Question

Hello! I need help solving these problems for engineering economy. Please show the full solution and all work for BOTH PROBLEMS. please write neatly and large (the resolution of photos on the site are low). please be as detailed as possible and answer BOTH questions. Thank you

8. Find the present equivalent worth for the following cash flow diagram if the interest rate is 20%. compounded every three months 1500 1200 900 600 300 6 789 10 300 600 900 1200 1500

Answer 1

8)

A	B	C	D	E	F	G	H	I	J	K	L	M	N	O
2
3		Present equivalent worth will the present value of the cash flows.
4
5		Cash Flow at Year 0	$1,500.00
6		Yearly decrease in amount	$300.00
7		Interest rate	20.00%	(Compounding quaterly)
8
9		Since the cash flow is annual and the compounding is quarterly, therefore
10		equivalent annual rate needs to be calculated as follows:
11
12		APR	20.00%
13		m	4	(for quarterly compounding)
14
15		Effective annual rate	=((1+APR/m)^m)-1
16			21.55%	=((1+D12/D13)^D13)-1
17
18		Hence effective annual rate is	21.55%
19
20		Cash flow can be written as follows:
21		Year	0	1	2	3	4	5	6	7	8	9	10
22		Cash Flow	$1,500.00	$1,200.00	$900.00	$600.00	$300.00	$0.00	($300.00)	($600.00)	($900.00)	($1,200.00)	($1,500.00)
23		Annuity Component		$1,200.00	$1,200.00	$1,200.00	$1,200.00	$1,200.00	$1,200.00	$1,200.00	$1,200.00	$1,200.00	$1,200.00
24		Gradient component	0	$0.00	($300.00)	($600.00)	($900.00)	($1,200.00)	($1,500.00)	($1,800.00)	($2,100.00)	($2,400.00)	($2,700.00)
25
26		General gradient cash flows can be written as follows:
27		Period	0	1	2	3	4	…	n
28		Cash Flow		0	g	2g	3g	…	(n-1)g
29
30		Present value of the gradient is given by following formula:
31
32
33
34		n=	10
35		Present Equivalent Worth	=Cash flow at Year 0+Present value of annuity component +Present Value of gradient component
36			=1500+1200*(P/A,21.55%,10)+(-300)*(P/G,21.55%,10)
37			$1,524.52	=D22+E23*PV(D18,D34,-1,0)+(-400)*(((((1+D18)^D34)-1)/(D18^2))-(D34/D18))*(1/((1+D18)^D34))
38
39		Hence Present Equivalent Worth is	$1,524.52
40