Question

The following table lists possible rates of return on HighRisk stock (HR) and on the market (M). Table also lists their joint probabilities.

RHR                 RM             Probability (RHR, RM)

0.08                 0.06                       0.10

0.10                 0.06                       0.20

0.10                 0.07                       0.25

0.12                 0.07                       0.10

0.12                 0.08                       0.15

0.14                 0.08                        0.20

a. List the possible values for RHR and the probabilities that correspond to those values. Compute the expected value, variance, and standard deviation for RHR.

b. List the possible values for RM and the probabilities that correspond to those values. Compute the expected value, variance, and standard deviation for RM.

c. Calculate the covariance, and coefficient of correlation of RHR and RM.

d. Calculate the beta for RHR.

e. Determine the risk free rate of return.

f. HR is considering a project that will require an investment of $10,000,000 and will provide before tax cash flows of $1,000,000 one year from today, thereafter growing at 3% per year in perpetuity. HR has a target Debt/Equity ratio of 2.0. It can issue bonds at par value with a coupon rate of 6%. It can also increase the use of accounts payable to finance the project. HR assigns accounts payable same cost as the overall WACC. It has a target accounts payable/ (debt-accounts payable) ratio of 0.30. HR has a 40% tax rate. Determine the WACC, and the project’s NPV.

Answer 1

Answer :-a) Calculation of expected value for RHR

(1) Return of RHR	(2) Joint Probabilty	(3) Expected value = (1)*(2)	(4) = (1)- expected value	(5)= (4)*(4)	(6) variance =(2)*(5)
0.08	0.1	0.008	-0.31	0.000961	0.0000961
0.1	0.2	0.02	-0.011	0.000121	0.0000242
0.1	0.25	0.025	-0.011	0.000121	0.00003025
0.12	0.1	0.0.12	0.009	0.000081	0.0000081
0.12	0.15	0.018	0.009	0.000081	0.00001215
0.14	0.2	0.028	0.029	0.000841	0.0001682
Total		0.111			0.000339

Expected value of RHR is 0.111 , Variance is 0.000339 & standard deviation is 0.01841

b) Calculation of expected values for RM

(1) Return of RM	(2) Joint Probability	(3) Expected Value = (1)*(2)	(4) = (1)-expected value	(5)= (4)*(4)	(6) variance=(2)*(5)
0.06	0.1	0.006	-0.0105	0.00011025	0.000011025
0.06	0.2	0.012	-0.0105	0.00011025	0.00002205
0.07	0.25	0.0175	-0.0005	0.00000025	0.0000000625
0.07	0.1	0.007	-0.0005	0.00000025	0.000000025
0.08	0.15	0.012	0.0095	0.00009025	0.0000135375
0.08	0.2	0.016	0.0095	0.00009025	0.00001805
Total		0.0705			0.00006475

Expected value of RM is 0.0705 , variance is 0.00006475 & standard deviation is 0.008047

c) Calculation of covariance of RHR & RM

(1) Column (4) of RHR	(2) Column (4) of RM	(3) = (1)*(2)
-0.31	-0.0105
-0.011	-0.0105
-0.011	-0.0005
0.009	-0.0005
0.009	0.0095
0.029	0.0095