A project requires an initial investment in equipment of $90,000 and then requires an initial investment in working capital of $10,000 (at t = 0). You expect the project to produce sales revenue of $120,000 per year for three years. You estimate manufacturing costs at 60 percent of revenues. (Assume all revenues and costs occur at year-end, i.e., t = 1, t = 2, and t = 3). The equipment depreciates using straight-line depreciation over three years. At the end of the project, the firm can sell the equipment for $10,000 and also recover the investment in net working capital. The corporate tax rate is 21 percent and the cost of capital is 15 percent. Cash flows from the project are

 

a) CF₀: −90,000;CF₁: 12,600; CF₂: 12,600; CF₃: 29,600.

b) CF₀: −100,000; CF₁: 44,220; CF₂: 44,220; CF₃: 62,120.

c) CF₀: −100,000; CF₁: 42,600; CF₂: 42,600; CF₃: 42,600.

d) CF₀: −100,000; CF₁: 42,600; CF₂: 42,600; CF₃: 49,600.

 

The Solar Calculator Company proposes to invest $5 million in a new calculator-making plant that will depreciate on a straight-line basis. Fixed costs are $2 million per year. A calculator costs $5 per unit to manufacture and sells for $20 per unit. If the plant lasts for three years and the cost of capital is 12 percent, what is the accounting break-even level of annual sales? (Assume no taxes.)

a) 133,334 units

b) 272,117 units

c) 244,444 units

b) 466,666 units

 

Agency costs can be reduced by

a) monitoring managers' efforts only.

b) monitoring managers' efforts and managers' actions.

c) monitoring managers' efforts, monitoring managers' actions, and intervening when managers veer off-course.

d) intervening when managers veer off-course.

 

Percival Hygiene has $10 million invested in long-term corporate bonds. This bond portfolio's expected annual rate of return is 8%, and the annual standard deviation is 14%. Amanda Reckonwith, Percival's financial adviser, recommends that Percival consider investing in an index fund that closely tracks the Standard & Poor's 500 index. The index has an expected return of 16%, and its standard deviation is 22%.

 

a. Suppose Percival puts all his money in a combination of the index fund and Treasury bills. Can he thereby improve his expected rate of return without changing the risk of his portfolio? The Treasury bill yield is 4%.

 

·      Yes

·      No

 

b. Could Percival do even better by investing equal amounts in the corporate bond portfolio and the index fund? The correlation between the bond portfolio and the index fund is +0.1.

 

·      Yes

·      No

Question 1 :

Initial investment in equipment = $90,000

Add : Initial investment in working capital = $10,000

Cash outflow in year 0 = $100,000

 

Calculation of cash inflows :

Year 1 :

Sales = $120,000 

Less : Cost (60%) = $72,000

Gross profit = $48,000

Less : Depreciation ($90,000 / 3) = $30,000

Net profit = $18,000

Less : Tax (21%) = $3,780

Profit after tax = $14,220

Add : Depreciation = $30,000

Cash inflow = $44,220

 

Year 2 :

Same as year 1 = $44,220

 

Year 3 :

Profit from sale of equipment :

Sale value = $10,000

Less : Book value = 0

Profit = $10,000

Less : Tax (21%) = $2,100

Profit after tax = $7,900

 

Cash inflow for year 3 :

Cash inflow from operations = $44,220

Add : Profit from sale of equipment = $7,900

Add : Recovery of initial investment in working capital = $10,000

Total = $62,120

 

Hence, answer is : b) CF₀: −100,000; CF₁: 44,220; CF₂: 44,220; CF₃: 62,120.

 

Question 2 :

The accounting break-even level = (Fixed cost + Depreciation) / (Price - Variable cost)

where,

Fixed cost = $2 million 

Depreciation = $5 million / 3 = $1,666,667

Price = $20

Variable cost = $5

The accounting break-even level = (2,000,0000 + 1,666,667) / (20 - 5)

The accounting break-even level = 244,444 units

 

Hence, answer is : c) 244,444 units

 

Question 3 : 

Agency costs can be reduced by monitoring a manager's efforts and actions and by intervening when the manager veers off course.

 

Hence, answer is : c) monitoring managers' efforts, monitoring managers' actions, and intervening when managers veer off-course.

 

Question 4 : 

a.
Percival's current portfolio provides an expected return of 8% with an annual standard deviation of 14%. First we find the portfolio weights for a combination of Treasury bills (security 1 : standard deviation = 0%) and the index fund (security 2 : standard deviation = 22%) such that portfolio standard deviation is 14%. In general, for a two security portfolio :

Portfolio standard deviation
σP² = w1² x σ1² + (2 x w1 x w2 x σ1 x σ2 x ρ1,2) + w2² xσ2²

where,

σP = Portfolio standard deviation = 14%

w1 = weight of security 1

σ1 = standard deviation of security 1 

w2 = weight of security 2

σ2 = standard deviation of security 2

ρ1,2 = coefficient of correlation between security 1 and security 2

Therefore,

(0.14)² = 0 + 0 + w2² x (0.22)²
w2 = 0.14 / 0.22 = 63.64%

w1 = 1 - 63.64% = 36.36%

Further:
rp = w1 x r1 + w2 x r2

where,

rp = Return of portfolio

w1 = 63.64%

r1 = Treasury bill yield is 4%

w2 = 36.36%

r2 = Expected return of index 16%

 

Therefore,
rp = 63.64% x 4 + 36.36% x 16 = 8.36%
Therefore, he can improve the expected rate of return without any change in the risk of the portfolio.

 

Hence, the answer is : Yes

 

b. With equal amounts in the corporate bond portfolio (security 1) and the index fund (security 2), the expected return is:
rp = w1 x r1 + w2 x r2
rp = (0.5 x 8%) + (0.5 x 16%) = 12.0%

σP² = w1² x σ1² + (2 x w1 x w2 x σ1 x σ2 x ρ1,2) + w2² xσ2²

σP² = 0.5² x 0.14² + (2 x 0.5 x 0.5 x 0.14 x 0.22 x 0.1) + 0.5² x0.22²

σP = 13.62%

Therefore, he can do even better by investing equal amounts in the corporate bond portfolio and the index fund. His expected return increases to 12.0% and the standard deviation of his portfolio decreases to 13.62%.

 

Hence, the answer is : Yes