- 10 Marks
FM – L2 – Q18 – Business valuations
Question
(a) Calculate the value of the following bonds:
(i) a zero coupon bond redeemable at par in ten years’ time
(ii) a bond with an 8% coupon, with interest payable half-yearly, and redeemable at par after ten years.
Assume that the yield required by investors is 5%, and that this is 2.5% each half year for the purpose of valuing the 8% coupon bond.
(b) Calculate the value of both bonds in part (a) of the question if the yield required by investors goes up by 1%, to 6% for the zero coupon bond and 3% each half year for the 8% coupon bond.
Answer
(a)
(i) Zero Coupon Bond
The value of a zero coupon bond is the present value of its redemption value, discounted at the required yield. Assuming a nominal value of GH₵100, redeemable at par in 10 years at a 5% annual yield:
Value = 100 / (1.05)¹⁰ = 100 × 0.6139 = GH₵61.39
(ii) 8% Coupon Bond
The bond pays 8% coupon half-yearly (4% per half-year) and is redeemable at par after 10 years (20 half-year periods). The half-yearly yield is 2.5%. Assuming a nominal value of GH₵100:
- Half-yearly coupon payment = 4% of 100 = GH₵4
- Present value of coupons (annuity for 20 periods at 2.5%):
PV = 4 × [1 − (1.025)⁻²⁰] / 0.025 = 4 × 15.589 = GH₵62.36 - Present value of redemption value (GH₵100 at end of 20 periods):
PV = 100 / (1.025)²⁰ = 100 × 0.6103 = GH₵61.03 - Total value = 62.36 + 61.03 = GH₵123.39
(b)
(i) Zero Coupon Bond
With a yield of 6%, the value of a zero coupon bond redeemable at par (GH₵100) in 10 years is:
Value = 100 / (1.06)¹⁰ = 100 × 0.5584 = GH₵55.84
(ii) 8% Coupon Bond
The bond pays 8% coupon half-yearly (4% per half-year), redeemable at par after 10 years (20 half-year periods), with a half-yearly yield of 3%. Assuming a nominal value of GH₵100:
- Half-yearly coupon payment = 4% of 100 = GH₵4
- Present value of coupons (annuity for 20 periods at 3%):
PV = 4 × [1 − (1.03)⁻²⁰] / 0.03 = 4 × 14.877 = GH₵59.51 - Present value of redemption value (GH₵100 at end of 20 periods):
PV = 100 / (1.03)²⁰ = 100 × 0.5537 = GH₵55.37 - Total value = 59.51 + 55.37 = GH₵114.88
- Tags: Bond valuation, Coupon bond, Discounted cash flow, Yield change, Zero coupon bond
- Level: Level 2
- Topic: Business valuations
- Uploader: Samuel Duah