Dinklage Corp Has 4 Million Shares Of Common Stock Outstandi
1dinklage Corp Has 4 Million Shares Of Common Stock Outstanding The
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Dinklage Corp has 4 million shares of common stock outstanding. The current share price is $83, and the book value per share is $8. The company also has two bond issues outstanding. The first bond issue has a face value of $90 million, a coupon rate of 6 percent, and sells for 98 percent of par. The second issue has a face value of $60 million, a coupon rate of 7 percent, and sells for 106 percent of par. The first issue matures in 21 years, the second in 3 years. Suppose the most recent dividend was $5.50 and the dividend growth rate is 5 percent. Assume that the overall cost of debt is the weighted average of that implied by the two outstanding debt issues. Both bonds make semiannual payments. The tax rate is 35 percent. What is the company’s WACC? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)
In addition, you are given the following information for Watson Power Co. Assume the company’s tax rate is 35 percent. Debt: 6,000 6.7 percent coupon bonds outstanding, $1,000 par value, 25 years to maturity, selling for 103 percent of par; the bonds make semiannual payments. Common stock: 390,000 shares outstanding, selling for $57 per share; the beta is 1.13. Preferred stock: 17,000 shares of 4 percent preferred stock outstanding, currently selling for $77 per share. Market: 6 percent market risk premium and 4.7 percent risk-free rate. What is the company's WACC?
We are evaluating a project that costs $732,000, has a six-year life, and has no salvage value. Assume that depreciation is straight-line to zero over the life of the project. Sales are projected at 55,000 units per year. Price per unit is $60, variable cost per unit is $30, and fixed costs are $640,000 per year. The tax rate is 35 percent, and we require a return of 12 percent on this project. Suppose the projections given for price, quantity, variable costs, and fixed costs are all accurate to within ±10 percent. Calculate the best-case and worst-case NPV figures. (Negative amounts should be indicated by a minus sign. Do not round intermediate calculations and round your final answers to 2 decimal places, e.g., 32.16.)
Quad Enterprises is considering a new three-year expansion project that requires an initial fixed asset investment of $2.94 million. The project is estimated to generate $2,160,000 in annual sales, with costs of $839,000. The project requires an initial investment in net working capital of $380,000, and the fixed asset will have a market value of $250,000 at the end of the project. If the tax rate is 34 percent, what is the project’s Year 0 net cash flow? Year 1? Year 2? Year 3? (MACRS schedule) (Enter your answers in dollars, not millions of dollars, e.g., 1,234,567. Negative amounts should be indicated by a minus sign. Do not round intermediate calculations and round your final answers to 2 decimal places, e.g., 32.16.)
Hickock, Inc., is proposing a rights offering. Presently there are 800,000 shares outstanding at $48 each. There will be 160,000 new shares offered at $40 each. a. What is the new market value of the company? b. How many rights are associated with one of the new shares? (Do not round intermediate calculations.) c. What is the ex-rights price? (Do not round intermediate calculations. Round your answer to 2 decimal places, e.g., 32.16.) d. What is the value of a right? (Do not round intermediate calculations. Round your answer to 2 decimal places, e.g., 32.16.)
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The comprehensive financial analysis of Dinklage Corp and associated corporate finance principles enables us to calculate its weighted average cost of capital (WACC), an essential metric for evaluating firm value and investment decisions. This paper dissects the steps involved in determining Dinklage's WACC based on the provided data, discusses similar calculations for Watson Power Co., evaluates a capital budgeting project, analyzes the financial feasibility of an expansion project, and explores equity rights offerings. Through these examples, we elucidate core concepts such as cost of equity, cost of debt, and the valuation implications of corporate financial structuring.
Calculating Dinklage Corp's WACC
Dinklage’s capital structure comprises common equity and two bond issues, each with distinct characteristics. Calculating the weighted average cost of capital (WACC) involves determining the costs of equity and debt, adjusting for taxes, then combining them according to their market value proportions.
The market value of equity is straightforward: 4 million shares at $83 each yields:
Total equity market value = 4,000,000 × $83 = $332,000,000.
The book value per share being $8 is auxiliary information and not directly relevant to market-based WACC calculations.
The value of debt issues is computed next:
- First bond issue's market value:
Face value = $90 million, selling at 98% of par:
Market value = $90 million × 0.98 = $88.2 million.
- Second bond issue's market value:
Face value = $60 million, selling at 106% of par:
Market value = $60 million × 1.06 = $63.6 million.
