Question

Time Value of Money and Bonds Valuation

As Laura’s new year resolution, she wants to begin saving money for her retirement. You are hired as her financial advisor. Following your suggestion, today Laura will deposit $100,000, which she inherited from her parents, into a 5-year savings account at Citi bank, which pays 3.25% interest annually.

Use the above information to answer the following questions. When answering your question, make sure to include the calculation steps or formula. (Assume END mode)

Laura asks you to help her invest in the bonds market. You have the following three bonds good for investment. Assume all coupons are paid annually and END mode, find the best option for your friend?

Option One: Treasury bond has 4% annual coupon, matures in 10 years, and has a $10,000 face value. Its price is $9,550

Option Two: Corporate Bond A has a 9% annual coupon, matures in 5 years, and has a $10,000 face value. Its price is $10,500

Option Three: Corporate Bond B has a 10% annual coupon, matures in 8 years, and has a $10,000 face value. Its price is $9,950

5. Calculate YTM for each bond.

6. Compare YTM with coupon rate, indicate whether each bond is trading at a premium, at a discount, or almost at par.

7. Which one do you recommend Laura to buy and why, assume Laura has a high-risk tolerance and the current market interest rate is around 6%, Corporate Bond A is rated as BB bond and Corporate Bond B is a high-yield risky bond?

8. Assume Laura also told you her expected residual savings from 2019 to 2023 will be: $15,000, $20,000, $25,000, $30,000, $35,000. She wants to know the present values of these savings at an 8% discount rate. Calculate PVs of the streams.

Answer 1

Answer 5:Calculation of YTM
Option 1
Treasury bond 4%
YTM=	((C+(F-P/n)/(F+P)/2
=	(400+((10000-9550)/10))/10000+9550/2
=	((400+(450/10)/(19550/2)
=	(400+45)/9775
=	445/9775
=	0.04571
=	4.571	%
Option 2
Corporate bond 9%
YTM=	((C+(F-P/n)/(F+P)/2
=	(900+((10000-10500)/5)))/(10000+10500)/2
=	((900+(-500/5))/(20500/2)
=	800/10250
=	0.07804878
=	7.805	%
Option 3
Corporate bond 9%		1000
YTM=	((C+(F-P/n)/(F+P)/2
=	(1000+((10000-9950)/8)))/(10000+9950)/2
=	(1000+(50/8))/19950/2
=	(1000+6.25)/9975
=	0.10087719
=	10.0877	%
ANSWER 6
Option 1
YTM=	4.571	%
Coupon rate=	4	%
If bond's coupon rate is less than its YTM,then bond is selling at DISCOUNT
Option 2
YTM=	7.805	%
Coupon rate=	9	%
If bond's coupon rate is more than its YTM,then bond is selling at PREMIUM.
Option 3
YTM=	10.0877	%
Coupon rate=	10	%
If bond's coupon rate is equal to its YTM,then bond is selling at PAR.
Answer 7
Value of bond at market interest rate
Option 1
value=	coupon(pvaf6%,10)+facevalue(pvif6%,10)
=	400*7.360087+10000*0.558395
=	2944.035+5583.948
=	8527.983
Current market price 9550,thus bond is trading at higher than its value investor sholudnot purchase it
Option 2
value=	coupon(pvaf6%,5)+facevalue(pvif6%,5)
=	900*4.212364+10000*0.704961
=	3791.127+7472.582
=	11263.709
Current market price 10500,thus bond is trading cheap investor can go long
Option 3
value=	coupon(pvaf6%,8)+facevalue(pvif6%,8)
=	1000*6.20979+10000*0.627412
=	6209.794+6274.124
=	12483.918
Current market price 9950,thus bond is trading cheap investor can go long
Laura can buy option 2 or option 3 bond.But as the option 2 bond is BB bond and option 3 bond is high yield risky bond,and laura has a high risk tolerance thus laura should buy option 3 bond.
Answer 8
Year	Saving	Pv @ 8%	Pv of saving
2019	15000	0.925926	13888.8889
2020	20000	0.857339	17146.7764
2021	25000	0.793832	19845.806
2022	30000	0.73503	22050.8956
2023	35000	0.680583	23820.4119