Question

In: Accounting

What is the annual capital gains yield expected over the next year for a 12 year...

What is the annual capital gains yield expected over the next year for a 12 year bond with 6.9% coupon rate paying the coupons every six months and selling at $1,045

Solutions

Expert Solution

Calculation of yield to maturity:

Face Value = $1,000
Current Price = $1,045

Annual Coupon Rate = 6.90%
Semiannual Coupon Rate = 3.45%
Semiannual Coupon = 3.45% * $1,000
Semiannual Coupon = $34.50

Time to Maturity = 12 years
Semiannual Period to Maturity = 24

Let Semiannual YTM be i%

$1,045 = $34.50 * PVIFA(i%, 24) + $1,000 * PVIF(i%, 24)

Using financial calculator:
N = 24
PV = -1045
PMT = 34.50
FV = 1000

I = 3.179%

Semiannual YTM = 3.179%

Calculation of price after 1 year:

Face Value = $1,000
Semiannual Coupon = $34.50
Semiannual YTM = 3.179%

Time to Maturity = 11 years
Semiannual Period to Maturity = 22

Price in 1 year = $34.50 * PVIFA(3.179%, 22) + $1,000 * PVIF(3.179%, 22)
Price in 1 year = $34.50 * (1 - (1/1.03179)^22) / 0.03179 + $1,000 / 1.03179^22
Price in 1 year = $1,042.42

Calculation of capital gain yield:

Capital Gain Yield = (Price in 1 year - Current Price) / Current Price
Capital Gain Yield = ($1,042.42 - $1,045) / $1,045
Capital Gain Yield = -0.0025 or -0.25%


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