(0.0020833 -0.001)*(1-(1.001/1.0020833)^600) = 3,525,680.69 SEK