Retained Earnings Versus External Capital

Why the Source of Funds Matters

A company may have a profitable project and several ways to pay for it: use cash generated and retained in the business, borrow, or issue shares. Choosing retained earnings does not make the project costless. That cash could have been distributed to shareholders, kept available for future needs, or invested elsewhere. Conversely, raising external capital can involve fees and contractual or ownership consequences, while preserving internal cash may protect the company against a future funding shortfall.

The comparison therefore has two parts: identify the amount that is genuinely available from each source, then compare its economic cost and the value of the flexibility it preserves. A financing choice is not established by comparing a debt coupon with zero; nor is it established by comparing only the interest rate with the required return on equity. Issuance costs, tax assumptions, liquidity needs, and the timing of costs must be treated consistently.

Definition: Retained earnings are cumulative profits not distributed to owners. They are an accounting equity balance, not necessarily a cash balance. The opportunity cost of retained funds is the return those funds could earn in their best available alternative use, expressed in this comparison as the required return on equity applied to the amount invested. External capital is financing raised from lenders or new investors; its usable proceeds may be less than the amount raised because of issuance costs.

Availability Comes Before Cost

A company cannot use every dollar shown as retained earnings to fund a project. Some resources may be tied up in receivables, inventory, or other assets, and some cash may be needed for normal operations or obligations coming due. For a financing decision, start with the amount of cash available after the company’s stated reserve requirement. If the project exceeds that amount, the remaining funding need must come from another source or the project must be changed.

This is a practical constraint, not a claim that a particular reserve is always correct. The appropriate reserve depends on the company’s expected cash flows and commitments. In the examples below, reserve amounts are specified as assumptions so the arithmetic isolates the financing comparison.

Worked Example: Find the Amount of Retained Cash That Can Be Used

A hypothetical equipment project requires $600,000. The company has $900,000 in cash that could otherwise be considered for financing, but management has specified that $350,000 must remain available for operations and near-term obligations. Determine the amount of the project that retained cash can fund and the remaining financing need.

Step 1: Calculate usable retained cash. Subtract the required reserve from the cash available:

\$900{,}000-\$350{,}000=\$550{,}000.

Step 2: Compare usable cash with the project cost. The project costs $600,000, so the internal funds fall short by:

\$600{,}000-\$550{,}000=\$50{,}000.

The company can fund $550,000 from retained cash without violating the assumed reserve, and it needs another $50,000 from an external source or a project adjustment. The method avoids a common availability error: treating all $900,000 as freely spendable. The check is that $550,000 used plus $350,000 reserved equals the original $900,000.

Opportunity Cost and a Consistent Comparison

If a project uses $K$ of retained funds and the appropriate required return on equity is $r_E$, a simple one-year opportunity-cost measure is $K r_E$. This is an economic hurdle charge, not an extra cash payment made by the company. It represents the return shareholders could expect from an alternative use of the capital at comparable risk.

For debt, let $N$ be the required net proceeds and let a fee equal to proportion $f$ of the debt raised. If the fee is paid from the proceeds, the gross borrowing $B$ must satisfy $N=B(1-f)$. When interest is deductible and the firm can use the tax deduction, the after-tax interest for one year at rate $r_D$ and tax rate $T$ is $B r_D(1-T)$. These formulas rely on the stated assumptions: the fee is proportional to the amount borrowed, interest is charged on the full borrowing, and the interest tax shield is usable. If the company cannot use the deduction, use the full interest amount instead.

The examples use a clearly labelled undiscounted first-year cost comparison: the first-year after-tax interest and the upfront fee are added as nominal dollar costs, and the result is compared with the one-year equity hurdle charge. This is a simple screening measure, not a present-value calculation; it does not adjust for the different dates on which a fee and interest are paid. For a multi-year decision or a precise valuation, cash flows should instead be compared at consistent dates using an appropriate discount rate.

Derivation: If the lender advances $B$ and a fee $fB$ is withheld, the borrower receives $B-fB=B(1-f)$. To receive net proceeds $N$, set $B(1-f)=N$, so $B=N/(1-f)$. Interest is charged on $B$, not on the smaller net proceeds $N$. If the interest deduction saves tax at rate $T$, the tax saving is $TBr_D$; subtracting that saving from gross interest gives $Br_D-TBr_D=Br_D(1-T)$. The fee is not included in this tax adjustment unless the problem explicitly states that it is deductible.

