A fictional BDC bought at 80 per cent of NAV, its return split into dividends, NAV and discount, and the exit discount that decides it.
Not by itself. A BDC bought at a discount to NAV earns the discount only if NAV holds and the discount narrows; if NAV erodes and the discount widens, the discount was a forecast, not a bargain. The fictional Corlett Credit, bought at 9.00 against a NAV of 11.25 (a 20.0 per cent discount) and displaying a 14.67 per cent yield, returned 7.76 per cent a year over three years, less than the BDC bought at 5 per cent below NAV.
Worked in full in The Credit Investor by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
In The Credit Investor an investor puts $25,000 into Corlett, the most heavily discounted of three listed BDCs. Every figure is the book's illustrative assumption. The dividend of 0.33 a quarter is not covered by income, and it is cut to 0.25 from quarter 6. NAV falls with credit losses of 3.5 per cent a year and with the part of each dividend that income did not pay. After twelve quarters the shares are sold at a 25 per cent discount.
| Input | Value |
|---|---|
| Amount invested | $25,000 |
| Price at purchase | 9.00 |
| NAV per share at purchase | 11.25 |
| Discount at purchase | 20.0% |
| Quarterly dividend, quarters 1 to 5 | 0.33 |
| Quarterly dividend, quarters 6 to 12 | 0.25 |
| NAV per share at quarter 12 | 9.94 |
| Discount at quarter 12 | 25% |
A discount raises every NAV-based yield by the factor 1 / (1 − discount), here 1.25. Corlett's net investment income is 10.69 per cent of NAV, which becomes 13.36 per cent on the price paid. That is the arithmetic behind the pitch for discounted BDCs, and it is correct as far as it goes.
The same factor applies to everything else measured on NAV. Credit losses of 3.5 per cent of NAV are 4.38 per cent of the price paid. A discount magnifies the losses exactly as it magnifies the income, so it is only cheap if the losses are smaller than the market expects.
The investor buys 2,777.78 shares. Total gain splits into three parts, and each has a formula.
Dividends = shares × dividends per share = 2,777.78 × 3.40 = 9,444.44
NAV effect = shares × (NAV12 − NAV0) × (1 − entry discount) = 2,777.78 × (−1.31) × 0.80 = −2,904.02
Discount effect = shares × NAV12 × (entry discount − exit discount) = 2,777.78 × 9.94 × (20% − 25%) = −1,381.00
Total gain = 9,444.44 − 2,904.02 − 1,381.00 = 5,159.42
Excel, for the return: =(1+IRR(Flows))^4-1 on the quarterly flows, the sale at 7.46 added to the last dividend
The three effects add up to the cash: the shares are sold for 20,714.98, a capital loss of 4,285.02 against the 9,444.44 of dividends. The quarterly internal rate of return, annualised, is 7.76 per cent.
NAV fell 11.6 per cent over the three years. The discount, which was supposed to be the margin of safety, became a second loss when it widened by five points. Both moves have the same cause: a dividend that income did not cover and a loan book that lost value. The 20 per cent at purchase was the market pricing that risk, not a gift, and by the exit it priced in a little more.
The book's other two BDCs, bought at a 5 per cent discount and at a premium, returned 10.16 and 9.09 per cent. The cheapest-looking line was the worst performer of the three.
Hold the NAV path and the dividends as booked and change only the discount at exit:
| Exit discount | Exit price | IRR |
|---|---|---|
| 0% | 9.94 | 16.53% |
| 10% | 8.95 | 13.20% |
| 20% | 7.95 | 9.64% |
| 25% | 7.46 | 7.76% |
| 30% | 6.96 | 5.81% |
Even if the discount had stayed at 20 per cent, the return would have been 9.64 per cent, still below the line bought near NAV. The discount closing completely would have produced 16.53 per cent; that is the bet a buyer of a discounted BDC is actually making.
The entry price matters as much, and in the other direction:
| Entry price | Entry discount | IRR |
|---|---|---|
| 11.25 | 0.0% | −1.39% |
| 10.00 | 11.1% | 3.31% |
| 9.00 | 20.0% | 7.76% |
| 8.00 | 28.9% | 13.04% |
To match Ledgerwood's 10.16 per cent, Corlett had to be bought at 8.52, a discount of 24.2 per cent. Had NAV held at 11.25 and the discount stayed at 20 per cent, the same shares would have returned 13.38 per cent. The difference between 13.38 and 7.76 is the price of NAV erosion and a wider exit discount, and neither showed up in the yield on the screen.
The common mistake is to treat the discount as free return that the market will hand back. A discount on a BDC is the market's estimate of three things: dividends not covered by income, credit losses yet to be recognised in NAV, and the fees and leverage that sit between the loans and the shareholder. Before calling a discount cheap, compute the dividend coverage, project NAV with a realistic loss rate, and run the return with the discount unchanged. If the return only works when the discount closes, the position is a bet on sentiment, not on credit.
A second error is to compare discounted BDCs on dividend yield. Corlett displayed 14.67 per cent against 10.11 per cent for Ledgerwood; it earned 2.40 points a year less.
The quarterly NAV paths, the decomposition for all three BDCs and the stress scenarios are in the free workbook for this case. The income side of the same BDC, and why its dividend is only 91.1 per cent covered, is worked in how to calculate a BDC's dividend coverage ratio.
The discount is the market's estimate of what NAV does not yet show: dividends not covered by income, credit losses still to be recognised, and the cost of fees and leverage. In the worked case Corlett trades at a 20.0 per cent discount while its dividend is 91.1 per cent covered and its loan book loses 3.5 per cent of NAV a year; NAV fell 11.6 per cent over three years.
Into three parts: dividends received; the NAV effect, shares times the change in NAV times one minus the entry discount; and the discount effect, shares times final NAV times the entry discount less the exit discount. For $25,000 in Corlett they are 9,444.44, -2,904.02 and -1,381.00, a total gain of 5,159.42 and an IRR of 7.76 per cent.
A narrowing discount adds return, but it is a bet on sentiment rather than credit. Holding Corlett's NAV path, closing the discount fully at exit would have produced 16.53 per cent; holding it at the 20 per cent entry level gives 9.64 per cent; widening to 30 per cent gives 5.81 per cent. Underwrite on the unchanged discount and treat any narrowing as upside.
This article is one calculation from The Credit Investor. The book takes the same case from first principles to the decision, chapter by chapter, and every figure it prints is a live formula in the free companion workbooks.
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