Question

A bond has a par value of $1,000, a time to maturity of 10 years, and a coupon rate of 8% with interest paid annually. If the current market price is $750, what is the capital gain yield of this bond over the next year?

Answer 1

Yield to Maturity = [Coupon + Pro-rated Discount]/[(Purchase Price + Redemption Price)/2]

Where,

Coupon = Par Value*Coupon Rate = 1000*8% = 80

Pro Rated Discount = [(Redemption Price-Purchase Price)/Period to Maturity] = [(1000-750)/10] = 25

Redemption Price (assuming at par) = 1000

Therefore, YTM = [80+25]/[(750+1000))/2] = 105/875 = 0.12 = 12%

Period	Cash Flow	Discounting Factor [1/(1.12^year)]	PV of Cash Flows (cash flows*discounting factor)
1	80	0.892857143	71.42857143
2	80	0.797193878	63.7755102
3	80	0.711780248	56.94241983
4	80	0.635518078	50.84144627
5	80	0.567426856	45.39414846
6	80	0.506631121	40.53048969
7	80	0.452349215	36.18793723
8	80	0.403883228	32.31065824
9	80	0.360610025	28.848802
9	1000	0.360610025	360.610025
		Price of the Bond = Sum of PVs	786.8700083

Price After 1 year = $786.87

Capital Gain Yield over next year = [(Price after 1 year-Current Price)/Current Price] = [(786.87-750)/750] = 36.87/750 = 0.04916 = 4.916%