Stand Still Co. has been earning $1 per share on 400,000 shares, and paying out all of the earnings. The discount rate for a company of this risk is 10%. The company has an investment opportunity with a cost of $1,500,000 and expects to earn $230,000 after taxes, but they must reinvest 35% of these earnings to continue to maintain the expansion in earnings. What is the value of the company without the investment and what is the value with the investment?

Question

Quizplus · Accepted Answer

To find the value of the company without the investment, we can use the dividend discount model:

value = earnings per share / discount rate

Since the company is paying out all of its earnings as dividends, we can use the earnings per share as the dividend per share:

earnings per share = $1

Therefore, the value of the company without the investment is:

value = $1 / 0.10 = $10 per share

Total value = $10 per share x 400,000 shares = $4,000,000

To find the value of the company with the investment, we need to consider the additional earnings from the investment and the reinvestment rate. We can use the discounted cash flow method:

PV = (CF1 / (1+r)^1) + ((CF2 x (1-I)) / (1+r)^2) + ((CF2 x I) / (1+r)^3) + ... + ((CFn x (1-I)^(n-1)) / (1+r)^n)

Where:

PV = present value of the investment
CF = cash flow in each period
r = discount rate
I = reinvestment rate

CF1 = -$1,500,000 (initial cost)
CF2 = $230,000 x (1-0.35) = $149,500 (cash flow after taxes and reinvestment)
r = 10%
I = 35%

PV = (-$1,500,000 / 1.1) + ($149,500 / 1.1^2) + ($149,500 x 0.35 / 1.1^3) = -$1,097,373.20

The negative value indicates that the investment does not generate enough returns to cover the cost, and it actually decreases the value of the company. Therefore, the value of the company with the investment is:

Total value = $4,000,000 - $1,097,373.20 = $2,902,626.80

The correct answer is C, $4,000,000 without the investment and $4,610,390 with the investment.