Question

1. Find the present values of the following cash flow streams at a 5% discount rate. Do not round intermediate calculations. Round your answers to the nearest cent.

   0

   1

   2

   3

   4

   5

   Stream A	$0	$150	$450	$450	$450	$300
   Stream B	$0	$300	$450	$450	$450	$150

   Stream A: $  

   Stream B: $  

2. 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

(a) Stream A:

Here we will use the following formula:

PV = FV / (1 + r%)ⁿ

where, FV = Future value, PV = Present value, r = rate of interest = 5%, n= time period

For calculating the present value the given cash flows, we will calculate the present values of all the years and add them up. Now,putting the values in the above equation, we get,

PV = $150 / (1 + 5%)+ $450 / (1 + 5%)² + $450 / (1 + 5%)³ + $450 / (1 + 5%)⁴ + $300 / (1 + 5%)⁵

PV = $150 / (1 + 0.05)+ $450 / (1 + 0.05)² + $450 / (1 + 0.05)³ + $450 / (1 + 0.05)⁴ + $300 / (1 + 0.05)⁵

PV = $150 / (1.05)+ $450 / (1.05)² + $450 / (1.05)³ + $450 / (1.05)⁴ + $300 / (1.05)⁵

PV = $142.8571+ ($450 / 1.1025) + ($450 / 1.157625) + ($450 / 1.21550625) + ($300 / 1.27628)

PV = $142.8571 + $408.1632 + $388.7269 + $370.21611 + $235.0581

PV = $1545.02

So, required present value is $1545.02

Stream B:

Here we will use the following formula:

PV = FV / (1 + r%)ⁿ

where, FV = Future value, PV = Present value, r = rate of interest = 5%, n= time period

For calculating the present value the given cash flows, we will calculate the present values of all the years and add them up. Now,putting the values in the above equation, we get,

PV = $300 / (1 + 5%)+ $450 / (1 + 5%)² + $450 / (1 + 5%)³ + $450 / (1 + 5%)⁴ + $150 / (1 + 5%)⁵

PV = $300 / (1 + 0.05)+ $450 / (1 + 0.05)² + $450 / (1 + 0.05)³ + $450 / (1 + 0.05)⁴ + $150 / (1 + 0.05)⁵

PV = $300 / (1.05)+ $450 / (1.05)² + $450 / (1.05)³ + $450 / (1.05)⁴ + $150 / (1.05)⁵

PV = $285.7142+ ($450 / 1.1025) + ($450 / 1.157625) + ($450 / 1.21550625) + ($150 / 1.27628)

PV = $285.7142 + $408.1632 + $388.7269 + $370.21611 + $117.5290

PV = $1570.35

So, required present value is $1570.35

(b) When the discount rate is 0%, then present value will be the sum of the cash flows:

Stream A:

Present value = $150 + $450 + $450 + $450 + $300 = $1800

Stream B:

Present value = $300 + $450 + $450 + $450 + $150 = $1800