You bought a house for $250,000 and incurred additional transaction costs of $2,000 at the time of your purchase. You sold the house one year later for $325,000. The selling broker charged a
6% commission, and you incurred other costs associated with the sale, both direct and indirect,
Of $5,000. An alternative investment of similar risk offers a 10% annual return, but has a 60
Basis point transaction cost. What is the NPV of this investment?

Question

Quizplus · Accepted Answer

To calculate the NPV of the investment, we need to first calculate the net proceeds from the sale of the house.

Sale price of the house = $325,000
Transaction costs = $2,000 + $5,000 + (6% of $325,000) = $24,500
Net proceeds = Sale price - transaction costs = $300,500

Now, we can calculate the NPV of the alternative investment.

Initial investment = $300,500
Annual return = 10%
Transaction cost = 60 basis points = 0.6%
Risk-adjusted return = 10% - 0.6% = 9.4%
Time period = 1 year

Using the formula for NPV:

NPV = (-Initial investment) + (Cash flows / (1 + Risk-adjusted return)^Time period)

NPV = (-$300,500) + ($300,500 * 1.094 / 1.094^1) = $22,680

Therefore, the NPV of this investment is $22,680.

The best choice is B, as it has the highest NPV, indicating a better return on investment compared to the house. The total cost of buying and selling the house is:

$2,000 + $5,000 + ($325,000 × 6%) = $24,500

The net proceeds from the sale are:

$325,000 − $24,500 − $250,000 = $50,500

The total cost of the alternative investment is:

($250,000 × 0.60%) × 2 = $3,000

The net return from the alternative investment is:

($250,000 × 10%) − $3,000 = $22,500

The NPV of this investment is:

NPV = ($22,500 ÷ 1.10) − $22,500 = $2,680

Since the NPV of the alternative investment is positive, it is a better choice than the investment in the house. Therefore, the best choice is to invest in the alternative investment.

You Bought a House for $250,000 and Incurred Additional Transaction