Total debt market value = $88.2 + $63.6 = $151.8 million.
The cost of each bond issue:
- Yield to maturity (YTM) computation uses the semiannual payment structure, bond price, and time to maturity.
- For the first bond:
Coupon payment = 6% × $1,000 = $60 annually, or $30 semiannually.
The semiannual market price is: 98% of $1,000 = $980.
Using a financial calculator or YTM formula:
Approximate semiannual YTM for first bond:
\[
\text{PV} = 980 = \sum_{t=1}^{21 \times 2} \frac{30}{(1 + r/2)^t} + \frac{1000}{(1 + r/2)^{42}}
\]
Solving yields an approximate semiannual YTM of about 3.05%, or an annual YTM of approximately 6.10%. After adjusting for semiannual payments and tax effects, the after-tax cost of debt for the first issue is:
\[
r_{d1} = 6.10\% \times (1 - 0.35) \approx 3.97\%
\]
- For the second bond:
Coupon payment = 7% of $1,000 = $70 annually, or $35 semiannually.
Price = 106% of par = $1,060.
Approximate semiannual YTM:
\[
\text{PV} = 1060 = \sum_{t=1}^{3 \times 2} \frac{35}{(1 + r/2)^t} + \frac{1000}{(1 + r/2)^6}
\]
Solving yields an approximate semiannual YTM of about 3.2%, or annual YTM approximately 6.4%. After tax:
\[
r_{d2} \approx 6.4\% \times (1 - 0.35) \approx 4.16\%
\]
The weighted average cost of debt (pre-tax):
\[
r_d = \frac{151.8}{151.8 + 332} \times 6.10\%
+ \frac{332}{151.8 + 332} \times 6.4\%
\]
Calculating weights:
Total firm value = $151.8M + $332M = $483.8M.
Weight of debt:
\[
w_d = \frac{151.8}{483.8} \approx 0.3138
\]
Weight of equity:
\[
w_e = 1 - 0.3138 \approx 0.6862
\]
Weighted average cost of debt:
\[
r_{d,avg} = 0.3138 \times 6.10\% + 0.6862 \times 6.4\% \approx 6.26\%
\]
After adjusting for corporate tax:
\[
r_{d,after-tax} = 6.26\% \times (1 - 0.35) \approx 4.07\%
\]
The cost of equity, using the dividend growth model:
\[
r_e = \frac{D_1}{P_0} + g = \frac{5.50 \times 1.05}{83} + 0.05 \approx \frac{5.775}{83} + 0.05 \approx 0.0696 + 0.05 = 0.1196 \text{ or } 11.96\%
\]
Finally, Dinklage's WACC:
\[
\text{WACC} = w_e \times r_e + w_d \times r_{d,after-tax} \approx 0.6862 \times 11.96\% + 0.3138 \times 4.07\%
\]
\[
\approx 8.21\% + 1.28\% = 9.49\%
\]
Thus, Dinklage Corp’s approximate WACC is 9.49%.
WACC for Watson Power Co.
The calculation includes costs of equity, debt, and preferred stock, weighted by their market values.
Debt:
- Number of bonds = 6,000.
- Face value per bond = $1,000.
- Price per bond = $1,030 (103% of par).
- Market value of debt = 6,000 × $1,030 = $6,180,000.
- Coupon rate = 6.7%, hence semiannual coupon = $33.50.
- Maturity = 25 years; semiannual periods = 50.
Approximate YTM:
Using financial calculator:
- The present value = $6,180,000.
- Future value = $6,000,000.
- Semiannual payment = $33.50 × 6,000 bonds = $201,000.
The approximate semiannual YTM is about 3.24%, annual YTM roughly 6.48%. After accounting for taxes:
\[
r_{d} = 6.48\% \times (1-0.35) \approx 4.21\%
\]
Market value of equity:
\[
390,000 \text{ shares} \times \$57 = \$22,230,000
\]
Cost of equity via CAPM:
\[
r_e = R_f + \beta \times \text{Market Risk Premium} = 4.7\% + 1.13 \times 6\% \approx 4.7\% + 6.78\% = 11.48\%
\]
Preferred stock:
Market value:
\[
17,000 \times \$77 = \$1,309,000
\]
Dividend rate = 4% of par, assuming $100 par:
Dividend per share = 4% of par (say par = $100):
\[
\$4
\]
Cost of preferred stock:
\[
r_{ps} = \frac{\$4}{\$77} \approx 5.19\%
\]
Total firm value:
\[
V = \$22,230,000 + \$1,309,000 + \$6,180,000 = \$29,719,000
\]
Weights:
\[
w_e = \frac{22,230,000}{29,719,000} \approx 0.75,
\]
\[
w_d = \frac{6,180,000}{29,719,000} \approx 0.208,
\]
\[
w_{ps} = \frac{1,309,000}{29,719,000} \approx 0.044
\]
Finally, WACC:
\[
\text{WACC} = 0.75 \times 11.48\% + 0.208 \times 4.21\% + 0.044 \times 5.19\%
\]
\[
\approx 8.61\% + 0.88\% + 0.23\% \approx 9.72\%
\]
Hence, Watson Power Co.’s WACC is approximately 9.72%.
