Question

A project has these cash flows: $2,000 3 years ago, $1,000 now and -$2,000 three years from now. Which is the correct formula for computing today's value of these cash flows given a 6% rate of interest?

Answer 1

Answer:

Today's value of all the cash flow=$1,702.793

Explanation:

Today's cash flows is the same as the present value of cash flows. To determine the present value of cash flows one needs to determine the value of the cash flow at a specific point in time, then use the interest rate to convert it into a present value. This can be done using the formula below;

Step 1: Formula for present value of future cash flows

P.V=F.V/(1+r)^n

where;

P.V=present value of future cash flows

F.V=future value of cash flows

r=rate of interest

n=number of years

In our case;

P.V=unknown, to be determined

F.V=-2,000

r=6%=6/100=0.06

n=3 years

replacing;

P.V=-2,000{(1+0.06)^3}=-$1,679.239

Step 2: Formula for present value of past cash flows

P.V=p.v{(1+r)^n}

where;

P.V=Present value of past cash flows=unknown

p.v=Past value of cash flows=$2,000

r=rate of interest=0.06

n=number of years=3 years

replacing;

P.V=2,000{(1+0.06)^3}=2,000(1.06^3)=$2,382.032

Step 3: Determine present cash flows

Present cash flows=$1,000 now

Step 4: Determine total present value of all the cash flows

Total present value=present value of future cash flows+present value of past cash flows+cash flows now

where;

Total present value=unknown, to be determined

present value of future cash flows=-$1,679.239

present value of past cash flows=$2,382.032

cash flows now=$1,000

replacing;

Total present value=-1,679.239+2,382.032+1,000=$1,702.793

Today's value of all the cash flow=$1,702.793