Question

3. The index model has been estimated for stocks A and B with the following results: R(A) = 0.01 + 1.4Rm R(B) = 0.03 + 1.1Rm Additionally, the standard deviation of the market index is 21%. What is the covariance between stocks A and B?

3a. You now have $9101. At what annual interest rate would you have to invest this money so you can double it in 8 years? Assume annual compounding.

3b. A firm is considering the purchase of a machine which would represent an investment of $29 million, and would be depreciated in a straightline basis over 5 years. Sales are expected to be $12 million per year, and operating costs 32% of sales. The company is currently paying $3 million in interest per year, has a tax rate of 40%, and a WACC of 10%. What is the company’s free cash flow for year 1 of this project?

Answer 1

Part 1 - Calculation of Covariance

Covariance[R(A), R(B)] = (B1)*(B2)*(S.D.)2 B1 (beta) = 1.4 B2 (Beta) = 1.1 S.D. = Standard Deviation = 21% or 0.21

Cov[(R(A), R(B)] = (1.4)*(1.1)*(0.21)2 = 0.0679

Part 2 - Calculation of Compounding Rate of Interest

Rate = n*[(A/P)1/nt - 1] Rate = Let 'x' A = Accrued Amount after 8 years i.e. $9101*2 = $18202 P = Principal = $9101 t = Time i.e. 8 years n = Number of times compounding is done i.e. annually = 1

x = 1*[($18202/$9101)1/1*8 - 1] x = 1*[(2)]1/8 - 1] x = 1*[1.0905 - 1] x = 0.0905 or 9.050%

Part 3 - Calculation of free cash flow for year 1

Particulars	Amount (In million)
Sales	$12
Less : Operating cost ($12*32%)	$3.84
Operating Income	$8.16
Less : Depreciation ($29/5) as per straight line method [Assets value - salvage value]/Estimates Life	$5.8
EBIT (earning before income and tax)	$2.36
Less : Interest cost	$3
EBT (Earning before tax)	($0.64)
Less : (Tax) rate @40%	Nil (due to loss)
Add : Depreciation	$5.8
Free cash flow for y	$5.16