Question

A small manufacturer has net annual cash flows as follows over the first 4 years of business. The applicable interest rate varies from year to year.

End of Year	0	1	2	3	4
Cash Flow	-$80,000	$70,000	-$25,000	$60,000	$100,000
Interest Rate During Year		7%	9%	5%	4%

Determine the present worth, future worth, and uniform series annual equivalents for each of the 5 flows in the series. Determine a uniform series from t=0 to t=4.

Present Worth
Future Worth
Uniform Series Annual Equivalents

Answer 1

Interest rate varies from year to year

Present worth:

Present worth of cash flow in year 0 is -80,000

Present value of cash flow in year 1 is (70,000 / 1.07) = 65,420.56

Present value of cash flow in year 2 is [-25,000 / (1.09 * 1.07)] = -21,435.30

Present value of cash flow in year 3 is [60,000 / (1.05 * 1.09 * 1.07)] = 48,994.99

Present value of cash flow in year 4 is [100,000 / (1.04 * 1.05 * 1.09 * 1.07)] = 78,517.61

Sum of present cash flow is = 91,497.86

Future value

Future value of cash flow in year 0 is [-80,000 * 1.07 * 1.09 * 1.05 * 1.04] = -101,887.96

Future value of cash flow in year 1 is [70,000 * 1.09 * 1.05 * 1.04] = 83,319.6

Future value of cash flow in year 2 is [-25,000 * 1.05 * 1.04] = -27,300

Future value of cash flow in year 3 is [60,000 * 1.04] = 62,400

Future value of cash flow in year 4 is 100,000

Sum of future value of cash flow = 116,531.64

Uniform series annual equivalent:

Let us take a average interest rate of (7%, 9%, 5%, 4%) to determine annual equipment which is 6.25%

91,497.86 / {[1 - 1.0625^^-4] / 0.0625} = 26,556.82

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