# Discounted Cash Flows Discounted cash flows

When working with capital budgeting techniques, future cash inflows and outflow are discounted to its present value. This is undertaken for number of reasons. Firstly, according to the time value of money, the dollar to be received in the future has less value than the dollar to be received in the present.

Moreover, adjustment for risk and inflation must also be made. Therefore, compensation is necessary to equalize future and present values of cash flows. Such compensation is known as the required rate of return. The higher is the required return (which is used as a discount rate) the lower will be the present value of the future cash flows from the proposed project.

To ensure that such compensation is in place, the future cash inflows are discounted to its present value with the use of required return. To do so, the following calculation can be made with the help of the financial calculator:

FV: (future cash flow)

N: number of periods between future cash flow and present

I: required return

PV: calculate

Test yourself:

ABC expects to have cash inflows of \$5,000 over the next 5 years from the project A. The required return of ABC is 8%. What is the present value of the cash inflows?

Solution:

In this problem we have an annuity, which refers to a terminating an equal periodic cash flows over specific period of time, such as 10 years. Due to the fact that we are dealing with an annuity, we can calculate the present value of all cash inflows much faster and easier than if we were dealing with the mixed stream of cash flows. If we were dealing with the mixed stream, which refers to unequal cash flows during specific period with no precise pattern, than we would have to calculate present value of each cash flow separately and than add them together. We will do such calculation in the next problem. An annuity allows us to calculate present value of all cash flows in one step.

The calculation for this problem is as follows:

PMT: 5,000 (PMT here refers to equivalent cash inflows over period of time)

N: 5

I: 8

PV: calculate = 19,963.55

Test yourself:

ABC also have option to invest in project B. Cash flows from that project will be \$3,000 at the end of year 1, \$5,000 at the end of year 2, \$4,000 at the end of years 3 and 4 and \$8,000 at the end of year 5. Calculate the present value of above cash flows if required return of ABC is 8%.

Solution:

As promised, now we are dealing with the mixed stream of cash inflows. We will need to calculate present value of each cash flow separately and than add all present values. With the help of financial calculator, calculation will be as follows:

Cash flow in year 1:

FV: 3,000 (cash inflow at the end of year one)

N: 1

I: 8

PV: calculate 2,777.78

Cash flow in year 2:

FV: 5,000 (cash inflow at the end of year two)

N: 2

I: 8

PV: calculate 4,286.69

Cash flow in year 3:

FV: 4,000 (cash inflow at the end of year three)

N: 3

I: 8

PV: calculate 3,175.33

Cash flow in year 4:

FV: 4,000 (cash inflow at the end of year four)

N: 4

I: 8

PV: calculate 2,940.12

Cash flow in year 5:

FV: 8,000 (cash inflow at the end of year five)

N: 5

I: 8

PV: calculate 5,444.67

Now we will add up all present values to obtain the final answer:

=2,777.78 + 4,286.69 + 3,175.33 + 2,940.12 + 5,444.67

=18,624.59

Therefore, the present value of a mixed stream of cash flows from project B is \$18,624.59.

If we look at this a previous problem we can conclude that, assuming that projects A and B require equal investment, project A is a better choice for capital expenditure because it offers a higher present value of future cash inflows (\$19,963.55) from investment than does project B (\$18,624.59).