Question

You purchase a 3 year bond for $980 (FV=$1000). The bond pays a 5% annual coupon. What is the current yield of the bond? If the YTM remains constant, what will be your total return over the next year? What will be your capital gains/losses on the bond?

Answer 1

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

Where,

Coupon = Par Value*Coupon Rate = 1000*5% = 50

Pro Rated Discount = [(Redemption Price-Purchase Price)/Period to Maturity] = [(1000-980)/3] = 6.6667

Redemption Price (assuming at par) = 1000

Therefore, Current Yield = YTM = [50+6.6667]/[(980+1000))/2] = 56.6667/990 = 0.057239 = 5.7239%

Period	Cash Flow	Discounting Factor [1/(1.057239^year)]	PV of Cash Flows (cash flows*discounting factor)
1	50	0.945859924	47.29299619
2	50	0.894650995	44.73254977
2	1000	0.894650995	894.6509955
		Price of the Bond NEXT YEAR = Sum of PVs	986.6765415

Total Return over next year = [Price next year-Purchase Price+Coupon]/Purchase Price = [986.68-980+50]/980 = 56.68/980 = 0.057837 = 5.7837%

Capital Gain = [Price next year-Purchase Price]/Purchase Price = [986.68-980]/980 = 6.68/980 = 0.006816= 0.6816%