Question

Question 1 (6 pts): Both devices A and B have useful lives of 6 years. Their costs, annual benefits,

and salvage values are shown below. With interest at 8% per year, which device should you choose using the present worth? Draw the cash flow diagrams for both devices (3 pts) and show all work (3 pts).

Alternatives	A	B
Initial cost	$2,000	$3,000
Uniform annual benefit	$450	$600
End-of-life salvage value	$200	$700

Answer 1

To choose between the device A and B using the present worth we have to calculate the net present value of both devices.

Net present value is the difference between present value of cash inflows and cash outflows. All the present value of expected cash inflows are added and cash outflow is then subtracted from it.

Positive NPV: Accept the project.

Negative NPV: Reject the project.

For converting future value of cash inflow to inflow we use the formula

Present value = 1/(1+r)ⁿ

n = number of years

r = interest rate

FOR DEVICE A

YEARS	CASH FLOWS	DISCOUNTING FACTOR @8%	PRESENT VALUE
0	($2000)	-	($2000)
1	$450	0.926	$416.7
2	$450	0.857	$385.65
3	$450	0.794	$357.3
4	$450	0.735	$330.75
5	$450	0.681	$306.45
6	$450	0.630	$283.5
6	$200	0.630	$126
NET PRESENT VALUE =   $206.35

We have given uniform cash inflow of $450 for 6 years, salvage value is $200 at 6^th year and interest rate is 8%. Cash outflow is $2000 which is represented in red because it is a negative value. With the use of formula of present value given above we calculated all the discounting factor and then calculated the   present value of cash inflow by multiplying the discounting factor and future cash outflow.

By adding all the present value of cash inflow we deduct cash outflow from it and NPV here is POSITIVE so we can ACCEPT the device A.

FOR DEVICE B

YEARS	CASH FLOWS	DISCOUNTING FACTOR @8%	PRESENT VALUE
0	($3000)	-	($3000)
1	$600	0.926	$555.6
2	$600	0.857	$514.4
3	$600	0.794	$476.29
4	$600	0.735	$441.01
5	$600	0.681	$408.6
6	$600	0.630	$378.10
6	$700	0.630	$441.11
NET PRESENT VALUE =    215.11

For device B we have uniform cash inflow of $600, salvage value is $700 and cash outflow is $3000 it is also given in red because it is a negative value. Discounting factor will same because for both devices interest rate is 8%. We then multiply the future cash inflow by discounting rate to calculate present value of cash inflow and then add all the present cash inflows and deduct cash outflow from it. Here the NPV is POSITIVE so we can ACCEPT the device B.

Since both the projects have NPV positive but we have to choose one, we will choose Device B over A because NPV of device B is greater than NPV of device A.