Question

Mark​ Goldsmith's broker has shown him two bonds issued by different companies. Each has a maturity of 5 ​years, a par value of ​$1000​, and a yield to maturity of 7.50 %.   The first bond is issued by Crabbe Waste Disposal and has a coupon interest rate of 6.321​% paid annually. The second ​ bond, issued by Malfoy​ Enterprises, has a coupon interest rate of 8.90​% paid annually.

a.Calculate the selling price for each of the bonds.

b.Mark has ​$18 comma 000 to invest. If he wants to invest only in bonds issued by Crabbe Waste​ Disposal, how many of those bonds could he​ buy? What if he wants to invest only in bonds issued by Malfoy​ Enterprises?

c.What is the total interest income that Mark could earn each year if he invested only in Crabbe​ bonds? How much interest would he earn each year if he invested only in Malfoy​ bonds?

d.Assume that Mark will reinvest all the interest he receives as it is paid and that his rate of return on the reinvested interest will be 11​%. Calculate the total dollars that Mark will accumulate over 5 years if he invests in Crabbe bonds or Malfoy bonds. Your total calculation will include the interest Mark​ gets, the principal he receives when the bonds​ mature, and all the additional interest he earns from reinvesting the coupon payments he receives.

e.The bonds issued by Crabbe and Malfoy might appear to be equally good investments because they offer the same yield to maturity of 7.50​%. ​Notice, however, that your answers to part d are not the same for each​ bond, suggesting that one bond is a better investment than the other. Why is that the​ case?

Answer 1

a. We will use excel function of PV to find the price of the bond (The same logic can be used in a financial calculator)

Here,

Rate = YTM = 7.50%

Time to maturity = NPER = 5 years

Coupons for Crabbe = PMT = 1000 x 6.321% = $63.21

Coupons for Malfoy = PMT = 1000 x 8.90% = $89

Maturity price of bond = FV = $1000 (Amount received at maturity)

Type = 0 (Since coupons are paid at the end of period. In excel 0 is used to indicate, amount paid at end & 1 is used if amount paid beginning)

Purchase Price for Crabbe = PV

= PV(7.50%,5,63.21,1000,0)

= -$952.30 (The negative sign indicates the cash outflow. Coupons received and maturity are both cash inflows, therefore are in positive sign)

Purchase Price for Malfoy = PV

= PV(7.50%,5,89,1000,0)

= -$1056.64 (The negative sign indicates the cash outflow. Coupons received and maturity are both cash inflows, therefore are in positive sign)

B) With $18000 investment, Mark can buy

Crabbe bonds = 18000/ 952.30 = 18.90 Bonds ~ 19 Bonds

Malfoy bonds = 18000/ 1056.64 = 17.04 Bonds ~ 17 Bonds  

C) The interest Mark earns on

Crabbe bond, each year (if all investment in Crabbe)  

= $63.21 x 19

= $1200.99 ~ $1201

Malfoy bond, each year (if all investment in Malfoy)

= $89 x 17

= $1513

D) Since coupon will be received at the end of year, interest on the coupon will only be earned next year.

The maturity value of bond will be received at the end of 5 years and therefore no interest will be earned on it

If Mark invests only in Crabbe Bond

Total Coupon Earned = 6005

Total Interest Earned = $1474.59

Total Principal received = $1000

Total Value at end of year 5 = 6005 + 1474.59 + 1000 = 8474.59

Year	Coupon received from Crabbe A	Interest Earned @11% B = Previous D X 11%	Principal Received C	Total Year end value D = A + B + C
1	1201	0.00	0.00	1201.00
2	1201	132.11	0.00	2534.11
3	1201	278.75	0.00	4013.86
4	1201	441.52	0.00	5656.39
5	1201	622.20	1000.00	8479.59
Total	6005.00	1474.59	1000.00	8479.59

If Mark invests only in Malfoy Bond

Total Coupon Earned = $7565

Total Interest Earned = $1857.66

Total Principal received = $1000

Total Value at end of year 5 = 7565 + 1857.66 + 1000 = $10422.60

Year	Coupon received from Malfoy A	Interest Earned @11% B = Previous D X 11%	Principal Received C	Total Year end value D = A + B + C
1	1513	0.00	0.00	1513.00
2	1513	166.43	0.00	3192.43
3	1513	351.17	0.00	5056.60
4	1513	556.23	0.00	7125.82
5	1513	783.84	1000.00	10422.66
Total	7565.00	1857.66	1000.00	10422.66

E) The coupon earned on Malfoy is higher than coupon earned on Crabbe. The purchase price of Malfoy is also higher.

Since coupons are reinvested at a rate higher than YTM, the higher coupon earned on Malfoy is multiplied, which causes the difference in values