Question

armour consulting is downsizing. the company paid an annual dividend of $4.20 last year and has announced plans to lower the dividend by 25 percent each year. once the dividend amount becomes zero, the company will go out of business. you have a required rate of return of 18 percent on this particular stock. what are your shares in this firm worth today on a per share basis?

Answer 1

The worth of one share in Armour Consulting today, on a per share basis, is $6.72.

Step-by-step explanation:

To calculate the worth of one share in Armour Consulting today, we need to determine the present value of the future dividends. The dividend payment is decreasing by 25% each year until it reaches zero. Given that the company paid an annual dividend of $4.20 last year, we can calculate the future dividends using a geometric series formula. The present value of the dividends can be found by discounting each future dividend using the required rate of return of 18%. Once we have the present value of the future dividends, we divide it by the number of shares to find the worth of one share.

Let's calculate:

1. Year 1 dividend: $4.20 * (1 - 0.25) = $3.15
2. Year 2 dividend: $3.15 * (1 - 0.25) = $2.36
3. Year 3 dividend: $2.36 * (1 - 0.25) = $1.77
4. Year 4 dividend: $1.77 * (1 - 0.25) = $1.33
5. Year 5 dividend: $1.33 * (1 - 0.25) = $1.00

Next, we calculate the present value of each dividend:

1. Present value of Year 1 dividend: $3.15 / (1 + 0.18) = $2.66
2. Present value of Year 2 dividend: $2.36 / (1 + 0.18)^2 = $1.70
3. Present value of Year 3 dividend: $1.77 / (1 + 0.18)^3 = $1.11
4. Present value of Year 4 dividend: $1.33 / (1 + 0.18)^4 = $0.72
5. Present value of Year 5 dividend: $1.00 / (1 + 0.18)^5 = $0.53

Finally, we sum up the present values of the dividends:

Total present value of dividends: $2.66 + $1.70 + $1.11 + $0.72 + $0.53 = $6.72

Since the company is downsizing and will go out of business when the dividend reaches zero, the worth of one share in Armour Consulting today is $6.72.