Question

Expected value analysis: San Lucas Corporation

San Lucas Corporation is considering investment in robotic machinery based upon the following estimates:

Cost of robotic machinery	$4,000,000
Residual value	300,000
Useful life	10 years

Assume San Lucas Corporation assigns the following probabilities to the estimated annual net cash flows:

Annual Net Cash Flow	Probability of Occurring
$900,000	0.10
700,000	0.50
500,000	0.40
Total	1.00

a. Compute the expected value of the annual net cash flows.

Annual Net Cash Flow		Expected Value
$900,000		$
700,000
500,000
Total		$

b. Determine the expected net present value of the equipment, assuming a desired rate of return of 10% and the expected annual net cash flows computed in part (a). Use the present value tables (Exhibit 2 and 5) provided in the chapter in determining your answer.

Net present value: $?

San Lucas Corporation is considering investment in robotic machinery based upon the following estimates:

Cost of robotic machinery	$4,000,000
Residual value	300,000
Useful life	10 years

a. Determine the net present value of the equipment, assuming a desired rate of return of 10% and annual net cash flows of $700,000. Use the present value tables appearing in Exhibit 2 and 5 of this chapter.

Net present value: $?

b. Determine the net present value of the equipment, assuming a desired rate of return of 10% and annual net cash flows of $500,000, $700,000, and $900,000. Use the present value tables (Exhibit 2 and 5) provided in the chapter in determining your answer. If required, use the minus sign to indicate a negative net present value.

Annual Net Cash Flow	$500,000	$700,000	$900,000
Net present value	$?	$?	$?

c. Determine the minimum annual net cash flow necessary to generate a positive net present value, assuming a desired rate of return of 10%. Round to the nearest dollar.

Annual Net Cash Flow: $?

Answer 1

(a.) Computation of Expected value of annual net cash flows -

Annual Net Cash flow(a)	Probability (b)	Expected value of net cash flows (a*b)
900000	0.1	90000
700000	0.5	350000
500000	0.4	200000
Total		640000

(b) Calculation of Net present value

Year	Cash flows	Discounting @ 10%	PV
0	-4000000	1.0000	-4000000.00
1	640000	0.9091	581818.18
2	640000	0.8264	528925.62
3	640000	0.7513	480841.47
4	640000	0.6830	437128.61
5	640000	0.6209	397389.65
6	640000	0.5645	361263.32
7	640000	0.5132	328421.20
8	640000	0.4665	298564.72
9	640000	0.4241	271422.48
10	940000	0.3855	362410.69
			48185.93

Part 2

Calculation of Net Present value

Year	Cash flows	Discounting @ 10%	PV
0	-4000000	1.0000	-4000000.00
1	700000	0.9091	636363.64
2	700000	0.8264	578512.40
3	700000	0.7513	525920.36
4	700000	0.6830	478109.42
5	700000	0.6209	434644.93
6	700000	0.5645	395131.75
7	700000	0.5132	359210.68
8	700000	0.4665	326555.17
9	700000	0.4241	296868.33
10	1000000	0.3855	385543.29
			416859.96

(b) Calculation of NPV

Year	Cash flows	Discounting @ 10%	PV
0	-4000000	1.0000	-4000000.00
1	500000	0.9091	454545.45
2	700000	0.8264	578512.40
3	900000	0.7513	676183.32
4
5
6
7
8
9
10	300000	0.3855	115662.99
		NPV	-2175095.84

(c) Calculation of Annual Net cash flow necessary to generate a positive net present value -

Suppose Annual net cash flow = x to generate positive cash flow

so x*PVIFA(10%,3years) + 300000*PVIF(10%,10 Years) = 4000000

x*2.4869 + 300000*0.3855= 4000000

x = (4000000-115663)/2.4869

= 1561919

1561919 is min. cash flow to break even the investment more than this annual cash flow will generate positive cash flows.

Please check with your answer and let me know.