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 11,000 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 5.0% (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 5.0% 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 11,000 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 5.0% 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

Part (a)

The rental income stream constitutes a perpetuity.

Price of the house is the present value of this perpetuity = SEK 3.47 Million

Computation as follows:

Part (b)

If the discount rate is 1% lower than 5.0%, ie., 4%,

Price of the house = SEK 4.71 Million

Computation as follows:

Part (c):

If the time horizon is assumed at 50 years, the rental income stream will constitute a growing annuity for 600 months (50 years*12). Price of the house is the Present value of this annuity.

With growth rate of 1.2% per year and discount rate of 5% per year,

Price of the house= SEK 2.95 Million

Computation as follows:

Part (d):

With the same assumptions as in part (c) but discount rate is reduced by 1% to 4%,

Price of the house= SEK 3.55 Million

Computation as follows: