How to apply for a loan

The bank offers Frw 6,000,000 over 24 months at 18% a year on the reducing balance. Mutoni's statements show an average net cash flow, before any loan payments, of Frw 900,000 a month, and she already pays Frw 150,000 a month on an older loan. The bank requires a debt service coverage ratio (DSCR) of at least 1.25. (Illustrative policy; lenders set their own.)

Instalment: $i=\frac{0.18}{12}=0.015i\; =\; \backslash frac\{0.18\}\{12\}\; =\; 0.015$, $N=24N\; =\; 24$.

$$M=6000000\times \frac{0.015}{1-{1.015}^{-24}}\approx 299545\text{ Frw a month}M\; =\; 6\backslash ,000\backslash ,000\; \backslash times\; \backslash frac\{0.015\}\{1\; -\; 1.015^\{-24\}\}\; \backslash approx\; 299\backslash ,545\backslash \; \backslash text\{Frw\; a\; month\}$$

Coverage:

$$\text{DSCR}=\frac{\text{net cash flow available}}{\text{total debt payments}}=\frac{900000}{150000+299545}\approx 2.00\backslash text\{DSCR\}\; =\; \backslash frac\{\backslash text\{net\; cash\; flow\; available\}\}\{\backslash text\{total\; debt\; payments\}\}\; =\; \backslash frac\{900\backslash ,000\}\{150\backslash ,000\; +\; 299\backslash ,545\}\; \backslash approx\; 2.00$$

Since $2.00\ge 1.252.00\; \backslash ge\; 1.25$, capacity is adequate. The most she could pay while keeping DSCR at 1.25:

$$\frac{900000}{1.25}-150000=570000\text{ Frw a month}\backslash frac\{900\backslash ,000\}\{1.25\}\; -\; 150\backslash ,000\; =\; 570\backslash ,000\backslash \; \backslash text\{Frw\; a\; month\}$$

Interpretation: the loan uses about half of her safe repayment capacity, leaving room for a slow month. Total interest over two years is $24\times 299545-6000000\approx 118907124\; \backslash times\; 299\backslash ,545\; -\; 6\backslash ,000\backslash ,000\; \backslash approx\; 1\backslash ,189\backslash ,071$ Frw, which the extra sales must cover.

The bank deducts a 2% processing fee and 1% loan insurance from the loan when it is paid out. What does Mutoni actually receive, and what does the loan really cost?

$$\text{Fees}=0.03\times 6000000=180000\text{ Frw};\text{received}=6000000-180000=5820000\text{ Frw}\backslash text\{Fees\}\; =\; 0.03\; \backslash times\; 6\backslash ,000\backslash ,000\; =\; 180\backslash ,000\backslash \; \backslash text\{Frw\};\; \backslash qquad\; \backslash text\{received\}\; =\; 6\backslash ,000\backslash ,000\; -\; 180\backslash ,000\; =\; 5\backslash ,820\backslash ,000\backslash \; \backslash text\{Frw\}$$ $$\text{Total cost}=1189071+180000=1369071\text{ Frw}\backslash text\{Total\; cost\}\; =\; 1\backslash ,189\backslash ,071\; +\; 180\backslash ,000\; =\; 1\backslash ,369\backslash ,071\backslash \; \backslash text\{Frw\}$$

She still repays 24 instalments of Frw 299,545 on the full Frw 6 million, but has received only Frw 5,820,000. The monthly rate that links these two figures, found by trial and improvement, is about 1.76%, roughly 21.2% a year instead of the advertised 18%. Interpretation: when comparing lenders, compare the total cost and the effective rate, including fees, not the headline rate alone.