Question

In: Finance

Suppose that you will receive $5,000 in year 1, $5,000 in year 2, $5,000 in year...

Suppose that you will receive $5,000 in year 1, $5,000 in year 2, $5,000 in year 3 and $7,000 in year 5. And somehow you know that the present value for the whole cash stream is $23,071.30. At a 7% discount rate, the cash flow received in year 4 will be ــــــــــــــــــــــــــــ.

Select one:

a. $7,000

b. $7,200

c. $6,500

d. $6,800

Solutions

Expert Solution

Let the cash flow received in year 4 will be X.

Computation of total PW of cash flows:

Year (n)

Cash Flow (C)

Computation of PV Factor 1/(1+r) n

PV Factor @ 7 % (F)

PV (C x F)

1

$5,000

1/ (1+0.07)1

0.934579439252336

$4,672.897196

2

5,000

1/ (1+0.07)2

0.873438728273212

4,367.193641

3

5,000

1/ (1+0.07)3

0.816297876890852

4,081.489384

4

X

1/ (1+0.07)4

0.762895212047525

0.762895212047525 X

5

7,000

1/ (1+0.07)5

0.712986179483668

4,990.903256

                Total PV

$18,112.48348 + 0.762895212047525 X

$18,112.48348 + 0.762895212047525 X = $ 23,071.30

0.762895212047525 X = $ 23,071.30 - $18,112.48348

                                      = $ 4,958.81652

X = $ 4,958.81652/0.762895212047525

= $ 6,499.996909 or $ 6,500

The cash flow received in year 4 will be $ 6,500

Hence option “c. $ 6,500” is correct answer.

jeff jeffy answered 1 year ago
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