Worked Example: Compare Retained Cash With a Debt Offer

A hypothetical project needs $300,000 of net financing for one year. The company can use retained cash with a required return on equity of 9%. A lender offers a one-year loan with a 7.5% interest rate and a fee equal to 1% of the amount borrowed, withheld at issuance. Interest is deductible, the company can use the deduction, and its tax rate is 25%. The fee is not deductible. Compare the two sources using the stated undiscounted first-year cost convention.

Step 1: Calculate the retained-funds hurdle charge.

\$300{,}000(0.09)=\$27{,}000.

Step 2: Find the gross debt needed to net $300,000. With $f=0.01$, the company retains 99% of the borrowing:

B=\frac{\$300{,}000}{1-0.01} =\frac{\$300{,}000}{0.99} =\$303{,}030.303030\ldots.

Step 3: Calculate after-tax interest and the fee. The unrounded interest is $ \$303{,}030.303030\ldots(0.075)=\$22{,}727.272727\ldots $. The tax saving is $ \$22{,}727.272727\ldots(0.25)=\$5{,}681.818181\ldots $. Thus after-tax interest is $ \$17{,}045.454545\ldots $. The fee is $ \$303{,}030.303030\ldots(0.01)=\$3{,}030.303030\ldots $.

Step 4: Compare total costs. Add the unrounded components first, then round the result to the nearest cent:

\text{Debt cost} =\$17{,}045.454545\ldots+\$3{,}030.303030\ldots =\$20{,}075.757575\ldots =\$20{,}075.76.

The debt cost is lower by $\$27{,}000-\$20{,}075.757575\ldots=\$6{,}924.242424\ldots$, or $6,924.24 to the nearest cent. Under these assumptions and this first-year screening convention, debt has the lower measured cost. The check is that the fee plus net proceeds equals the gross borrowing: $3,030.303030… + $300,000 = $303,030.303030…. This comparison does not establish that the company should borrow; the reserve it must maintain and other financing constraints still matter.

External Equity and the Cost of Preserving Cash

New equity can preserve cash that would otherwise be committed to a project, but it does not eliminate the required return on the capital. If investors require return $r_E$, and an issuance fee is a fraction $f$ of gross proceeds, raising net proceeds $N$ requires gross proceeds $N/(1-f)$. A simple first-year hurdle charge on the gross amount is $r_E N/(1-f)$; the issuance fee is $fN/(1-f)$. This makes clear why comparing retained earnings with new equity is not a comparison between “free” internal funds and costly external funds: both use equity capital with an opportunity cost, while new equity also incurs issuance costs.

Preserving cash may nevertheless be worth paying for when it avoids an expected future funding problem. That benefit should be stated and estimated rather than treated as an unmeasured preference. For example, if a company assigns a probability to a future cash shortfall and estimates the extra financing cost if it occurs, the probability-weighted cost can be compared with the incremental cost of raising funds now. The estimate is only as useful as its assumptions; it is not a guaranteed saving.

Worked Example: Evaluate Equity Issuance Against a Liquidity Benefit

A hypothetical company needs $400,000 for a project. It can use retained cash, whose required return is 8%, or issue equity with a 5% fee. New equity investors require the same 8% return. Management estimates that retaining the $400,000 rather than spending it would avoid a possible future emergency financing premium: there is a 40% probability of needing $300,000, and that financing would cost an additional 8% for one year. Use the undiscounted first-year convention to determine whether the stated liquidity benefit offsets the issuance cost.

Step 1: Calculate the retained-funds hurdle charge.

\$400{,}000(0.08)=\$32{,}000.

Step 2: Calculate gross equity proceeds and the fee. To net $400,000 after a 5% fee:

\text{Gross proceeds} =\frac{\$400{,}000}{0.95} =\$421{,}052.631578\ldots.

The fee is $ \$421{,}052.631578\ldots(0.05)=\$21{,}052.631578\ldots $. The one-year equity hurdle charge on gross proceeds is $ \$421{,}052.631578\ldots(0.08)=\$33{,}684.210526\ldots $. Thus the equity cost measure, including the fee, is $ \$54{,}736.842105\ldots $, or $54,736.84.

