Question

You want to make a 5-year investment on bonds, and if you buy bonds with longer period of maturity, they will be sold at the prevailing market price at the end of the fifth year. All coupons will be reinvested. You forecast that the rates are going to change after you purchase the bonds. Now you have three bonds with same initial YTM to consider: A. 5-year maturity, 6% coupon paid annually, YTM=9% B. 10-year maturity, 8% coupon paid annually, YTM=9% C. 15-year maturity, 4% coupon paid annually, YTM=9% To pick the best one, you want to calculate the following:

1) What are the current prices of three bonds based on the initial YTM given? [2 points]

2) If the coupon payments are reinvested at the prevailing market rate (7% for the coming 5 years), what are the future values (at the end of the fifth year) of all five coupon payments for three bonds respectively? [3 points]

3) What are the selling prices of three bonds at the end of the fifth year, given that the prevailing market rate is 8% at that time? (For bond A, use its par value as the final selling price, as it will mature in 5 years). [2 points]

4) What are the HPRs for the three bonds? [2 points]

5) What’s your recommendation? [1 point]

Answer 1

ANSWER

1)

1,000.00 6.00% 60.00 1 Bond par value 2 Coupon rate 3 Number of compounding periods per year 4 = 1*2/3 Interest per period (PMT) 5 Number of years to maturity 6 = 3*5 Number of compounding periods till maturity (NPER) 7 Market rate of return/Required rate of return 8 = 7/3 Market rate of return/Required rate of return per period (RATE) current price of bond A 9.00% 9.00% PV(RATE,NPER,PMT,FV)-1 current price of bond A 883.31

1,000.00 8.00% 1 Bond par value 2 Coupon rate 3 Number of compounding periods per year 4 = 1*2/3 Interest per period (PMT) 5 Number of years to maturity 6 =3*5 Number of compounding periods till maturity (NPER) 7 Market rate of return/Required rate of return 8 = 7/3 Market rate of return/Required rate of return per period (RATE) current price of bond B 80.00 10 10 9.00% 9.00% PV(RATE,NPER,PMT,FV)*-1 TE current price of bond B 935.82

1,000.00 4.00% 1 Bond par value 2 Coupon rate 3 Number of compounding periods per year 4 = 1*2/3 Interest per period (PMT) 5 Number of years to maturity 6 = 3*5 Number of compounding periods till maturity (NPER) 7 Market rate of return/Required rate of return 8 = 7/3 Market rate of return/Required rate of return per period (RATE) current price of bond C 40.00 15 9.00% 9.00% PV(RATE,NPER, PMT,FV)*-1 current price of bond C 596.97

2)

Rate 7% = 0.07 Nper 5 = 5 Pmt -1000*6% = -60 Pv| = number Type = number = 345.0443406 Returns the future value of an investment based on periodic, constant payments and a constant interest rate. Pv is the present value, or the lump-sum amount that a series of future payments is worth now. If omitted, Py = 0. Formula result = $345.04

Future value of Bond A=$345.04

Rate 7% Nper Pmt -1000*8% Pv Type = 0.07 = 5 = -80 = number = number * = 460.0591208 Returns the future value of an investment based on periodic, constant payments and a constant interest rate. Py is the present value, or the lump-sum amount that a series of future payments is worth now. If omitted, Pv = 0. Formula result = $460.06

Future value of Bond B=$460.06

* = 0.07 Rate 7% Nper 5 Pmt -1000*4% PV * = -40 = number = number Type = 230.0295604 Returns the future value of an investment based on periodic, constant payments and a constant interest rate. Pv is the present value, or the lump-sum amount that a series of future payments is worth now. If omitted, Py = 0. Formula result = $230.03

Future value of the bond C =$230.03

3)
Selling price of bond A=$1000

Bond B coupon rate and market rate are same therefore selling price of bond B is $1000

1,000.00 4.00% 40.00 1 Bond par value 2 Coupon rate 3 Number of compounding periods per year 4 = 1*2/3 Interest per period (PMT) 5 Number of years to maturity 6 =3*5 Number of compounding periods till maturity (NPER) 7 Market rate of return/Required rate of return 8 = 7/3 Market rate of return/Required rate of return per period (RATE) price of the bond 101 101 8.00% 8.00% PV(RATE,NPER, PMT,FV)*-1 price of the bond 731.60

Selling price of the bond C is $731.60

4)

1,000.00 6.00% 1 Bond sale price after 5 year 2 Coupon rate 3 Number of compounding periods per year 1*2/3 Interest per period (PMT) Bond price (PV) 4 Number of years to sell 5=4*3 Number of compounding periods till sale (NPER) Holding period Return 60.00 (883.31) RATE(NPER,PMT,PV,FV) Holding period Return 9.00%

HPR of bond A is 9%

1,000.00 8.00% 1 Bond sale price after 5 year 2 Coupon rate 3 Number of compounding periods per year 1*2/3 Interest per period (PMT) Bond price (PV) 4 Number of years to sell 5=4*3 Number of compounding periods till sale (NPER) Holding period Return 80.00 (935.82) RATE(NPER, PMT,PV,FV) Holding period Return 9.68%

HPR of bond B is 9.68%

731.60 4.00% 40.00 1 Bond sale price after 5 year 2 Coupon rate 3 Number of compounding periods per year 1*2/3 Interest per period (PMT) Bond price (PV) 4 Number of years to sell 5=4*3 Number of compounding periods till sale (NPER) Holding period Return (596.97) RATE(NPER, PMT,PV,FV) Holding period Return 10.37%

HPR of Bond C is 10.37%

5)

The Purchase price of the bond C is less and the holding period return is high for bond C. Hence it is recommended to purchase Bond C.

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