Sources of business capital, with pros and cons

Hakizimana compares two ways of raising Frw 18 million. Plan A: all equity, his Frw 3 million plus Frw 15 million from his friend as a partner. Plan B: Frw 8 million of equity and a Frw 10 million bank loan at 16% a year. The workshop is expected to earn Frw 4.5 million a year before interest; in a bad year (long rains, few orders) only Frw 1.8 million. Ignore tax. Compare the return on the owners' equity.

Interest under Plan B: $10000000\times 0.16=160000010\backslash ,000\backslash ,000\; \backslash times\; 0.16\; =\; 1\backslash ,600\backslash ,000$ Frw a year.

Good year:

$$\text{A: }\frac{4.5}{18}\times 100\mathrm{\%}=25\mathrm{\%},\text{B: }\frac{4.5-1.6}{8}\times 100\mathrm{\%}=36.25\mathrm{\%}\backslash text\{A:\; \}\; \backslash frac\{4.5\}\{18\}\; \backslash times\; 100\backslash \%\; =\; 25\backslash \%,\; \backslash qquad\; \backslash text\{B:\; \}\; \backslash frac\{4.5\; -\; 1.6\}\{8\}\; \backslash times\; 100\backslash \%\; =\; 36.25\backslash \%$$

Bad year:

$$\text{A: }\frac{1.8}{18}\times 100\mathrm{\%}=10\mathrm{\%},\text{B: }\frac{1.8-1.6}{8}\times 100\mathrm{\%}=2.5\mathrm{\%}\backslash text\{A:\; \}\; \backslash frac\{1.8\}\{18\}\; \backslash times\; 100\backslash \%\; =\; 10\backslash \%,\; \backslash qquad\; \backslash text\{B:\; \}\; \backslash frac\{1.8\; -\; 1.6\}\{8\}\; \backslash times\; 100\backslash \%\; =\; 2.5\backslash \%$$

Gearing of Plan B: $\frac{10}{18}\times 100\mathrm{\%}\approx 55.6\mathrm{\%}\backslash frac\{10\}\{18\}\; \backslash times\; 100\backslash \%\; \backslash approx\; 55.6\backslash \%$.

Conclusion: debt magnifies the owners' return in both directions. With steady earnings above the interest cost, borrowing lets the owners earn more on less of their own money. In a bad year almost all the profit goes to the bank, and if earnings fell below Frw 1.6 million, the interest would have to come from the owners' pockets. A high-geared firm needs reliable cash flows.

The steel supplier's terms are: pay within 30 days, or take a 2% discount by paying within 10 days. Hakizimana's overdraft costs 17% a year. Should he borrow on the overdraft to pay early?

By not paying early he keeps Frw 98 (the discounted price) for 20 extra days and pays Frw 2 for it. As an annual rate (simple approximation):

$$\text{Cost of not taking the discount}=\frac{2}{98}\times \frac{365}{30-10}=0.0204\times 18.25\approx 37.2\mathrm{\%}\text{ a year}\backslash text\{Cost\; of\; not\; taking\; the\; discount\}\; =\; \backslash frac\{2\}\{98\}\; \backslash times\; \backslash frac\{365\}\{30\; -\; 10\}\; =\; 0.0204\; \backslash times\; 18.25\; \backslash approx\; 37.2\backslash \%\backslash \; \backslash text\{a\; year\}$$

Decision: $37.2\mathrm{\%}>17\mathrm{\%}37.2\backslash \%\; >\; 17\backslash \%$, so it is cheaper to borrow on the overdraft and take the discount. Trade credit is interest-free only up to the discount date; after that, it is one of the most expensive sources there is.