PDI Ltd has recently restructured its outstanding bond issue. The bond issue has 8 years remaining to maturity and a coupon rate of 10% per annum, with coupons being paid semi- annually. The new arrangement allows the firm to make no coupon payments for the next 5 years. After that period, normal semi-annual coupon payments will resume. At maturity, the face value of $1,000 per bond plus all the deferred (that is, unpaid coupons) will be paid. If the required rate of return on these bonds is 15% per annum, the current market price of PDI Ltd’s bonds should be closest to:[Fill in the blank]

Question

BlackTom AI · Accepted Answer

We start by restating the scenario to ensure clarity: the bond has 8 years to maturity, a 10% annual coupon paid semiannually (so 5% of 1000 = 50 every half-year), but for the first 5 years no coupon payments are made. After year 5, regular semiannual coupons resume for the remaining 3 years (6 semiannual periods). At maturity, the bondholder receives the face value of 1000 plus all the deferred (unpaid) coupons from the 5-year deferral. The required return is 15% per year, i.e., 7.5% per half-year, and we discount all cash flows at 7.5% per half-year.

Step-by-step analysis of each option:

Option a: $603.87
- To evaluate, note that the present value will consist of two parts: (i) the value of the six coupon payments of 50 starting after the deferral (periods 11 through 16), and (ii) the value at period 16 of the 1000 face value plus the accumulated deferred coupons (which total 500). In other words, at period 16 you effectively receive 1000 + 500 + 50 (the final regular coupon) = 1550, discounted back 16 periods, plus the present value of the 5 remaining coupons discounted from periods 11–15.
- If you run the math (using v = 1/1.075 ≈ 0.93023), the present value of the five interim coupons (periods 11–15) is 50*(v^11+v^12+v^13+v^14+v^15) ≈ 50*1.970 ≈ 98.5, and the present value of the final 1550 at period 16 is 1550*v^16 ≈ 1550*0.315 ≈ 488.3. Summing gives ≈ 586.8, which is very close to 585.45 but not exactly 603.87. The 603.87 figure is too high given the discounted cash flow structure above.
- Therefore, this option overstates the price given the cash-flow pattern.

Option b: $585.45
- This aligns with the calculated approach: PV of coupons for periods 11–15 is about 98.5, and PV of the 1550 received at period 16 is about 488.3. The total ≈ 586.8, which matches the target within rounding, and is closest to 585.45 among the choices.
- The logic captures the deferral effect correctly: no coupons for first 10 periods, six future coupons after the deferral, and a lump-sum payment at maturity consisting of the face value plus all deferred coupons (500) plus the final coupon.

Option c: $1206.63
- This would imply a much higher present value, which would require substantially larger cash flows being discounted back or a much smaller discount rate. Given the 7.5% half-year rate and the deferred coupons, obtaining a present value above 1000 is unlikely unless there are many large payments far in the future at a relatively small discount, which is not the case here. The final maturity cash flow is 1550 at period 16, whose PV is only about 488, so reaching a total PV around 1200 would requiremisplaced timing or amounts that do not occur in this structure.

Option d: $781.85
- This option overstimates the PV of the cash flows. While the late coupon payments do contribute, the overall PV we calculated is closer to mid-500s. Getting to about 782 would require higher than actual discounted values for the coupons or for the final payment, which conflicts with the given discount rate and the actual cash-flow schedule described.

Synthesis across options:
- The correct pricing requires summing the PV of five cash flows of 50 (periods 11–15) plus the PV of the 16th-period total receipt (1550). Using v = 1/1.075 and standard PV calculations yields roughly 98.5 + 488.3 ≈ 586.8. This result sits closest to 585.45 among the options, while the other choices are either too high or too low given the decay factor from the 7.5% semiannual discount.

In summary, evaluating the deferred-coupon structure with the 15% annual yield confirms that the market price should be near $585.45, with the reasoning reflecting the delayed coupons and the lump-sum payment at maturity.

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