Question

Consider the following project’s after-tax cash flow and the expected annual inflation rates during the project period.

1. Convert the cash flows in actual dollars into equivalent constant dollars with the base year 0. (complete the table for constant dollars cash flow)
2. If the annual real interest rate is 15%, what is the present worth of the cash flow? Is this project acceptable?

Final answer section (b):

actual cash flow
year	amount
0	- $295,000
1	$ 95,000
2	$ 45,000
3	$ 250,000
4	$ 30,000
5	$ 50,000

Constant dollars cash flow
year	amount
0
1
2
3
4
5

year	Inflation rate
1	8%
2	2%
3	2%
4	2%
5	6%

Answer 1

Solution a) Conversion factors for different years are calculated below:

Year	Conversion Factor	Conversion Value
1	=1/(1+8%)	0.925926
2	=1/(1+8%)(1+2%)	0.907771
3	=1/(1+8%)(1+2%)(1+2%)	0.889971
4	=1/(1+8%)(1+2%)(1+2%)(1+2%)	0.872521
5	=1/(1+8%)(1+2%)(1+2%)(1+2%)(1+6%)	0.823133

Year	Conversion Factor	Conversion Value	Cash Flow	Constant dollars cash flow
0	1	1	-295000	=-295000*1 =-295000
1	=1/(1+8%)	0.925926	95000	=95000*0.925926 = 87962.96
2	=1/(1+8%)(1+2%)	0.907771	45000	=0.907771*45000 = 40849.67
3	=1/(1+8%)(1+2%)(1+2%)	0.889971	250000	=0.889971*250000 = 222492.77
4	=1/(1+8%)(1+2%)(1+2%)(1+2%)	0.872521	30000	=0.872521*30000 = 26175.62
5	=1/(1+8%)(1+2%)(1+2%)(1+2%)(1+6%)	0.823133	50000	=0.823133*50000 = 41156.64

Solution 2) The real interest rate is 15%

The present worth of the constant dollars cash flows is calculated using the NPV function in the Excel

= NPV(Rate. Cash Flows from t=1) + Initial Investment

  

Since the NPV is positive and greater than 0, thus, the project is acceptable.

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