Question

Case Study: Time Value of Money and Bonds Valuation

As Michelle’s new year resolution, she wants to begin saving for her retirement. She hired you as her financial advisor. Follow your suggestion, today Michelle will deposit $100,000, an inheritance from her parents, into a 5-year savings account at Citi bank that pays 3.25% interest annually. Use the above information to answer the following questions. When you answer your question, make sure include the calculation steps or formula. (Assume END mode)

1.How much will be in Michelle’s account after 5 years? (1%)

2.If Citi bank pays 3.25% interest monthly, how much will be in her account after 5 years? (2%)

3.If Michelle wants to make 5 equal payments on each January 1 from 2018 through 2022 to accumulate $100,000, how large must each payment be if Citi banks pays 3.25 % interest annual? (Assume BEGIN mode for this question) (2%)

4. Now with $100,000 bonus that will be saved today, Michelle will then make 4 additional equal payments each year from 2019 to 2022 to end up with $150,000 at the end of 2022. If Citi Bank still pays 3.25% interest annual, how large must each payment be? (5%)

5. Assume after 5 years, Michelle will be 40 years old and will have $150,000 in her saving account, and she is planning to retire at 65 years old and she will need $1,000,000 at retirement. What annual interest rate must she earn to reach her goal, assuming each year she will only save $20,000. (5%)

Now Michelle asked you to help her invest in bonds market. You have the following three bonds good for investment. Assume all coupons are paid annually and END mode, can you please find the best option for Michelle? 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 (3%)?

6.Compare YTM with coupon rate, indicate whether each bond is trading at a premium, at a discount, or almost at par. (3%)

7. Which one do you recommend Michelle to buy and why, assume Michelle has 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? (4%)

8. Assume Michelle 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. (10%)

Answer 1

1)	PV=	100000
	No of years (n)	5
	Rate of Interest ('r)	3.25% p a
	FV=	PV(1+r)^n
	=	100000*(1+0.0325)^5
	=	117,341.14
	Michelle will have $ 117341.14 at the end of 5 years
2)	PV=	100000
	No of years (n)	5
	Rate of Interest ('r)	3.25% monthly
	m	12
	r/m=	0.0325/12
	r/m=	0.0027083
	n*m=	5*12
	n*m=	60
	FV=	PV(1+r/m)^n*m
	=	100000*(1+0.0027083)^60
	=	117,618.76
	Michelle will have $ 117618.76 at the end of 5 years if the interest rate is monthly
3)	FV	100000
	No of years (n)	5
	Rate of Interest ('r)	3.25% annually
	FV=	(P*[(1+r)^n-1]/r)*(1+r)
	P is the periodic payment
	P=	r*FV/[(1+r^n-1)*(1+r)]
	=	(0.0325*100000) / [(((1+0.0325)^5)-1)*(1+0.0325)]
	=	18,151.63
	Michelle has to make a payment of $18151.63 per year
4)	Amount needed=	150,000.00
	FV of $100000=	117,341.14
	(from 1)
	Balance	32,658.86
	FV=	32658.86
	No of years (n)	5
	Rate of Interest ('r)	3.25% annually
	FV=	(P*[(1+r)^n-1]/r)*(1+r)
	P is the periodic payment
	P=	r*FV/[(1+r^n-1)
	=	(0.0325*32658.86) / [(((1+0.0325)^5)-1)
	=	6,120.78
	Michelle should pay 6120.78 per payment