Question

1. Calculate the price if a 5% coupon, $1000 face value 5-year bond if the appropriate annual discount rates are 3% for the first 2 years and 8% for the final three years. Calculate this bond’s yield to maturity or average annual yield. Calculate your return if you hold this bond for one year. If we assume the change in annual rates is due to expectations of inflation, what does the bond market thing inflation is going to do in the future? Please show all work and do not use excel or a finance calculator.

Answer 1

Cash Flow = Coupon%*Face Value = 5% of 1000 = 50

PV of CF = CF of that year/(1+discount factor)^Year

Price = Sum of all the PV of CFs

Coupon	5%
Face Value	1000
Year	Cash Flow	Discount Factor	PV of CF
1	50	3%	48.544
2	50	3%	47.130
3	50	8%	39.692
4	50	8%	36.751
5	1050	8%	714.612
		Price	886.729

YTM = { Coupon amount + (Face value - Price)/Time to maturity}/{ (Face value + Price)/2 } = { 50 + (1000 - 886.729)/5 } / {1886.729/2 } = 7.702%

Price at year 1 = Sum of PV of all futher CFs i.e PV of CF at year 2,3,4,5 = 47.130+39.692+36.751+714.612 = 838.185

Return = (Coupon recived + Capital aprreciation)/Purchase Price

Capital appreciation = Price at Year1 - Purchase Price = 886.729 - 838.185 = - 48.544

Return = (50 - 48.544)/886.729 = 0.164%

If change in annual rates is due to expectations of inflation, then the bond market thinks inflation is going to increase in future so the discount rate increases accordingly.