Question

Bond	Coupon Rate	Maturity	Price Per $100 Face Value	Yield to Maturity- annual rate, compounded semi-annually
Vermeero Enterprises	4%	5 years	???	6.00%
Renwaro Company	0%	5.5 years	74.1993	????

a) Draw a diagram showing the cash flow for each of the bonds

b) Calculate the price of the Vermeero bond

c) Calculate the yield to maturity for the Renwaro bond

d) Suppose you purchase the Renwaro bond today. You plan to sell this bond one year from now, and you forecast that the yield to maturity of the Renwaro (at the sale date) will be 5% annual rate, compounded semiannually. If your forecast is correct, what will the holding period yield for this investment be?

Answer 1

a)

Year	Bond VeermanCash-flows
0.5	2
1	2
1.5	2
2	2
2.5	2
3	2
3.5	2
4	2
4.5	2
5	102

Year	Renwaro Cash-flows
0	-74.1993
0.5	0
1	0
1.5	0
2	0
2.5	0
3	0
3.5	0
4	0
4.5	0
5	0
5.5	100

b)

Bond Vermeero pays semi-annual coupon equal to $2 for 4 years every 6 months

Semi-annual rate = 6%/2 = 3%

Year	Semi-annual period	Cash-flows	PV of cash-flow (Cash-flow/(1.03^Year)
0.5	1	2	1.941747573
1	2	2	1.885191818
1.5	3	2	1.830283319
2	4	2	1.776974096
2.5	5	2	1.725217569
3	6	2	1.674968513
3.5	7	2	1.626183023
4	8	2	1.578818469
4.5	9	2	1.532833465
5	10	102	75.89757932
		Bond price	91.46979716

Hence, Price of the Veermano bond = $91.470

c)

Bond Renwaro pays no coupons

Zero-coupon bond yield = ((Face value/PV)^(1/n) )-1

Zero-coupon bond yield = ((100/74.1993)^(1/5.5) )-1 = 0.05576 = 5.576%

This is the annual yield

Semi-annual compounded zero-coupon bond yield = ((1+0.05576/2)^2)-1 = 0.05654

Semi-annual compounded zero-coupon bond yield = 5.654%

d)

Renwaro bond price after 1 year = Face value / ((1+y)^n)

where n is the years remaining for the bond to maturity and y is the annualized yield

Annualized yield = ((1+0.05/2)^2 ) -1

Annualized yield = 0.050625 = 5.0625%

Renwaro bond price after 1 year = 100 / ((1+0.050625 )^4.5) = $80.0728

Holding period yield = (80.0728-74.1993)/74.1993 = 0.07916 = 7.916%