Cannonier, Inc., has identified an investment project with the following cash flows.

Problem 6-3 Future Value and Multiple Cash Flows [LO1]

Cannonier, Inc., has identified an investment project with the following cash flows.

 

Year	Cash Flow
1		$	960
2			1,190
3			1,410
4			2,150

If the discount rate is 9 percent, what is the future value of these cash flows in Year 4? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Future value

$

What is the future value at a discount rate of 12 percent? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Future value

$

What is the future value at a discount rate of 23 percent? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Future value

$

 

Explanation:

The time line is:
 

0	1	2	3	4
FV	$960	$1,190	$1,410	$2,150

 

To solve this problem, we must find the FV of each cash flow and sum. To find the FV of a lump sum, we use:

FV = PV(1 + r)t

FV@9% = $960(1.09)3 + $1,190(1.09)2 + $1,410(1.09) + $2,150 = $6,343.97

FV@12% = $960(1.12)3 + $1,190(1.12)2 + $1,410(1.12) + $2,150 = $6,570.67

FV@23% = $960(1.23)3 + $1,190(1.23)2 + $1,410(1.23) + $2,150 = $7,471.08

Notice, since we are finding the value at Year 4, the cash flow at Year 4 is added to the FV of the other cash flows. In other words, we do not need to compound this cash flow.

 

Calculator Solution:

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

CFo	$0	CFo	$0	CFo	$0
C01	$960	C01	$960	C01	$960
F01	1	F01	1	F01	1
C02	$1,190	C02	$1,190	C02	$1,190
F02	1	F02	1	F02	1
C03	$1,410	C03	$1,410	C03	$1,410
F03	1	F03	1	F03	1
C04	$2,150	C04	$2,150	C04	$2,150
F04	1	F04	1	F04	1
I = 9		I = 12		I = 23
NFV CPT		NFV CPT		NFV CPT
$6,343.97		$6,570.67		$7,471.08