Question

Compute your after-transaction-costs rate of return on purchasing a house for $1,000,000 if you have to pay 0.5% transaction fees up front and pay a 6% broker’s commission (plus 2% in waiting costs) at the end of 1 year. Assume a $4,000/month effective dividend of enjoying living in the house. Assume that your opportunity cost of capital (not the bank quoted interest rate) is 7% per year. At what rate of capital appreciation would the NPV be zero if you resold the house after 1 year?

Answer 1

Assumed that the dividend enjoyed is effective at the end of each month (arrear).

The initial outflow is 1,000,000 + 0.5% * (1,000,000) = $1,005,000

For each of the months from 1st to the 11th, the inflow would be $4000

At the end of 12th month there is inflow of $4000 as well as outflow of 8% on 1,000,000 = 0.08* 1,000,000 = $ 76000 (where 8% is 6% broker commission plus 2% waiting cost)

The array of notional cash flows would look like below:

month	flow
0	-1005000
1	4000
2	4000
3	4000
4	4000
5	4000
6	4000
7	4000
8	4000
9	4000
10	4000
11	4000
12	-76000

These flows are discounted at 7% or 0.07 to arrive at Net Present Value. In Excel, the formula =NPV(0.07, value of month1, value of month2, ........, value of month 12) is used to arrive at a value which is added to the value in period 0 (month zero). Thus, discounted flows will amount to $ 1,008,750.

The house must be sold at $ 1,008,750 to ensure zero NPV i.e. no profit and no loss situation.

Hence, the current value of $ 1,000,000 must appreciate by a percentage that is equal to:

(future value * 100 / present value) - 100 = (1,008,750 *100 /1,000,000) - 100 = 0.8750 %

The capital appreciation rate is thus 0.8750 %