The present value of the following cash flow stream is $8,550 when discounted at 9.3 percent

The present value of the following cash flow stream is $8,550 when discounted at 9.3 percent annually. What is the value of the missing cash flow? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

  

Year				Cash Flow
	1			$	2,150
	2
	3				2,750
	4				3,350

Explanation:

We are given the total PV of all four cash flows. If we find the PV of the three cash flows we know, and subtract them from the total PV, the amount left over must be the PV of the missing cash flow. So, the PV of the cash flows we know are:

 

PV of Year 1 CF: $2,150 / 1.093  = $1,967.06

PV of Year 3 CF: $2,750 / 1.0933 = $2,106.07

PV of Year 4 CF: $3,350 / 1.0934 = $2,347.28

 

So, the PV of the missing CF is:

$8,550 – 1,967.06 – 2,106.07 – 2,347.28 = $2,129.59

  

The question asks for the value of the cash flow in Year 2, so we must find the future value of this amount. The value of the missing CF is:

$2,129.59(1.093)2 = $2,544.12

  

Calculator Solution:

Note: Intermediate answers are shown below as rounded, but the full answer was used to complete the calculation.

  

	CF0	$0
	C01	$2,150
	F01	1
	C02	$0
	F02	1
	C03	$2,750
	F03	1
	C03	$3,350
	F04	1
	I = 9.3%
	NPV CPT
	$6,420.41

PV of missing CF = $8,550 – 6,420.41 = $2,129.59

Value of missing CF:

 

Enter

2

9.3%

$2,129.59

N

I/Y

PV

PMT

FV

Solve for

$2,544.12