5.1. Eugene Corporation may raise new capital in one of the following three ways
ID: 2713687 • Letter: 5
Question
5.1. Eugene Corporation may raise new capital in one of the following three ways. It has tax rate of 40%. Find the after-tax cost of new capital.
A. It can sell common stock at $51 a share, which will pay a dividend of $2.20 next year. The expected rate of growth of dividends is 6% per annum forever. Answer: (10.31%) Show solutions.
B. It can sell 8.0% bonds at $875 each, which will mature in 5 years. Assume that the bonds pay interest twice a year and the company pays taxes once a year. Answer: (Approximately, 6.720%, exactly, 6.958%) Show solutions.
Explanation / Answer
A.
Current price = Dividend of next year/Cost of capital - Growth rate
51 = 2.2/k - 0.06
k i.e. Cost of capital = (2.2/51) + 0.06 = 0.1031 i.e. 10.31%
B.
YTM = [80 + {(1000-875)/5}]/{(1000+875)/2}
YTM = 105/937.5
Estimated Cost of capital before taxes = 0.112 i.e. 11.2%
Approx Cost of capital after tax of 40% = 11.2 * 60% or 11.2 (1-0.4) = 6.720%
Exact calculation
Discounting cash outflow at 11.2%
Year 1 to 5= 80 * 3.67737769 = $294.1902152
Year 5 = 1000 * 0.588133696 = $588.133696
Discounted cash outflow = $882.3239112
These discounted cash flow is not equal to the current price $875 therefore increasing the discount rate to 11.6%
Year 1 to 5 = 80 * Annualised cash flow for 5 years of 11.6% discount rate = 80* 3.640784879 = $291.2627903
Year 5 = 1000 * 0.5776689511 = $577.6689511
Discounted cash flow = $868.9317414
When discounting rate increased by 0.4% discounted cash flow reduced by $13.39 ($882.3239112-$868.9317414)
If we want to reduce cash flow by $7.32 ($882.3239112-$875) discounting rate is to be reduced by = 0.4*7.32/13.39 = 0.21867%
Therefore,exact cost of capital before tax = 11.2% + 0.21867% = 11.419%
Therefore exact cost of capital after tax = 11.419 * 60% = 6.8514%
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