Question

9-55 Year E Sens 0 $90 -$110-$100 $120 35 35 35 35 9-60 20 2 20 20 4 20 5 20 6 20 10 20 30 40 50 180 )Based on the payback period, which altermnative-41 Amal (b) Based on future worth analysis, which of the (c) Based on future worth analysis, which alterna- (a) At 10% interest, what is the benefit-cost ratio is preferred? four alternatives is preferred at 5% interest? tive is preferred at 20% interest? for Alt. G? change (a) W (b) V 9-62 Co tory equipment costing

Answer 1

a) Based on PBP, alt F is a better option

Year	E	Cumulative Cash flow	F	Cumulative Cash flow	G	Cumulative Cash flow	H	Cumulative Cash flow
0	-90	-90	-110	-110	-100	-100	-120	-120
1	20	-70	35	-75	0	-100	0	-120
2	20	-50	35	-40	10	-90	0	-120
3	20	-30	35	-5	20	-70	0	-120
4	20	-10	35	30	30	-40	0	-120
5	20	10	0	30	40	0	0	-120
6	20	30	0	30	50	50	180	60
	PBP	4.50		3.14		5.00		6.00

The formula = negative last cumulative cash flow period+(abs(negative last cumulative cash flow/positive cash flow of next period)

So, here for alt F, PBP = 3+(5/35) = 3.14

b. Based on FW, alt H is a better option

FW- Compounded cash flow at 5%
Year	E	F	G	H
0	-90.00	-110.00	-100.00	-120.00
1	21.00	36.75	0.00	0.00
2	22.05	38.59	11.03	0.00
3	23.15	40.52	23.15	0.00
4	24.31	42.54	36.47	0.00
5	25.53	0.00	51.05	0.00
6	26.80	0.00	67.00	241.22
FW	52.84	48.40	88.70	121.22

The formula is cashflow*(1+0.05)^n, n is number of years

c Here too, alt H is a better option

FW- Compounded cash flow at 20%
Year	E	F	G	H
0	-90.00	-110.00	-100.00	-120.00
1	24.00	42.00	0.00	0.00
2	28.80	50.40	14.40	0.00
3	34.56	60.48	34.56	0.00
4	41.47	72.58	62.21	0.00
5	49.77	0.00	99.53	0.00
6	59.72	0.00	149.30	537.48
FW	148.32	115.46	260.00	417.48

The formula is cashflow*(1+0.2)^n, n is number of years

d. Alt G B:C ratio is 0.97

Year	G	Discounted Benefit	Discounted Cost
0	-100		100
1	0	0.00
2	10	8.26
3	20	15.03
4	30	20.49
5	40	24.84
6	50	28.22
		96.84	100

B:C = Sum of discounted Benefit/ Sum of discounted Cost = 96.84/100 = 0.9684

Discounting formula = Cashflow/(1+0.1)^n , n is number of years