Question

Discounted Payback An investment project costs $13,500 and has annual cash flows of ars. What is the discounted payback period if the discount rate is 0 percent? What f the ount rate is 7 percent? If it is 21 percent? noturn Your firm is considering purchasing a machine with the following annual,

please show work

Answer 1

Answer::

given

Initial Investment P=$13500

Annual cash flow A=$3900

If discount rate r=0%

Discounted cashflow= A/(1+r)^n

where n= year in which cash flow occur

for year 1

Discounted cashflow D=3900/(1+0%)^1=$3900

Remaining value of  Investment=P-D=13500-3900=$9600

Since after 1 year we have to only recover $9600 so this become our investment for second year.

r	0%
Year	Investment P	Cashflow	discounted cash flow D	Remaining value of  Investment P-D
1	13500	3900	3900	9600
2	9600	3900	3900	5700
3	5700	3900	3900	1800
4	1800	3900	3900	-2100
5	-2100	3900	3900	-6000
6	-6000	3900	3900	-9900

Since payback period occur when Remaining value of  Investment =0

so from above table we found that payback period will occur between 3 and 4 years

So payback period =3+(1800/3900)=3.46 years

If discount rate r=7%

Discounted cashflow= A/(1+r)^n

where n= year in which cash flow occur

for year 1

Discounted cashflow D=3900/(1+7%)^1=$3644.86

Remaining value of  Investment=P-D=13500-3644.86=$9855.14

Since after 1 year we have to only recover $9844.15 so this become our investment for second year.

r	7%
Year	Investment P	Cashflow	discounted cash flow D	Remaining value of  Investment P-D
1	13500.00	3900.00	3644.86	9855.14
2	9855.14	3900.00	3406.41	6448.73
3	6448.73	3900.00	3183.56	3265.17
4	3265.17	3900.00	2975.29	289.88
5	289.88	3900.00	2780.65	-2490.77
6	-2490.77	3900.00	2598.73	-5089.50

Since payback period occur when Remaining value of  Investment =0

so from above table we found that payback period will occur between 4 and 5 years

So payback period =4+(289.88/2975.29)=4.097 years

If discount rate r=21%

Discounted cashflow= A/(1+r)^n

where n= year in which cash flow occur

for year 1

Discounted cashflow D=3900/(1+21%)^1=$3223.14

Remaining value of  Investment=P-D=13500-3644.86=$10276.86

Since after 1 year we have to only recover $10276.86 so this become our investment for second year.

r	21%
Year	Investment P	Cashflow	discounted cash flow D	Remaining value of  Investment P-D
1	13500.00	3900.00	3223.14	10276.86
2	10276.86	3900.00	2663.75	7613.11
3	7613.11	3900.00	2201.45	5411.66
4	5411.66	3900.00	1819.38	3592.28
5	3592.28	3900.00	1503.62	2088.66
6	2088.66	3900.00	1242.66	846.00

Since payback period occur when Remaining value of  Investment =0

So from above table we found that payback period will be more than 6 years