Question

Bond X is noncallable and has 20 years to maturity, a 8% annual coupon, and a $1,000 par value. Your required return on Bond X is 8%; if you buy it, you plan to hold it for 5 years. You (and the market) have expectations that in 5 years, the yield to maturity on a 15-year bond with similar risk will be 9.5%. How much should you be willing to pay for Bond X today? (Hint: You will need to know how much the bond will be worth at the end of 5 years.) Do not round intermediate calculations. Round your answer to the nearest cent. $

Answer 1

Expected price at the end of 5 years
PV of all future coupon payments plus PV of redemption value
PV of annuity for making pthly payment
P = PMT x (((1-(1 + r) ^- n)) / i)
Where:
P = the present value of an annuity stream
PMT = the dollar amount of each annuity payment
r = the effective interest rate (also known as the discount rate)
i=nominal Interest rate
n = the number of periods in which payments will be made
Bond price	1000
Coupon	8%	80
rate		9.50%
PV of coupon payments	PMT x (((1-(1 + r) ^- n)) / i)
PV of coupon payments	80*(((1-(1 + 9.5%) ^- 15)) / 9.5%)
PV of coupon payments	626.254
PV of redemption value	=1000/(1+9.5%)^15
	256.3234
PV of all future payments	=626.25+256.32
PV of all future payments	882.57
So to calculate bond price today, we should calculate the PV of all future cash flows in 5 years
Year	Cashflows	PV factor	Present Value
1	80	0.9259	74
2	80	0.8573	69
3	80	0.7938	64
4	80	0.7350	59
5	963	0.6806	655
		Total Present Value	920
Cash flow in 5th year will be (882.57+80)
So with expected return of 8%, the buyer will be willing to pay 920 for this bond today