Step 3: Quantify the expected liquidity benefit. If the shortfall occurs, the extra one-year premium is $ \$300{,}000(0.08)=\$24{,}000 $. Weighting by the 40% probability gives:

0.40(\$24{,}000)=\$9{,}600.

Step 4: Compare the measures. After subtracting the stated liquidity benefit, the equity measure is $ \$54{,}736.842105\ldots-\$9{,}600=\$45{,}136.842105\ldots $, or $45,136.84. This remains $13,136.84 above the $32,000 retained-funds hurdle. On the assumptions supplied, the estimated liquidity benefit does not offset the issuance cost and higher gross equity hurdle charge. The check is that equity investors receive $421,052.631578… less the $21,052.631578… fee, leaving exactly $400,000 net. The conclusion is conditional: a larger or more consequential future liquidity need could change it.

Decision Process and Common Traps

Establish the funding need.
State the project’s required funds and the date or period for which financing is needed.

Measure internal availability.
Separate cash that can be used from the reserve required for operations and near-term obligations. Do not equate retained earnings on the balance sheet with spendable cash.

Calculate comparable costs.
For retained funds, apply the appropriate equity hurdle rate. For external funds, use net proceeds, fees, interest or the equity hurdle, and any tax effects that are explicitly supported by the assumptions.

Value flexibility and check the conclusion.
State any estimated benefit from preserving cash, compare it with incremental financing costs, and verify that sources cover the project while the required reserve remains intact.

A frequent exam trap is to compare the interest rate directly with the equity return and declare the lower rate the winner. That ignores both the amount raised and the costs required to obtain usable funds. For example, if a company needs $300,000 net and pays a 1% fee, calculating interest on only $300,000 understates the debt cost because the fee is charged on a larger gross loan. The correction is to solve $B(1-f)=N$ first, then calculate interest on $B$.

A second trap is to count an interest tax shield when the company cannot use the deduction, or to apply the tax shield to a fee that the problem says is nondeductible. A third is to count the same liquidity benefit twice: if an expected emergency financing cost is already included in the comparison, do not also subtract it as a separate “flexibility value.” Make each cost and benefit explicit and use one consistent convention.

Key takeaway: Retained earnings have an opportunity cost and may not all be available as cash. External financing can incur fees and may preserve liquidity, but its net proceeds and full economic cost must be calculated. A sound comparison states its assumptions, treats timing consistently, and tests whether the value of cash preserved justifies the incremental financing cost. This framework is aligned with the SOA VEE Accounting and Finance syllabus.

Check Your Understanding

For each question, use the assumptions stated and keep full precision until the final rounding step.

A company has $780,000 in cash, must retain a $260,000 operating reserve, and is considering a $600,000 project. How much can retained cash fund, and what is the funding shortfall? (Answer: $520,000 from retained cash; $80,000 shortfall.)
A project uses $250,000 of retained funds, and the required return on equity is 9.2% per year. What is the one-year opportunity-cost hurdle charge? (Answer: $23,000.)
A company needs $200,000 net from a one-year loan. The lender withholds a 2% fee from gross proceeds, charges 7% annual interest on the gross loan, and interest is deductible at a 25% tax rate; the fee is nondeductible. What is the undiscounted first-year cost, rounded to cents? (Answer: $14,795.92.)
A company needs $350,000 net from an equity issue with a 4% issuance fee. The required return on equity is 10%. Using the undiscounted first-year convention, calculate the gross proceeds, issuance fee, and total first-year cost measure. (Answer: Gross proceeds $364,583.33; fee $14,583.33; total cost measure $51,041.67.)
A company needs $400,000 for a project and can either use retained funds with an 8% required return or borrow the net amount. The one-year debt has a 1.5% fee withheld from proceeds, a 6% interest rate on gross borrowing, and a usable tax deduction at 25%; the fee is nondeductible. Preserving the cash instead is estimated to avoid an emergency financing premium of $200,000 at an additional 10% for one year, with probability 25%. Using the undiscounted first-year convention, compare debt cost with retained-funds hurdle plus expected emergency premium. (Answer: Debt cost $24,365.48; retained-funds hurdle plus expected premium $37,000.00; debt is lower by $12,634.52 under these assumptions.)

What You'll Learn