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The King Inc and the Prince Limited are identical in every aspect, except that ...
Jul 27, 2024
Solution by Steps
step 1
Calculate the total earnings for both firms. For King Inc, the earnings before interest and taxes (EBIT) is 400,000.ForPrinceLimited,theEBITisalso400,000. For Prince Limited, the EBIT is also 400,000
step 2
Determine the cost of equity for Prince Limited. Since Prince Limited has debt, we use the formula for the weighted average cost of capital (WACC). The WACC for Prince Limited is given by: WACC=EV⋅rE+DV⋅rD \text{WACC} = \frac{E}{V} \cdot r_E + \frac{D}{V} \cdot r_D where E E is the market value of equity, V V is the total market value of the firm, rE r_E is the cost of equity, D D is the market value of debt, and rD r_D is the cost of debt
step 3
Calculate the market value of equity for Prince Limited. The market value of equity E E is given by: E=Current Market Price×Outstanding Shares E = \text{Current Market Price} \times \text{Outstanding Shares} E=36×100,000=$3,600,000 E = 36 \times 100,000 = \$3,600,000
step 4
Calculate the total market value of Prince Limited. The total market value V V is given by: V=E+D V = E + D V=3,600,000+1,000,000=$4,600,000 V = 3,600,000 + 1,000,000 = \$4,600,000
step 5
Calculate the WACC for Prince Limited. Using the given cost of debt rD=6% r_D = 6\% and the calculated values: WACC=3,600,0004,600,000⋅rE+1,000,0004,600,000⋅0.06 \text{WACC} = \frac{3,600,000}{4,600,000} \cdot r_E + \frac{1,000,000}{4,600,000} \cdot 0.06 0.10=3,600,0004,600,000⋅rE+1,000,0004,600,000⋅0.06 0.10 = \frac{3,600,000}{4,600,000} \cdot r_E + \frac{1,000,000}{4,600,000} \cdot 0.06 0.10=0.7826⋅rE+0.013 0.10 = 0.7826 \cdot r_E + 0.013 0.087=0.7826⋅rE 0.087 = 0.7826 \cdot r_E rE=0.0870.7826≈0.1112 or 11.12% r_E = \frac{0.087}{0.7826} \approx 0.1112 \text{ or } 11.12\%
step 6
Calculate the return for Melissa Chow if she invests in Prince Limited. Melissa owns 10% of Prince's equity, so her share of the earnings is: Earnings=0.10×400,000=$40,000 \text{Earnings} = 0.10 \times 400,000 = \$40,000 Her return on investment is: Return=40,000360,000≈11.11% \text{Return} = \frac{40,000}{360,000} \approx 11.11\%
step 7
Calculate the return for Melissa Chow if she invests in King Inc. If she borrows at 5% interest rate to invest in King Inc, her net investment remains the same. She borrows: Borrowed Amount=0.10×400,000=$40,000 \text{Borrowed Amount} = 0.10 \times 400,000 = \$40,000 Her return on investment is: Return=40,000−(40,000×0.05)360,000≈10.56% \text{Return} = \frac{40,000 - (40,000 \times 0.05)}{360,000} \approx 10.56\%
[a] Answer
A
Key Concept
Weighted Average Cost of Capital (WACC)
Explanation
WACC is used to determine the cost of equity for a firm with debt by considering the proportionate costs of equity and debt.
Solution by Steps
step 1
To find the interest rate at which investing in King will not be attractive to Melissa, we set the returns from both investments equal. Let r r be the interest rate
step 2
Set up the equation for the return on investment in King Inc: 40,000−(40,000×r)360,000=11.11% \frac{40,000 - (40,000 \times r)}{360,000} = 11.11\% 40,000−(40,000×r)=40,000×0.1111 40,000 - (40,000 \times r) = 40,000 \times 0.1111 40,000−40,000r=4,444 40,000 - 40,000r = 4,444 40,000−4,444=40,000r 40,000 - 4,444 = 40,000r 35,556=40,000r 35,556 = 40,000r r=35,55640,000≈0.889 or 8.89% r = \frac{35,556}{40,000} \approx 0.889 \text{ or } 8.89\%
[b] Answer
B
Key Concept
Equating Returns
Explanation
To find the interest rate at which two investments yield the same return, set their returns equal and solve for the interest rate.
Solution by Steps
step 1
To find the debt level at which investing in Prince will be more attractive, we need to determine the point where the return on investment in Prince exceeds that in King
step 2
Let D D be the new debt level. The new market value of equity E E is: E=4,600,000−D E = 4,600,000 - D The new WACC is: WACC=E4,600,000⋅0.1112+D4,600,000⋅0.06 \text{WACC} = \frac{E}{4,600,000} \cdot 0.1112 + \frac{D}{4,600,000} \cdot 0.06 Set the WACC equal to the return on King: 0.10=4,600,000−D4,600,000⋅0.1112+D4,600,000⋅0.06 0.10 = \frac{4,600,000 - D}{4,600,000} \cdot 0.1112 + \frac{D}{4,600,000} \cdot 0.06 0.10=0.1112−0.1112D4,600,000+0.06D4,600,000 0.10 = 0.1112 - \frac{0.1112D}{4,600,000} + \frac{0.06D}{4,600,000} 0.10=0.1112−0.0512D4,600,000 0.10 = 0.1112 - \frac{0.0512D}{4,600,000} 0.10−0.1112=−0.0512D4,600,000 0.10 - 0.1112 = - \frac{0.0512D}{4,600,000} −0.0112=−0.0512D4,600,000 -0.0112 = - \frac{0.0512D}{4,600,000} D=0.0112×4,600,0000.0512≈1,000,000 D = \frac{0.0112 \times 4,600,000}{0.0512} \approx 1,000,000
[c] Answer
C
Key Concept
Debt Level and Return
Explanation
The debt level affects the WACC and, consequently, the return on investment. By adjusting the debt level, the return can be made more attractive.
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