Dde 321 - Solutions Exercise 3

Advanced Corporate Finance

Leonidas Rompolis

EXERCISES -3 (SOLUTIONS) Chapter 9, Practice Questions 1.

a. requity = rf + β × (rm – rf) = 0.04 + (1.5 × 0.06) = 0.13 = 13% b.

rassets =

D E ⎛ $4million ⎞ ⎛ $6million ⎞ rdebt + requity = ⎜ ×0.04 ⎟ + ⎜ ×0.13 ⎟ V V ⎝ $10million ⎠ ⎝ $10million ⎠

rassets = 0.094 = 9.4% c. The cost of capital depends on the risk of the project being evaluated. If the risk of the project is similar to the risk of the other assets of the company, then the appropriate rate of return is the company cost of capital. Here, the appropriate discount rate is 9.4%. d. requity = rf + β × (rm – rf) = 0.04 + (1.2 × 0.06) = 0.112 = 11.2% rassets =

D E ⎛ $4million ⎞ ⎛ $6million ⎞ rdebt + requity = ⎜ ×0.04 ⎟ + ⎜ ×0.112 ⎟ V V ⎝ $10million ⎠ ⎝ $10million ⎠

rassets = 0.0832 = 8.32% 5.

a. The R2 value for BP was 0.27, which means that 27% of total risk comes from movements in the market (i.e., market risk). Therefore, 73% of total risk is unique risk. The R2 value for BA was 0.37, which means that 37% of total risk comes from movements in the market (i.e., market risk). Therefore, 63% of total risk is unique risk. b. The variance of BP is: (0.25)2 = 0.0625 Market risk for BP: 0.27 × 0.0625 = 0.0168 Unique risk for BP: 0.73 × 0.0625 = 0.456 d. rBA = rf + βBA × (rm – rf) = 0.05 + 2.12 × (0.12 – 0.05) = 0.01984 = 1.98% e. rBA = rf + βBA × (rm – rf) = 0.05 + 2.12 × (0 – 0.05) = -0.056 = -5.6%

9.

a. The threat of a coup d’état means that the expected cash flow is less than $NZ 900 million. The threat could also increase the discount rate, but only if it increases market risk. b. The expected cash flow is: (0.2 × 0) + (0.8 × 900) = $NZ 720 million. Assuming that the cash flow is about as risky as the rest of the company’s business:

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Advanced Corporate Finance

Leonidas Rompolis

NPV = −1, 200 + 500 +

10.

720 = −105 1.12

a. If you agree to the fixed price contract, operating leverage increases. Changes in revenue result in greater than proportionate changes in profit. If all costs are variable, then changes in revenue result in proportionate changes in profit. Business risk, measured by βassets, also increases as a result of the fixed price contract. If fixed costs equal zero, then: βassets = βrevenue. However, as PV(fixed cost) increases, βassets increases. b. With the fixed price contract: PV(assets) = PV(revenue) – PV(fixed cost) – PV(variable cost) PV(assets)=

$20million $10million -($10million)×(annuity factor 6%,10years)0.09 (0.09)×(1.09)10 PV(assets) = $101,687,000

Without the fixed price contract: PV(assets) = PV(revenue) – PV(variable cost) PV(assets)=

$20million $10million 0.09 0.09

PV(assets) = $111,111,111

15.

a. Using the Security Market Line, we find the cost of capital: r = 0.07 + 1.5 × (0.16 – 0.07) = 0.205 = 20.5% Therefore:

PV =

40 60 50 + + = 103.09 2 1.205 1.205 1.2053

b. CEQ1 = 40×(1.07/1.205) = 35.52 CEQ2 = 60×(1.07/1.205)2 = 47.31 CEQ3 = 50×(1.07/1.205)3 = 35.01 c. a1 = 35.52/40 = 0.8880 a2 = 47.31/60 = 0.7885 a3 = 35.01/50 = 0.7002

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Advanced Corporate Finance

Leonidas Rompolis

d. Using a constant risk-adjusted discount rate is equivalent to assuming that at decreases at a constant compounded rate.

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