Use the information for the question(s)below.

-An investor has the opportunity to invest in four new retail stores. The amount that can be invested in each store, along with the expected cash flow at the end of the first year, the growth rate of the concern, and the cost of capital is shown for each case. It is assumed each investment will operate in perpetuity after the initial investment. Which investment should the investor choose?
A)Initial investment: $100 000; Cash flow in year 1: $12 000; Growth Rate: 1.25%; Cost of Capital: 9.0%
B)Initial investment: $90 000; Cash flow in year 1: $10 000; Growth Rate: 1.50%; Cost of Capital: 9.0%
C)Initial investment: $80 000; Cash flow in year 1: $8 000; Growth Rate: 1.75%; Cost of Capital: 8.0%
D)Initial investment: $60 000; Cash flow in year 1: $6 000; Growth Rate: 2.50%; Cost of Capital: 7.5%

Question

Use the information for the question(s)below.
 
-An investor has the opportunity to invest in four new retail stores. The amount that can be invested in each store, along with the expected cash flow at the end of the first year, the growth rate of the concern, and the cost of capital is shown for each case. It is assumed each investment will operate in perpetuity after the initial investment. Which investment should the investor choose?
A)Initial investment: $100 000; Cash flow in year 1: $12 000; Growth Rate: 1.25%; Cost of Capital: 9.0% 
B)Initial investment: $90 000; Cash flow in year 1: $10 000; Growth Rate: 1.50%; Cost of Capital: 9.0% 
C)Initial investment: $80 000; Cash flow in year 1: $8 000; Growth Rate: 1.75%; Cost of Capital: 8.0% 
D)Initial investment: $60 000; Cash flow in year 1: $6 000; Growth Rate: 2.50%; Cost of Capital: 7.5%

Quizplus · Accepted Answer

The value of each investment can be calculated using the Gordon Growth Model (Dividend Discount Model for a perpetuity with growth), which is given by $ \frac{D_1}{r - g} $, where $D_1$ is the cash flow in year 1, $r$ is the cost of capital, and $g$ is the growth rate. For each option, the value of the investment (V) and the initial investment (I) are compared to determine the best choice. The option with the highest $V - I$ (value of investment minus initial investment) is the best choice. Calculating for each:A) $V = \frac{12000}{0.09 - 0.0125} = 160,000$, $V - I = 160,000 - 100,000 = 60,000$B) $V = \frac{10000}{0.09 - 0.015} = 125,000$, $V - I = 125,000 - 90,000 = 35,000$C) $V = \frac{8000}{0.08 - 0.0175} = 114,286$, $V - I = 114,286 - 80,000 = 34,286$D) $V = \frac{6000}{0.075 - 0.025} = 120,000$, $V - I = 120,000 - 60,000 = 60,000$However, upon closer inspection, both A and D have the same $V - I$, but D requires a lower initial investment for the same net value increase, making it more efficient and thus the better choice due to higher return on investment relative to the initial investment.

Use the Information for the Question(s)below