Question

4. Relaxation Resorts Inc. is a large company that is considering three long-term capital investments. Each investment has a useful life of five (5) years. Consider the profit for the following three alternative investment options:

	Discount Factor	Project A	Project B	Project C
Capital Investment		$175,000	$195,000	$205,000
Annual Profit:
Year 1	0.86957	$15,500	$21,000	$25,000
Year 2	0.75614	15,500	19,500	23,000
Year 3	0.65752	15,500	17,000	20,500
Year 4	0.57175	15,500	15,500	17,000
Year 5	0.49718	15,500	13,000	14,500
Total		$77,500	$86,000	$100,000

The discount factor for a five-year annuity at 15% is 3.35216.

Depreciation is calculated using the straight-line method with no residual/salvage value. The company’s cost of capital is 15%.

Required:

1. Calculate the following for each option:

1. Payback period
2. Average accounting rate of return
3. Net present value

Answer 1

Answer :

a. Payback period :

Project A

Payback period = Initial Investment / Net Cash Flow per Period

=  $175,000 / $15,500

= 11.29 years

Project B

Period	Cash Flow	Cumulative Cash Flow
0	($195,000)	($195,000)
1	$21,000	($174,000)
2	$19,500	($154,500)
3	$17,000	($137,500)
4	$15,500	($122,000)
5	$13,000	($109,000)

Payback period can't be calculated because Cumulative Cash Flow remains negative throughout the entire life of project.

Project C

Period	Cash Flow	Cumulative Cash Flow
0	($205,000)	($205,000)
1	$25,000	($180,000)
2	$23,000	($157,000)
3	$20,500	($136,500)
4	$17,000	($119,500)
5	$14,500	($105,000)

Payback period can't be calculated because Cumulative Cash Flow remains negative throughout the entire life of project.

b. Average accounting rate of return ;

Project A

= Average return after depreciation / Average Investment

Average return = ($15,500 x 5 years) / 5 = $15,500

Average Investment = $175,000 / 2 = $87,500

Depreciation = $175,000 / 5 years = $35,000

Average accounting rate of return

= ($15,500 - $35,000) / $87,500 x 100

= ($19,500) / $87,500 x 100

= (22.29%)

Project B

= Average return after depreciation / Average Investment

Average return = $86,000 / 5 = $17,200

Average Investment = $195,000 / 2 = $97,500

Depreciation = $195,000 / 5 years = $39,000

Average accounting rate of return

= ($17,200 - $39,000) / $97,500 x 100

= ($21,800) / $97,500 x 100

= (22.36%)

Project C

= Average return after depreciation / Average Investment

Average return = $100,000 / 5 = $20,000

Average Investment = $205,000 / 2 = $102,500

Depreciation = $205,000 / 5 years = $41,000

Average accounting rate of return

= ($20,000 - $41,000) / $102,500 x 100

= ($21,000) / $102,500 x 100

= (20.49%)

c. Net present value :

Net present value = Present value of annual cash inflow - Initial Investment

Project A

Net present value

= [$15,500 x PVAF(15%,5years)] - $175,000

= [$15,500 x 3.35216] - $175,000

= $51,958.48 - $175,000

= ($123,041.52)

Project B

Year	Cash Flow	PVF @15%	Present Value
0	($195,000)	1.00	($195,000)
1	$21,000	0.86957	$18,260.97
2	$19,500	0.75614	$14,744.73
3	$17,000	0.65752	$11,177.84
4	$15,500	0.57175	$8,862.13
5	$13,000	0.49718	$6,463.34
		NPV	($135,490.99)

Project C

Year	Cash Flow	PVF @15%	Present Value
0	($205,000)	1.00	($205,000)
1	$25,000	0.86957	$21,739.25
2	$23,000	0.75614	$17,391.22
3	$20,500	0.65752	$13,479.16
4	$17,000	0.57175	$9,719.75
5	$14,500	0.49718	$7,209.11
		NPV	($135,461.51)