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?

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amcool amcool · Answer 1 · 2020-09-24T03:23:15+02:00

Answer:

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

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.