Question

Answer the question. Consider the three mutually exclusive alternatives below. Determine which alternative is preferable at an interest rate of 10% per year. Assume all of these projects are repeating perpetually, Alternative A B C Capital investment $400,000 $100,000 $150,000 Annual expense $189,000 $94,500 $134,000 Annual revenue $309,000 $204,500 $300,000 Salvage value $65,000 $50,000 $100,000 Life, years | 24 36 12 1 i FBI , O EE % 5 % Solution: AW(M) - -400,000 (A/P, 10%,24) - 189,000 + 309,000 + 65,000 (A/F, 10%,24) = -400,000

please solve in word format

Answer 1

	A	B	C
Annual revenue	309,000	204,500	300,000
annual expense	-189,000	-94,500	-134,000
Total cash flow	120,000	110,000	166,000

For project A,

Project cost = 400,000

Salvage value = 65000

Life= 24

Interest = 10%

Present value of all the cash flow for the next 24 years= P* (1- (1+r)^-n)/r

P =120,000

R= 10%

N= 24

PV = 120000* (1-(1+0.10)^(-24))/0.10

= 1,078,169.28

Profit from sale of asset = PV of the future value = Future Value / (1 + interest rate%)^n

= 65000/(1+0.10)^24

= 6599.16

So total cash inflow= 1078169.28+6599.16= 1084768.45

Total cash outflow= 400000

So the NPV= Total cash inflow – total cash outflow

= 1084768.45-400000

= $684,768.45

Project B:

Project cost = 100,000

Salvage value = 50000

Life= 36

Interest = 10%

Present value of all the cash flow for the next 36 years= P* (1- (1+r)^-n)/r

P =110,000

R= 10%

N= 36

PV = 110000* (1-(1+0.10)^(-36))/0.10

= 1,064415.90

Profit from sale of asset = PV of the future value = Future Value / (1 + interest rate%)^n

= 50000/(1+0.10)^36

= 1617.45

So total cash inflow= 1066033.36

Total cash outflow= 100000

So the NPV= Total cash inflow – total cash outflow

= 1066033-100000= $966,033.36

Project C:

Project cost = 150,000

Salvage value = 100,000

Life= 12

Interest = 10%

Present value of all the cash flow for the next 36 years= P* (1- (1+r)^-n)/r

P =166,000

R= 10%

N= 12

PV = 166,000* (1-(1+0.10)^(-12))/0.10

= 1,131072.84

Profit from sale of asset = PV of the future value = Future Value / (1 + interest rate%)^n

= 100000/(1+0.10)^12

= 31863.08

So total cash inflow= 1162935.92

Total cash outflow= 150,000

So the NPV= Total cash inflow – total cash outflow

= $1,162,935.92

So , in conclusion

	A	B	C
NPV	$ 684,768.45	$ 966,033.36	$ 1,162,935.92

So the alternative A is closest to $0 and so it is preferably at 10%