Question

ABC plc plans to issue bonds with a face value of £10,000 each, coupon rate of 4 percent, paid annually, and 10 years to maturity. The current market interest rate on similar bonds is 4 percent. In one years’ time, the long-term interest rate for this type of bond is predicted to be either 5 percent or 3 percent with equal probability. Assume investors are risk-neutral.

a. If the bonds are non-callable, what is the price of the bonds today, taking into account only the current market interest rate on similar bonds? Explain your answer

b.If the bonds are non-callable, what is the price of the bonds today, taking into account both the current market interest rates and the long-term interest rates after one year?

c.What is the current yield of the bond for a bondholder based on the value you computed in (b) above?

d.If the bonds are callable one year from today at 110 per cent of the face value, will their price be greater than or less than the price you computed in (b)? Explain your answer

e. Why would a firm choose to issue callable bonds?

f. In an efficient market, would callable bonds be priced higher or lower than the non-callable bonds, other things being equal? Explain your answer.

g. Why do investors pay attention to bond ratings and demand a higher interest rate for bonds with lower rating? What does lower rating imply in terms of credit risk?

Answer 1

Answer to Question a,

The price of the bond will be the face value, because we discounts the 4% interest by using the same rate of 4%.

We know that the Price of the bond is the present value of future cash flow. Present value = (Uniform Annual Cash flow X PV Annuity factor ) + (las t year cash flow X discount factor for the last year).

here the life is for 10 years, the interest of £400 (£10,000 X 4%) will be received for 9 years and £10,400 including interest for 10th year with principal Amount will be received.

so we can use PV Annuity Factor from year 1-9 and discount factor for 10th year.

PV Annuity Factor from year 1-9 = (((1+i)ⁿ)-1) / (((1+i)ⁿ) X (i)).

"i" is the market interest rate = 4%, n is the number of years = 9,

discount factor for 10th year = 1/(1+i)ⁿ, n is the number of year, n = 10, "i" is the market interest rate = 4%,

year1-9 400 7.4353316105292400 2,974.1326442117 year 10 10400 0.6755641688257990 7,025.8673557883 Total Present Value 10,000.000000000 Answer to Question b, Considering Current interest rate of 4% in year 1 and possible longterm interest rate of 5% from year 2 to year 10 Table 1 year Cash flow Discount Factor PV of Cash flow year1 400 0.9615384615384610 384.6153846153850 year2 400 0.9157509157509160 366.3003663003660 year3 400 0.8721437292865860 348.8574917146340 year4 400 0.8306130755110340 332.2452302044140 year5 400 0.7910600719152710 316.4240287661080 year6 400 0.7533905446812100 301.3562178724840 year7 400 0.7175148044582960 287.0059217833180 year8 400 0.6833474328174240 273.3389731269700 year9 400 0.6508070788737370 260.3228315494950 year10 10400 0.6198162655940360 6446.089162177970 Total Present Value 9316.555608111140 Considering Current interest rate of 4% in year 1 and possible longterm interest rate of 3% from year 2 to year 10 Table 2 year Cash flow Discount Factor PV of Cash flow year1 400 0.9615384615384610 384.6153846153850 year2 400 0.9335324869305450 373.4129947722180 year3 400 0.9063422203209170 362.5368881283670 year4 400 0.8799439032241920 351.9775612896770 year5 400 0.8543144691497010 341.7257876598800 year6 400 0.8294315234463110 331.7726093785250 year7 400 0.8052733237342830 322.1093294937130 year8 400 0.7818187609070710 312.7275043628280 year9 400 0.7590473406864760 303.6189362745910 year10 10400 0.7369391657150260 7664.167323436270 Total Present Value 10748.664319411400 Value of Table 1 X 0.5 (Probability) 4658.277804055570 Value of Table 2 X 0.5 (Probability) 5374.332159705720 Value of bond After Considering current interest of 4% and longterm interest of 5% or 3% with equal probability 10032.609963761300 Rounded to  £10,032.61

Answer to Question c,

Current yeild coupon / current price X 100 ,

= £400/£10,032.61 X 100,

= 3.9869984126248%, rounded to 2 decimal places =3.99%

Answer to question d,

Price if bonds are callable one year from today at 110%, then the relevant interest rate for discounting the cash flow is 4% because the long-term interest rate for this type of bond is predicted to be either 5 percent or 3 percent with equal probability in one years’ time. the value is computed today. so the relevant interest rate for discounting the cash flow is 4%.

The cash flow will be 4% coupon + repayment of principal investment of £10,000 at 110% = £400 + £11,000 = £11,400

PV = £11,400 / 1.04 = £10,961.5384615385, rounded to 2 decimal places = £10,961.54.

the price is more than computed in answer (b) above.

Answer to Question e,

The firm choose to issue callable bonds when  the firm can choose to repay them before the official statedmaturity date. Companies issue callable bonds to take banefit of a possible reduction in interest rates at some future dates.

Answer to Question f,

Callable bonds be priced higher than the non-callable bonds because the issuer company will pay a slight higher interest rate than would be necessary for a similar non-callable bond.

Answer to Question g,

Bonds with lower rating denotes the comparatively risky than higher rated bonds. In all investments, the investors are considering the risk - return trade off. Risk - return trade off means where ever we take more risk, we will expect more return. Because of this, investors pay attention to bond ratings and demand a higher interest rate for bonds with lower rating.

Lower rating imply the risk in serving or repayment of the interest or repayment of principal.

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