Question

Consider the following information on returns and probabilities:

Invest 100% of your money in Asset A and  0% in Asset B.

State      Probability           A             B                           

Boom         .25                   12%       4%         

Bust            .75                   6%         18%     

what is the standard deviation of the return on Stock A in %?

a. 1.7  

b. 2.6

c. 3.9  

d. 4.6   

e. 5.5   

f. 6.9    

g. 7.5    

h. 9.0

   i. 8.2  

j. 11         

2) An investment project has the following cash flows: CF0 = -1,200,000; C01 – C05 = 300,000 each

If the required rate of return is 12%, payback period of the project is ( ) years

Answer 1

Calculation of Standard deviation of return of stock X is-

State	Probability (p)	Return(x)	PX	P(X-EX)(X-EX)
Boom	0.25	12	3	5.0625
Bust	0.75	6	4.5	1.6875
		Expected rweturn (EX)	7.5	6.75

So, standard deviation of stock X is square root of summation of P(X-EX)(X-EX) i.e. 6.75

So, standard deviation is 2.59807621135.

i.e. 2.6 (Ans b-2.6)

2) Calculation of pay back period

Year	Cash flow	PV of cash flow	summation of cash inflows
0	-1200000	-1200000
1	300000	267857.1429	267857.1
2	300000	239158.1633	507015.3
3	300000	213534.0743	720549.4
4	300000	190655.4235	911204.8
5	300000	170228.0567	1081433

In this case till 5 years 1081433 is total cash inflow, whereas the outflow is 1200000.

So, pay back of 1200000 is not happen in the given senario. If income is contined for more years we could have calculated the pay back peroiod. Payback period must be than 5 years.