Question

Find the present value of $700 due in the future under each of these conditions: 9% nominal rate, semiannual compounding, discounted back 10 years. Do not round intermediate calculations. Round your answer to the nearest cent. $ 9% nominal rate, quarterly compounding, discounted back 10 years. Do not round intermediate calculations. Round your answer to the nearest cent. $ 9% nominal rate, monthly compounding, discounted back 1 year. Do not round intermediate calculations. Round your answer to the nearest cent. $ Why do the differences in the PVs occur?

1. Find the present values of the following cash flow streams at a 10% discount rate. Do not round intermediate calculations. Round your answers to the nearest cent.

   0

   1

   2

   3

   4

   5

   Stream A	$0	$150	$350	$350	$350	$250
   Stream B	$0	$250	$350	$350	$350	$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

Present value under different scenarios is computed as shown below:

Semi Annual Compounding

Rate of interest

= 9% / 2

= 4.5%

= $ 700 / 1.045^{10 x 2}

= $ 290.25 Approximately

Quarterly Compounding

Rate of interest

= 9% / 4

= 2.25%

= $ 700 / 1.0225^{10 x 4}

= $ 287.45 Approximately

Monthly Compounding

Rate of interest

= 9% / 12

= 0.75%

= $ 700 / 1.0075¹²

= $ 639.97 Approximately

The differences between the PV's occur because of the amount and timing of cash flows and also the discount rate at which we are discounting the cash flows

a. Present value of stream A is computed as shown below:

= $ 0 + $ 150 / 1.10¹ + $ 350 / 1.10² + $ 350 / 1.10³ + $ 350 / 1.10⁴ + $ 250 / 1.10⁵

= $ 1,083 Approximately

Present value of stream B is computed as shown below:

= $ 0 + $ 250 / 1.10¹ + $ 350 / 1.10² + $ 350 / 1.10³ + $ 350 / 1.10⁴ + $ 150 / 1.10⁵

= $ 1,112 Approximately

b. Present value of stream A is computed as shown below:

= $ 0 + $ 150 + $ 350 + $ 350 + $ 350 + $ 250

= $ 1,450

Present value of stream B is computed as shown below:

= $ 0 + $ 250 + $ 350 + $ 350 + $ 350 + $ 150

= $ 1,450

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