Energy Project Financing : Resources and Strategies for Success

214 Energy Project Financing: Resources and Strategies for Success

P = Fn * (1 + i)–n

P = F 5 * (P|F,i,n)

P = 1000 * (P|F,8%,5)

P = 1000 * (0.6806)

P = 680.60

To verify your solution, try multiplying 680.60 * (F|P,8%,5). What

would expect for a result? (Answer: $1000) If your still not convinced, try

building a table like Table A-5 to calculate the year end balances each year

for five years.

A.6.6 Series Cash Flows

Having considered the transformation of a single sum to a future

worth when given a present amount and vice versa, let us generalize to

a series of cash flows. The future worth of a series of cash flows is simply

the sum of the future worths of each individual cash flow. Similarly, the

present worth of a series of cash flows is the sum of the present worths of

the individual cash flows.

Example 7

Determine the future worth (accumulated total) at the end of seven

years in an account that earns 5%/yr if a $600 deposit is made today and

a $1000 deposit is made at the end of year two?

for the $600 deposit, n = 7 (years between today and end of year 7)

for the $1000 deposit, n = 5 (years between end of year 2 and end of year

7)

F7 = 600 * (F|P,5%,7) + 1000 * (F|P,5%,5)

F7 = 600 * (1.4071) + 1000 * (1.2763)

F7 = 844.26 + 1276.30 = $2120.56

Example 8

Determine the amount that would have to be deposited today (pres-

ent worth) in an account paying 6%/yr interest if you want to withdraw

$500 four years from today and $600 eight years from today (leaving zero

in the account after the $600 withdrawal).