Question

Marcia observed the following cash flow series (in $1000 units) in an accounting report at work. The actual amounts in years 1 and 4 are missing; however, the report states that the present worth in year 0 was $364,000 at an interest rate of 8% per year. Calculate the value of x.

Year	0	1	2	3	4	5	6
Cash flow, $×1000	40	x	40	40	x	40	40

The value of x is determined to be $ ?

Answer 1

Present value factor (PVF) = 1/(1+r)^n

Present value factor (PVF) = 1/(1+0.08)^n

Where, r = interest rate = 8% =0.08

n = number of year.

Present value in each year = PVF*cash flow

Present worth = sum of all present values in each year

year	PV factor	Cash Flow	Present Value
0	1	40000	40000
1	0.926	X	0.926 * X
2	0.857	40000	34294
3	0.794	40000	31753
4	0.735	X	0.735*X
5	0.681	40000	27223
6	0.630	40000	25207

Present Value = 158477 + 1.661X = 364000

1.661X = 364000 - 158477

1.661X = 205523

X =(205523 / 1.61)

X = $123737.82