Last year, a firm reported total assets of $2,000,000, sales of $745,000, net income of $175,000.

The firm paid $60,000 in dividends, holding its payout ratio constant. What annual rate of growth can the firm maintain without having to look for external financing?

Question

Last year, a  firm reported total assets of $2,000,000,  sales of $745,000, net income of $175,000.

The firm paid $60,000 in dividends, holding its payout ratio constant.  What annual rate of growth can the firm maintain without having to look for external financing?

BlackTom AI · Accepted Answer

We start by identifying the key variables given:
- Total assets = 2,000,000
- Sales = 745,000 (not needed for the growth calculation here)
- Net income = 175,000
- Dividends paid = 60,000
- Payout ratio is kept constant

First, compute the payout ratio and retention (plowback) ratio:
- Payout ratio = Dividends / Net income = 60,000 / 175,000 ≈ 0.3429 (about 34.29%)
- Retention ratio b = 1 − payout ≈ 1 − 0.3429 ≈ 0.6571 (about 65.71%)

Next, determine the basic profitability measure to use. The sustainable growth rate with dividends can be derived from ROA and the retention ratio, using the formula:
- g = ROA × b / (1 − ROA × b)
This form accounts for the fact that earnings reinvested (retained) contribute to asset growth, but the asset base itself grows as profits are earned.

Compute ROA from the data provided (assuming assets approximate the asset base being financed by earnings):
- ROA = Net income / Total assets = 175,000 / 2,000,000 = 0.0875 (8.75%)

Now plug the numbers into the formula:
- ROA × b = 0.0875 × 0.6571 ≈ 0.0575 (about 5.75%)
- Denominator: 1 − ROA × b ≈ 1 − 0.0575 = 0.9425
- g = 0.0575 / 0.9425 ≈ 0.0610, i.e., about 6.10%

Therefore, the annual sustainable growth rate, given the payout remains constant, is approximately 6.1%.

Evaluate the other options to see where they diverge:
- 7.7%: This would require a higher effective growth factor; using the same ROA and retention, the precise calculation yields around 6.1%, so 7.7% overstates sustainable growth under these numbers.
- 9.1%: Significantly higher than the computed 6.1% and cannot be supported by the ROA and retention combination using the standard sustainable growth framework here.
- 15.4%: This is far beyond what the internal financing from earnings (via ROA and retention) can sustain without external funds.
- 3.8%: This underestimates growth; with ROA and retention as given, the SGR sits closer to 6.1% rather than 3.8%.

Last year, a firm reported total assets of $2,000,000, sales of $745,000, net income of $175,000. The firm paid $60,000 in dividends, holding its payout ratio constant. What annual rate of growth can the firm maintain without having to look for external financing?单项选择题

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