5.The appropriate discount rate for the following cash flows is 14 percent compounded quarterly. Year Cash...

5.The appropriate discount rate for the following cash flows is 14 percent compounded quarterly.

Year	Cash Flow
1	$1,000
2	600
3	0
4	1,300

Required:

What is the present value of the cash flows?

Expert Solution

Given that, discounted rate for cash flows is 14% compounded quarterly.
So, quarterly interest rate =14%/4=3.5%

Effective annual rate = (1+quarterly interest rate)^4 -1= (1+3.5%)^4 -1 =(1.035)^4 -1=1.147523 -1 =0.147523=14.7523%
Cash flows are:
Year 1:$1000
Year 2:$600
Year 3:$0
Year 4:$1300

We can find the present value of the cash flows using the following formula:
Present value=Cash flow in year 1/(1+Effective annual rate)^1+Cash flow in year 2/(1+Effective annual rate)^2+Cash flow in year 3/(1+Effective annual rate)^3+Cash flow in year 4/(1+Effective annual rate)^4

Effective annual rate = 14.7523%

Present value=$1000/(1+14.7523%)^1+$600/(1+14.7523%)^2+$0/(1+14.7523%)^3+$1300/(1+14.7523%)^4
=$1000/(1.147523)^1+$600/(1.147523)^2+$0/(1.147523)^3+$1300/(1.147523)^4
=$1000/1.147523+$600/1.316809036+$0/1.511068655+$1300/1.733986036
=$871.4422282+$455.6469341+$0+$749.7176869
=$2076.807
The present value of the cash flows=$2076.807

jeff jeffy answered 1 year ago

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