Question

Vandalay Industries is considering the purchase of a new machine for the production of latex. Machine A costs $2,100,000 and will last for 4 years. Variable costs are 38 percent of sales, and fixed costs are $150,000 per year. Machine B costs $4,310,000 and will last for 7 years. Variable costs for this machine are 27 percent of sales and fixed costs are $115,000 per year. The sales for each machine will be $8.62 million per year. The required return is 10 percent and the tax rate is 35 percent. Both machines will be depreciated on a straight-line basis.

a) If the company plans to replace the machine when it wears out on a perpetual basis, what is the EAC for machine A?

b) If the company plans to replace the machine when it wears out on a perpetual basis, what is the EAC for machine B?

2. A stock has an expected return of 18 percent, its beta is 1.4, and the expected return on the market is 14 percent. What must the risk-free rate be? (Do not round your intermediate calculations.)

Answer 1

Question 1:

a. We first calculate the NPV for machine A and then the EAC for Machine as shown in the table below:

Machine A
Year	0	1	2	3	4
Initial Cost	-2100000
Sales		8620000	8620000	8620000	8620000
Variable costs		-3275600	-3275600	-3275600	-3275600
Fixed costs		-150000	-150000	-150000	-150000
Depreciation		-525000	-525000	-525000	-525000
Pre tax Income		4669400	4669400	4669400	4669400
Taxes at 35%		-1634290	-1634290	-1634290	-1634290
Net Income		3035110	3035110	3035110	3035110
Add back depreciation		525000	525000	525000	525000
Free cash flow	-2100000	3560110	3560110	3560110	3560110
NPV at 10%	$    9,185,069.67

EAC for Machine A = NPV*r/(1-(1+r)^-n = 9,186,069.67*0.10/(1-1.10^-4) = $2,897,936.78

The NPV for Machine B is calculated below and then the EAC for Machine B:

Machine B
Year	0	1	2	3	4	5	6	7
Initial Cost	-4310000
Sales		8620000	8620000	8620000	8620000	8620000	8620000	8620000
Variable costs		-2327400	-2327400	-2327400	-2327400	-2327400	-2327400	-2327400
Fixed costs		-115000	-115000	-115000	-115000	-115000	-115000	-115000
Depreciation		-615714	-615714	-615714	-615714	-615714	-615714	-615714
Pre tax Income		5561886	5561886	5561886	5561886	5561886	5561886	5561886
Taxes at 35%		-1946660	-1946660	-1946660	-1946660	-1946660	-1946660	-1946660
Net Income		3615226	3615226	3615226	3615226	3615226	3615226	3615226
Add back depreciation		615714	615714	615714	615714	615714	615714	615714
Free cash flow	-4310000	4230940	4230940	4230940	4230940	4230940	4230940	4230940
NPV at 10%	$ 16,287,987.91

EAC for Machine B = NPV*r/(1-(1+r)^-n = 16,287,987.91*0.10/(1-1.10^-7) = $3,345,642.30

Question 2:

As per CAPM, expected return Er = rf + beta*(Rm-Rf)

Er =18, rm =14 and beta = 1.4. We have to calculate rf (risk free return). So plugging in the above equation, we have,

18=rf +1.4*(14-rf)

18 = rf + 19.6 -1.4rf

1.6 = 0.4rf

rf = 1.6/0.4 =4%

Risk free rate =4%