Compute the value of P in the accompanying cash flow diagram, assuming that i = 9%.

EXPERT ANSWER

Let the cash flow for year n be denoted by CF_n where n = 1, 2, 3 …. and the discount rate be denoted by i.

i = 9%

Present value of cash flows (P) = CF₀ / (1 + i) ^ (0) + CF₁ / (1 + i) ^ (1) + CF₂ / (1 + i) ^ (2) + CF₃ / (1 + i) ^ (3) + …. + CF₇ / (1 + i) ^ (7)

= $100 / (1 + 0.09) ^ (0) + $100 / (1 + 0.09) ^ (1) + $150 / (1 + 0.09) ^ (2) + $150 / (1 + 0.09) ^ (3) + $200 / (1 + 0.09) ^ (4) + $200 / (1 + 0.09) ^ (5) + $250 / (1 + 0.09) ^ (6) + $250 / (1 + 0.09) ^ (7)

= $100 / 1 + $100 / 1.09 + $150 / 1.19 + $150 / 1.30 + $200 / 1.41 + $200 / 1.54 + $250 / 1.68 + $250 / 1.83

= $100 + $91.74 + $126.25 + $115.83 + $141.69 + $129.99 + $149.07 + $136.76

= $991.32

The value of P is $991.32 which is the sum of the present values of all future cash flows.