Question

Find the present values of the following cash flow streams at a 4% discount rate. Do not round intermediate calculations. Round your answers to the nearest cent.

0 1 2 3 4 5

Stream A $0 $100 $450 $450 $450 $250

Stream B $0 $250 $450 $450 $450 $100

Stream A: $ ____?

Stream B: $ ____?

What are the PVs of the streams at a 0% discount rate? Round your answers to the nearest dollar.

Stream A: $ ___?

Stream B: $____?

Answer 1

Present value can be calculated with the help of below formula-

where,

FV = future value

PV = present value

r = rate of interest

n = no. of years

Stream A at 4 % discount rate

Present value of all cashflow are calculated as -

For example- PV of year 3 is calculated as -

PV = 450 / ( 1 + 0.04)³ = 400.0483614 $

Like this, PV are calculated for all the years in below table -

year	cashflow	present value of cashflow
0	0	0
1	100	96.15384615
2	450	416.0502959
3	450	400.0483614
4	450	384.661886
5	250	205.4817767

Total present value of Stream A =Total of all years cashflows present value

= 1502.396166 $

= 1502 $ (approx)

Stream B at 4 % discount rate

Present value of all cashflow are calculated as -

PV of all years cash flow is calculated with help of PV formula mentioned as upon. The calculations are shown in table below-

year	cashflow	present value of cashflow
0	0	0
1	250	240.3846154
2	450	416.0502959
3	450	400.0483614
4	450	384.661886
5	100	82.19271068

Total present value of Stream A =Total of all years cashflows present value

= 1523.337869 $

= 1523 $ (approx)

At 0 % discount rate, there will not be any effect of discounting. Hence the total present value of the cashflows will be equal to total of all cashflows.

For example-

Csshflows of Stream A are shown in below table-

year	cashflow
0	0
1	100
2	450
3	450
4	450
5	250

If we find present value of an year cashflow with help of PV formula-

PV of 3rd year cashflow = 450 / ( 1 + 0)³

= 450 / 1

= 450 $

Like wise, at 0 % discount rate present value of all years cash flow will be equal to that year cashflow.

Hence,

Total present value of Stream A at 0 % discount rate = 100 + 450 + 450 + 450 + 250

= 1700 $

Likewise,

For stream B cash flows are -

year	cashflow
0	0
1	250
2	450
3	450
4	450
5	100

Total present value of Stream B at 0 % discount rate = 250 + 450 + 450 + 450 + 100

= 1700 $

Hope it helps!