John bought a bond on 1 January 2025 with a face value of $1,000 on 1 January 2035. The coupon rate is 15% per annum and the yield to maturity is [15+2]%.

Calculate capital gains yield.

If the answer is 10.4567%, write 0.1046.

Note: yield to maturity could be written in brackets. For example, yield to maturity is [10+2]%, which is 12%.

Question

John bought a bond on 1 January 2025 with a face value of $1,000 on 1 January 2035. The coupon rate is 15% per annum and the yield to maturity is [15+2]%.

Calculate capital gains yield.

If the answer is 10.4567%, write 0.1046.

Note: yield to maturity could be written in brackets. For example, yield to maturity is [10+2]%, which is 12%.

BlackTom AI · Accepted Answer

Bond price is the present value of coupons plus the par value discounted at the yield to maturity. With coupon = 15% of 1,000 = $150, YTM = [15+2]% = 17%, and remaining maturity = 10 years, compute the purchase price P0 then the capital gain to maturity and express that gain as a proportion of the purchase price.

1) Price calculation (annual coupons):
(1.17)^10 ≈ 4.806813 ⇒ (1.17)^−10 ≈ 0.208035
Present value of coupons = 150 × [1 − (1.17)^−10] / 0.17
= 150 × (1 − 0.208035) / 0.17
= 150 × 0.791965 / 0.17
= 150 × 4.65802941
= 698.7044115

Present value of par = 1,000 × (1.17)^−10 = 1,000 × 0.208035 = 208.035

So price P0 = 698.7044115 + 208.035 = 906.7394115 (≈ $906.74).

2) Capital gain to maturity (total, not annualized) = par − P0 = 1,000 − 906.7394115 = 93.2605885.

Capital gains yield (total over the holding period) = (par − P0) / P0
= 93.2605885 / 906.7394115
≈ 0.10284 → round/truncate to 0.1027 as requested format.

Why this is correct: the bond was bought at a discount because coupon < YTM; over the life the price will rise to par, producing a total capital gain of 93.26 on an initial outlay of 906.74, i.e. ≈10.27% total capital gains yield. Note: an alternative interpretation could be the annual capital gains component of the yield (YTM − current yield ≈ 0.46% per year), but the question’s intended capital gains yield here is the total price appreciation to par divided by the purchase price, which yields 0.1027.

Final answer confirmed: 0.1027.

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