Accrued Interest and Duration on a Corporate Bond
A client is considering buying £50,000 nominal of Kestrel Energy 5.5% 2031, a sterling corporate bond. The clean price is 96.50. Coupons are paid semiannually on 15 January and 15 July. Settlement is 1 April, which is 76 days into a 182-day coupon period. The bond is unsecured, rated BBB, and has a modified duration of 6.4. The comparable 2031 gilt yields 4.20%, and the bond's yield to maturity is 5.85%. The client's portfolio is 80% equities and 20% cash; she wants 'safe income' and expects to sell the bond in about 18 months to fund a house purchase. The broker quotes the clean price and says the total cost will be 'about £48,250'. The client asks whether the coupon of 5.5% means she will receive £2,750 each year and whether the bond is lower risk than her equity fund.
1. Calculate the accrued interest, the dirty price and the total consideration for the £50,000 nominal purchase. Comment on the broker's 'about £48,250' estimate.
Read the worked answer
Semiannual coupon per £100 nominal = 5.5% / 2 = 2.75.
Accrued interest per £100 = 2.75 x (76 / 182) = 2.75 x 0.41758 = 1.14835.
For £50,000 nominal, the holding is 500 units of £100. Accrued interest = 500 x 1.14835 = £574.18.
Dirty price = clean price + accrued interest = 96.50 + 1.14835 = 97.64835 per £100.
Total consideration = 500 x 97.64835 = £48,824.18, before any commission.
The broker's 'about £48,250' is simply the clean price: 500 x 96.50 = £48,250. It ignores accrued interest of about £574, so it understates the cash cost. The client should also ask about commission and any other charges. The coupon of 5.5% does mean £2,750 a year on £50,000 nominal, but the first coupon will include a payment for accrued interest she has effectively bought.
2. Assess the suitability of the bond for the client, given her 18-month horizon and 'safe income' objective. Include the effect of a 75 basis point rise in yields.
Read the worked answer
The bond is not a safe income asset for an 18-month horizon. It is unsecured, rated BBB, and offers a spread of 5.85% - 4.20% = 1.65% over the comparable gilt. That spread compensates for credit risk, liquidity risk and possibly structure risk. A default or downgrade would affect both price and income.
Interest-rate risk is material. With modified duration of 6.4, a 75 basis point rise in yields would reduce the price by approximately 6.4 x 0.75% = 4.8%. On a dirty consideration of about £48,824, that is a capital loss of roughly £2,343. That is close to one year's coupon of £2,750. If she must sell in 18 months, the total return could easily be negative.
The client says she wants 'safe income', but the main risk is price volatility, not the coupon. A shorter-dated gilt, a cash deposit or a diversified short-duration bond fund would better match her horizon, although none is risk-free. If she buys this bond, she should be prepared to hold to 2031 or accept the risk of a loss on early sale. The adviser should also explain that a 5.5% coupon does not make the bond lower risk than her equity fund; it changes the type of risk.