Question

Use the following information for questions 1 to 3.
Cumnock Corporation (CC) is estimating cash flows from a new product for the next year. The cash flow generated by the new product sales is uncertain.
It has estimated the following probability distribution of after-tax cash flows from these sales for the next year:
Possible State	Probability	After-tax Cash Flow
1	0.2	$9,000
2	0.3	$12,000
3	0.5	$15,000
Use the above information to answer the following questions. The tax rate is 35%
What is the expected value of the after-tax cash flows from the new design? What is the standard deviation of the after-tax cash flows? What is the coefficient of variation of after-tax cash flows?

Answer 1

Probability (i)	After tax cash flow (ii)	Expected cash flow (i) x (ii) = (iii)	{(ii) - 12,900)}2 = (iv)	(i) x (iv)
0.2	$9,000	0.2 x 9,000 = $1,800	15,210,000	3,042,000
0.3	$12,000	0.3 x 12,000 = $3,600	810,000	243,000
0.5	$15,000	0.5 x 15,000 = $7,500	4,410,000	2,205,000
		= 12,900		5,490,000

(a) Expected value of after tax cash flows = 1,800 + 3,600 + 7,500

= 12,900

(b) Standard deviation of after tax cash flows = 5,490,000

= 2,343

(c) Coefficient of variation of after tax cash flows = Standard deviation of after tax cash flows/Expected value of after tax cash flows

= 2,343/12,900

= 0.18