Question

An increasing amount cash flow has been projected for an investment in renewable energy. Based on an increases in the amount charged per unit of energy and growth in energy use, the payment of 3800 per period with the first payment one period from now is expected to increase by 300 each period thereafter for a total of 18 periods. Using a discount rate of 11.0 percent, what is the present worth of this payment stream?

Answer 1

The present worth is the sum of present value of all the 18 period which is approximately $47,472.89.

How is that so?

Step 1: Calculate the individual present values:

First period: Present value = Payment / (1 + Discount Rate) = 3800 / (1 + 0.11) = 3423.42

Second period: Present value = (Payment + Growth) / (1 + Discount Rate)² = (3800 + 300) / (1 + 0.11)² = 3153.43

Third period: Present value = (Payment + 2 * Growth) / (1 + Discount Rate)³ = (3800 + 600) / (1 + 0.11)³ = 2901.13

Continue this calculation for all 18 periods, adding the growth amount (300) to the payment for each subsequent period and raising the discount rate to the appropriate power for each period.

Step 2: Sum the present values:

Once you have calculated the present value of each individual payment, simply add them all together. This will give you the total present worth of the entire cash flow stream.

Present value = 3423.42 + 3153.43 + 2901.13 + ... (continue for all 18 periods)

Total present value = approximately $47,472.89

Answer 2

The present worth of this payment stream is 48,942.42.

Step-by-step explanation:

To calculate the present worth of the payment stream, the formula for calculating the present value of a growing annuity is used as

follows:

PW = (P / (r - g)) * (1 - ((1 + g) / (1 + r))^n) .................... (1)

Where;

PW = Present worth of the payment stream = ?

P = Payment per period = 3800

r = interest per year = 11.0%, or 0.11

g = growth rate of payment per period = 300 / 3800 = 0.0789473684210526

n = Number of period = 18

Substituting the values into equation (1), we have:

PW = (3800 / (0.11 - 0.0789473684210526)) * (1 - ((1 + 0.0789473684210526) / (1 + 0.11))^18)

PW = (3800 / 0.0310526315789474) * (1 - (1.0789473684210526 / 1.11)^18)

PW = 122372.881355932 * (1 - 0.97202465623518^18)

PW = 122372.881355932 * (1 - 0.60005500664059)

PW = 122372.881355932 * 0.39994499335941

PW = 48,942.42

Therefore, the present worth of this payment stream is 48,942.42.