
Ultimate access to all questions.
Explanation:
Using the formulas provided in the problem:
Break-even cost on borrowed funds
This requires accounting for both total interest paid and operating costs relative to earning assets:
Break-even cost = (Total Interest Paid + Operating Costs) / Earning Assets
Break-even cost = ($47.0 million + $9.0 million) / $700.0 million = $56.0 / $700.0 = 8.00%
Before-tax cost of stockholders' investment (%)
Pretax required rate of return = 12.0% / (1 - 0.21) = 15.18987%
Before-tax stockholder costs (%) = 15.18987% × ($100.0 million / $700.0 million)
Before-tax stockholder costs (%) = 15.18987% × 0.142857 = 2.16998%
Weighted Average Cost of Capital (WACC) WACC = Break-even cost on borrowed funds (%) + Before-tax cost of stockholders’ investment (%) WACC = 8.00% + 2.16998% = 10.16998%, which rounds to 10.17%.
No comments yet.
20.14.3. [Difficult] Suppose a bank is faced with the interest rates below for the sources of funds upon which it draws. The non-interest-bearing demand deposits have a rate of 0%, while the other sources have rates ranging from 3.0% to 6.0%. The total interest cost is $47.0 million:
| Sources of Funds Drawn Upon | Avg Amount of Funds Raised (millions) | Avg Rate of Interest Incurred | Tot Interest Paid for Each (millions) |
|---|---|---|---|
| Nonint-bearing demand deposits | $100.0 | 0.0% | $0.0 |
| Interest-bearing trans. deposits | $200.0 | 5.0% | $10.0 |
| Savings accounts | $100.0 | 3.0% | $3.0 |
| Time deposits | $500.0 | 6.0% | $30.0 |
| Money market borrowings | $100.0 | 4.0% | $4.0 |
| Total funds raised | $1,000.0 | $47.0 |
Operating costs (mm) | $9.0
Earning assets (mm) | $700.0
Shareholders' Investment | $100.0
Shareholders require 12.00% while the firm's tax rate is 21.00%
Also displayed in the exhibit: The bank's operating costs (including salaries and overhead) are $9.0 million. The bank has $700.0 million in (interest) earning assets and stockholders' investment (aka, equity) is $100.0 million. Finally, we can assume that stockholders have a required after-tax return of 12.0%, while the firm's tax rate is 21.0%; therefore, stockholders' pretax required rate of return is $12.0% / (1 - 21.0%) = 15.19%$. According to the historical average cost approach, the fully-loaded LOWEST rate of return overall fund-raising costs the bank can afford to earn on its assets is given by the bank's weighted average cost of capital (WACC).
Here is a key solving hint: WACC = break-even cost on borrowed funds (%) plus (+) before-tax cost of stockholders’ investment (%); in percentage terms, the before-tax stockholder costs = shareholder’s pretax required rate of return (%) × (stockholders’ investment / earning assets). What is this bank’s WACC?
A
9.38%
B
10.17%
C
11.54%
D
12.00%