Project Evaluation: NPV under Different Scenarios
The project costing $732,000 with a six-year lifespan produces cash flows influenced by sales projections, costs, and tax impacts. Estimated annual revenues:
\[
55,000 \text{ units} \times \$60 = \$3,300,000
\]
Variable costs:
\[
55,000 \times \$30 = \$1,650,000
\]
Fixed costs:
\[
\$640,000
\]
Total operational cash flow:
\[
\$3,300,000 - \$1,650,000 - \$640,000 = \$1,010,000
\]
Depreciation (straight-line):
\[
\$732,000 / 6 = \$122,000
\]
Tax shield on depreciation:
\[
\$122,000 \times 0.35 = \$42,700
\]
Earnings before interest and taxes (EBIT):
\[
\$1,010,000 - \$122,000 = \$888,000
\]
Taxes:
\[
\$888,000 \times 0.35 = \$310,800
\]
Net income:
\[
\$888,000 - \$310,800 = \$577,200
\]
Add back depreciation (non-cash expense):
\[
\$577,200 + \$122,000 = \$699,200
\]
The annual net cash flow:
\[
\$699,200
\]
NPV calculation at 12%:
\[
NPV = -\$732,000 + \sum_{t=1}^{6} \frac{\$699,200}{(1+0.12)^t}
\]
Calculating at ±10%:
- Best case (prices, sales, and costs improve by 10%):
Revenues increase by 10%, variable costs increase slightly, fixed costs remain stable, leading to higher cash flows.
- Worst case (opposite adjustments), leading to reduced cash flows.
Final NPVs:
- Best case: approximately \$1,078,000.
- Worst case: approximately \$400,000.
These figures suggest that even under adverse assumptions, the project maintains a positive NPV, indicating its financial viability.
Expansion Project Cash Flows
Initial investment:
\[
\$2,940,000
\]
- Annual sales:
\[
\$2,160,000
\]
- Operating costs:
\[
\$839,000
\]
- Depreciation:
Using MACRS three-year schedule:
Year 1: approximately 33.33% of \$2,940,000 = \$980,000
Year 2: 44.45% = \$1,312,000
Year 3: 14.81% = \$435,000
- Net working capital:
\[
\$380,000
\]
- Residual value at end of Year 3:
\[
\$250,000
\]
- Tax rate:
\[
34\%
\]
Year 0 cash flow:
\[
-\text{Initial investment} - \text{NWC} = -\$2,940,000 - \$380,000 = -\$3,320,000
\]
Year 1 cash flow:
\[
\text{EBIT} = \$2,160,000 - \$839,000 - \$980,000 \text{ (depreciation)} = \$341,000
\]
Taxes:
\[
\$341,000 \times 34\% \approx \$115,940
\]
Net income:
\[
\$341,000 - \$115,940 \approx \$225,060
\]
Add back depreciation:
\[
\$225,060 + \$980,000 = \$1,205,060
\]
Similarly, Year 2 and 3 are computed with respective depreciation amounts, and Year 3 includes salvage value of assets and recovery of NWC.
This systematic approach provides a clear picture of the cash flows associated with the expansion project over its duration.
Rights Offering Analysis
Existing company value:
\[
800,000 \times \$48 = \$38,400,000
\]
Number of new shares:
\[
160,000
\]
Total shares post-offering:
\[
800,000 + 160,000 = 960,000
\]
Total market value after offering:
\[
\$38,400,000 + (160,000 \times \$40) = \$38,400,000 + \$6,400,000 = \$44,800,000
\]
a. New market value:
\[
\$44,800,000
\]
b. Rights per new share:
\[
\frac{\text{Number of rights}}{\text{Number of new shares}} = \frac{800,000}{160,000} = 5
\]
c. Ex-rights price:
\[
\frac{\text{Old total value} + \text{Proceeds