Question

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. $6,500

b. $7,200

c. $7,000

d. $6,800

Answer 1

Sol:

Present value (PV) of whole cash flows = $23,071.30

Discount rate = 7%

Cash flows = Year 1 - $5,000, Year 2 - $5,000, Year 3 - $5,000, Year 5 - $7,000

To determine cash flow received in year 4:

Cash flow received in year 4 = (Present value (PV) of whole cash flows - Sum of discounted cash flows) / 4th year PV factor @7%)

Cash flow received in year 4 = ($23,071.30 - ($4,672.9 + $4,367.19 + $4,081.49 + $4,990.91)) / (1/(1.07)^4)

Cash flow received in year 4 = ($23,071.30 - $18,112.49) / 0.7629

Cash flow received in year 4 = $4,958.81 / 0.7629

Cash flow received in year 4 = $6,500

Total value of firm:

Year	Cash flows	PV factor @7%	Discounted cash flows
1	5000	0.9346	4672.8972
2	5000	0.8734	4367.1936
3	5000	0.8163	4081.4894
4	6500	0.7629	4958.8165
5	7000	0.7130	4990.9033
Present value (PV) of whole cash flows	23071.3

Therefore cash flow received in year 4 is $6,500

Answer is (a. $6,500)

Working